EP2612478A1

EP2612478A1 - Methods and apparatus for carrier frequency offset estimation and carrier frequency offset correction

Info

Publication number: EP2612478A1
Application number: EP10856567.2A
Authority: EP
Inventors: Kai Xu; Yong-Quan Qiang; Jin Yang
Original assignee: Motorola Mobility LLC
Current assignee: Google Technology Holdings LLC
Priority date: 2010-08-30
Filing date: 2010-08-30
Publication date: 2013-07-10
Also published as: WO2012027880A1; EP2612478A4; CN103081425B; CN103081425A

Abstract

Methods and apparatus are provided for synchronizing a wireless receiver with a transmitter including methods and apparatus for computing estimated Fractional Carrier Frequency Offset (FCFO). The wireless receiver receives a signal that includes an Orthogonal Frequency Division Multiplexing (OFDM)/Orthogonal Frequency Division Multiple Access (OFDMA) symbol that corresponds to a Primary Synchronization Channel (P-SCH) that is encoded or modulated in accordance with a constant amplitude zero auto-correlation (CAZAC) sequence. The wireless receiver generates an estimated FCFO value by computing a differential phase of a cross-correlation between a first-half of the received time-domain OFDM/OFDMA symbol and a second-half of the received time-domain OFDM/OFDMA symbol.

Description

METHODS AND APPARATUS FOR CARRIER FREQUENCY OFFSET ESTIMATION AND CARRIER FREQUENCY OFFSET CORRECTION

TECHNICAL FIELD

[0000] The present invention generally relates to wireless communications, and more particularly to methods and apparatus for carrier frequency synchronization between a transmitter, implemented at an apparatus such as a base station, and a receiver, implemented at another apparatus, such as a femtocell or user equipment (UE).

BACKGROUND

[0001] Orthogonal Frequency Division Multiplexing (OFDM) is a digital modulation technique that divides the available bandwidth into a large number of closely-spaced (or narrow band) orthogonal sub-carriers. Each sub-carrier is modulated individually using a conventional digital modulation scheme (such as quadrature amplitude modulation (QAM) or quadrature phase-shift keying (QPSK)) at a low symbol rate (i.e., where the symbols are relatively long compared to the channel time characteristics). Because the duration of each OFDM symbol is long, a guard interval, called a cyclic prefix (CP), can be inserted between the OFDM symbols. A modulated bit stream can then be communicated over a communication channel on individual orthogonal subcarriers as sequence of OFDM/OFDMA symbols, and the CP allows intersymbol interference caused by multipath propagation to be reduced or eliminated. OFDM supports only one user on a channel (i.e., the group of evenly spaced subcarriers) at any given time. To accommodate multiple users, OFDM can be combined with multiple access using time, frequency, or coding separation of the users to provide multi-user channel access. In Orthogonal Frequency Division Multiple Access (OFDMA), frequency-division multiple access is achieved by assigning different OFDM sub-channels to different users. Because of the high spectral efficiency, and robust performance in frequency selective channel conditions, OFDM/OFDMA are used in various existing and upcoming communication standards including IEEE 802.1 In, IEEE 802.16d, the 3GPP Long Term Evolution (LTE) mobile communication standard, and DVB-T/H.

[0002] It is well known that OFDM systems are sensitive to time and frequency synchronization errors. Any OFDM-based communication system requires very accurate time and frequency synchronization between the receiver (e.g., at user equipment) and the transmitter (e.g., at a base station or access point).

Time Synchronization

[0003] To promote Inter-Symbol Interference (ISI)-free detection, precise timing information (regarding where the OFDM/OFDMA symbol boundary lies) is needed so that an uncorrupted portion of a received OFDM/OFDMA symbol can be sampled for FFT. Thus, one objective of time synchronization is to estimate where the OFDM/OFDMA symbol starts. Numerous frame detection methods have been developed that allow the receiver to determine the OFDM/OFDMA symbol boundaries and hence OFDM/OFDMA symbol timing.

Carrier Frequency Synchronization

[0004] In OFDM, orthogonality presumes that a transmitter and a receiver operate with exactly the same frequency reference. Any carrier frequency difference between the transmitter and the receiver results in a Carrier Frequency Offset (CFO). CFO is particularly problematic in multi-carrier OFDM communication systems because the sub-carriers that make up OFDM signals are closely spaced, and even small CFOs between the transmitter and the receiver can cause the OFDM sub-carriers to lose orthogonality. This causes inter- carrier interference (ICI) (i.e., cross-talk between the sub-carriers), which can result in a severe increase in the bit error ratio (BER) of the recovered data at the receiver.

[0005] Thus, to enable ICI-free detection, it is desirable to reduce carrier frequency offset (CFO) as much as possible to help ensure that subcarrier orthogonality is maintained and that subcarrier "leakage" is reduced so that the OFDM/OFDMA symbols of a received OFDM signal can be properly demodulated. As such techniques for carrier frequency synchronization are implemented at a receiver to estimate the CFO between the receiver and the transmitter. The CFO estimates can then be used to correct the frequency of the reference oscillator at the receiver to compensate for the CFO between the transmitter and receiver.

[0006] It is sometimes useful to estimate the overall CFO at the receiver by separately estimating a fractional portion and an integer portion. In other words, one estimation estimates an integer part of the CFO, called an integer CFO (ICFO). Another estimation estimates a fractional part of the CFO, called a fractional CFO (FCFO). The receiver then uses both the estimated ICFO and the estimated FCFO to compute a total estimated CFO. The total estimated CFO can then be used to adjust an oscillator of the receiver in an effort to frequency synchronize the receiver with the transmitter.

[0007] Numerous techniques have been developed for estimating the ICFO and the FCFO. Conventional techniques for estimating FCFO have significant drawbacks since they are time-consuming, processing-intensive, and/or inaccurate. Thus, there is on-going need for improved techniques for estimating FCFO.

[0008] Accordingly, it is desirable to provide improved methods and systems at an OFDM receiver for frequency synchronization with an OFDM transmitter that are more efficient from a processing standpoint. It is also desirable to provide methods and systems for estimating and correcting a fractional carrier frequency offset (FCFO) between an OFDM receiver and an OFDM transmitter. It is also desirable to provide methods and systems for estimating FCFO that are accurate over a large range, that are efficient, and that are not sensitive to the fading channel timing selectivity and multipath delay. Furthermore, other desirable features and characteristics of the present invention will become apparent from the subsequent detailed description and the appended claims, taken in conjunction with the accompanying drawings and the foregoing technical field and background.

BRIEF DESCRIPTION OF THE DRAWINGS

[0009] A more complete understanding of the present invention may be derived by referring to the detailed description and claims when considered in conjunction with the following figures, wherein like reference numbers refer to similar elements throughout the figures.

[0010] FIG. 1 is a block diagram of an exemplary communication network in which some of the disclosed embodiments can be implemented;

[0011] FIG. 2A illustrates a radio frame structure type 1 for a Frequency Division Duplex (FDD) implementation;

[0012] FIG. 2B depicts an example of a downlink slot in normal CP mode and its corresponding a time-frequency resource grid of subcarriers and OFDM/OFDMA symbols;

[0013] FIG. 3 is diagram that schematically illustrates a mapping of an example Zadoff- Chu sequence (ZCS) to available subcarriers in the frequency-domain used in accordance with some of the disclosed embodiments; [0014] FIG. 4 is a graph that illustrates periodic autocorrelation property of P-SCH signals generated in FIG. 3 when it is assumed that there is no interference or fading;

[0015] FIG. 5 is a block diagram of a portion of a wireless receiver in accordance with one exemplary implementation of the disclosed embodiments;

[0016] FIG. 6 is timing diagram illustrating a plurality of multipath-affected versions of a received OFDM/ OFDM A symbol;

[0017] FIG. 7 is a block diagram that illustrates a Fractional Carrier Frequency Offset (FCFO) estimator for estimating a FCFO in accordance with some of the disclosed embodiments;

[0018] FIG. 8 is a block diagram that illustrates an Integer Carrier Frequency Offset (ICFO) estimator for estimating ICFO in accordance with some of the disclosed embodiments; and

[0019] FIG. 9 is a simulated graph that illustrates periodic autocorrelation property of P- SCH signals generated in FIG. 3 after transmission over a multipath fading channel.

DETAILED DESCRIPTION

[0020] As used herein, the word "exemplary" means "serving as an example, instance, or illustration." The following detailed description is merely exemplary in nature and is not intended to limit the invention or the application and uses of the invention. Any embodiment described herein as "exemplary" is not necessarily to be construed as preferred or advantageous over other embodiments. All of the embodiments described in this Detailed Description are exemplary embodiments provided to enable persons skilled in the art to make or use the invention and not to limit the scope of the invention which is defined by the claims. Furthermore, there is no intention to be bound by any expressed or implied theory presented in the preceding technical field, background, brief summary, or the following detailed description.

[0021] Before describing in detail embodiments that are in accordance with the present invention, it should be observed that the embodiments reside primarily in methods and apparatus are for synchronizing a wireless receiver with a transmitter. In one embodiment, the wireless receiver can be implemented in user equipment or a femtocell, and the transmitter can be implemented in a femtocell or a base station. In one implementation of the disclosed embodiments, methods are provided for frequency synchronizing the wireless receiver with a base station.

[0022] To achieve frequency synchronization between the wireless receiver and the transmitter, methods and appartus are provided for computing estimated Fractional Carrier Frequency Offset (FCFO) based on an OFDM/OFDMA symbol that corresponds to a Primary Synchronization Channel (P-SCH) that is encoded or modulated in accordance with a constant amplitude zero auto-correlation (CAZAC) sequence. The wireless receiver receives a signal that includes the OFDM/OFDMA symbol. The OFDM/OFDMA symbol includes a primary synchronization channel (P-SCH) sequence that is generated based on a constant amplitude zero auto-correlation (CAZAC) sequence. In one embodiment, the original transmitted time-domain P-SCH sequence is generated based on a frequency-domain Zadoff-Chu sequence mapped to sub-carriers.

[0023] The original transmitted time-domain P-SCH sequence of a transmitted OFDM/OFDMA symbol has a first-half and a second-half. Likewise, the received time- domain OFDM/OFDMA symbol has a received time-domain P-SCH sequence with a first- half and a second-half. The estimated FCFO value provides an estimate of the FCFO between the wireless receiver and the transmitter. The wireless receiver generates an estimated FCFO value by computing a differential phase of a cross-correlation between a first-half of the received time-domain OFDM/OFDMA symbol and a second-half of the received time-domain OFDM/OFDMA symbol. Using this approach, the estimated FCFO value can be estimated to within +/- one sub-carrier spacing.

[0024] In one embodiment, the wireless receiver computes a first cross-correlation between the first-half of the received time-domain P-SCH sequence and the first-half of the original transmitted time-domain P-SCH sequence, determines a complex conjugate of the first cross-correlation, and computes a second cross-correlation between the second-half of the received time-domain P-SCH sequence and the second-half of the original transmitted time-domain P-SCH sequence. For instance, in one implementation, the wireless receiver computes the first cross-correlation based on a summation of the product of (1) samples of a first-half of a time-shifted received time-domain P-SCH sequence after a timing offset has been applied to the first-half of the received time-domain P-SCH sequence, and (2) corresponding samples of a first-half of a complex conjugate of the original transmitted time- domain P-SCH sequence over the sample range n = 0 ... (N/2)-l . The wireless receiver computes the second cross-correlation based on a summation of the product of (1) samples of a second-half of a time-shifted received time-domain P-SCH sequence after a timing offset has been applied to the second-half of the received time-domain P-SCH sequence, and (2) corresponding samples of a second-half of a complex conjugate of the original transmitted time-domain P-SCH sequence over the sample range n = N/2...N-l .

[0025] The wireless receiver then computes a product of the complex conjugate of the first cross-correlation and the second cross-correlation to generate a value, computes a complex phase angle of the value, and scales the complex phase angle via a scaling factor to generate the estimated FCFO value.

[0026] In one embodiment, the wireless receiver generates a compensation signal based on the estimated FCFO value, and applies the compensation signal to the received time- domain OFDM/OFDMA symbol to generate a compensated received time-domain OFDM/OFDM A symbol. The compensated received time-domain OFDM/OFDMA symbol can then be transformed from the time-domain to the frequency-domain to generate a frequency-domain symbol that can be used to generate an estimated integer carrier frequency offset (ICFO) value. The estimated ICFO value estimates an integer part of a carrier frequency offset to within an integer number of sub-carrier spacings that a carrier frequency of the wireless receiver is offset from that of the transmitter. In one implementation, the wireless receiver generates the estimated ICFO value by determining a maximum absolute value of a correlation between a received frequency-domain P-SCH sequence and a complex conjugate of a frequency shifted version of the original transmitted frequency-domain P-SCH sequence to compute the estimated ICFO value. For example, the wireless receiver can correlate, over a possible range of ICFO values as a shift value of the ICFO is varied, samples of the received frequency-domain P-SCH sequence against corresponding samples of a complex conjugate of the frequency shifted version of the original transmitted frequency-domain P-SCH sequence to generate correlation values, and then determine a maximum absolute value of the correlation values to generate the estimated ICFO value.

[0027] The estimated FCFO value and the estimated ICFO value can be added to generate a total estimated CFO value that provides an estimate of the CFO between the wireless receiver and a transmitter that transmitted the signal. The total estimated CFO value can then be used to adjust a reference frequency of a digital output signal generated by an oscillator. A digital baseband signal can then be multiplied by the digital output signal to adjust the frequency of the digital baseband signal to the reference frequency to correct for CFO between the receiver and the transmitter

[0028] As will be described below, in one implementation of the disclosed embodiments, periodic auto-correlation features of P-SCH signals, generated through mapping of the Zadoff-Chu sequences, are exploited to generate the estimated FCFO. These FCFO estimates are accurate over a large range, and can be estimated using a single OFDM/OFDMA symbol. The greatly improves processing efficiency in comparison to conventional methods used to estimate FCFO. In addition, the disclosed methods and apparatus for computing estimated FCFO are not sensitive to fading channel timing selectivity and multipath delay.

[0029] Prior to describing the disclosed embodiments with reference to FIGS. 5-9, an example of an operating environment will be described with reference to FIG. 1 as well as a radio frame structure with reference to FIGS. 2 A and 2B, and primary synchronization channel (P-SCH) implemented within that radio frame structure with reference to FIGS. 3 and 4.

[0030] FIG. 1 is a block diagram of an exemplary communication network 100 in which some of the disclosed embodiments can be implemented. In one embodiment, the communication network 100 is an OFDMA network. An OFDMA network may implement a radio technology such as Evolved UTRA (E-UTRA). UTRA and E-UTRA are part of Universal Mobile Telecommunication System (UMTS). 3 GPP Long Term Evolution (LTE) and LTE- Advanced (LTE-A) are new releases of UMTS that use E-UTRA. UTRA, E-UTRA, UMTS, LTE, LTE-A are described in documents from an organization named "3rd Generation Partnership Project" (3 GPP). Further, system 100 can utilize substantially any type of duplexing technique to divide communication channels (e.g., downlink, uplink, . . . ) such as frequency division duplexing (FDD), frequency division multiplexing (FDM), time division duplexing (TDD), time division multiplexing (TDM), code division multiplexing (CDM), and the like. In an FDD system, downlink signals can utilize a different frequency band than that used by uplink signals, and in a TDD system, downlink signals and uplink signals can utilize a common frequency band but at different times. As used herein, a frequency band is a range of frequencies that may be used for communication and may be given by (i) a center frequency and a bandwidth or (ii) a lower frequency and an upper frequency. A frequency band may also be referred to as a band, a frequency channel, etc. The techniques described herein may be used for the wireless networks and radio technologies mentioned above as well as other wireless networks and radio technologies. For clarity, certain aspects of the techniques are described below using LTE terminology; however, those skilled in the art will appreciate that such descriptions are non-limiting and used only for purposes of illustrating one exemplary environment in which the disclosed embodiments can be implemented.

[0031] The system 100 includes a femtocell 110 (also known as an access point base station or a Home Node B (HNB)), user equipment (UE) 120, an IP network 140, such as the Internet, a mobile core network (MCN) 150, and a macrocell base station (BS) 160 also known as a Home evolved Node B (HeNB). For sake of clarity, FIG. 1 depicts one femtocell 110, one UE 120 and one macrocell BS 160. However, it is to be appreciated that network 100 can include more than one of each.

[0032] The macrocell BS 160 is communicatively coupled to the MCN 150 via a backhaul 155. The MCN 150 can include a network controller (not illustrated) that is coupled to the macrocell BS 160 (as well as other macrocell BSs) so that the network controller may provide coordination and control for these macrocell BSs. As used herein, the term "macrocell base station" may refer to a device in an access network that communicates over the air-interface, through one or more sectors, with UE(s), and with other base stations through backhaul network communication. A macrocell BS may act as a router between a UE and the rest of the access network, which may include an IP network, by converting received air-interface frames to IP packets. A macrocell BS also coordinates management of attributes for the air interface. A macrocell BS may also be referred to as an access point (AP), Node B, evolved Node B (eNodeB), evolved base station (eBS), access network (AN) or other terminology known to those skilled in the art. Although not illustrated, those skilled in the art will appreciate that the macrocell BS 160 includes antennas, a transmitter chain and a receiver chain, each of which can include components associated with signal transmission and reception (e.g., processors, modulators, multiplexers, demodulators, demultiplexers, antennas, etc.). [0033] The femtocell 110 is a low-power cellular base station or access point that shares the licensed electromagnetic spectrum allocated to cellular service providers, and provides a personal mobile phone signal for cellular service to help improve Received Signal Strength (RSS) at an indoor site such as a building or residential home. Because the femtocell 110 has low transmit power it may cover a relatively small geographic area (e.g., a home 130) relative to the macrocell BS. This way, a femtocell can provide better indoor signal strength and improve coverage and capacity within an indoor environment where coverage or capacity might otherwise be limited or unavailable. The femtocell 110 connects the UE 120 to a mobile operator's core network 150 using an IP -based backhaul 115 (e.g., a residential DSL or cable broadband connection). In the example deployment shown in FIG. 1, the femtocell 110 is coupled to a broadband IP network 140, such as the Internet, via a DSL router, a cable modem, and/or another suitable device (not shown) to provide the femtocell with access to the MCN 150 via the backhaul 145. The owner of the femtocell can subscribe to mobile service (e.g., a 3G/4G mobile service offered through mobile operator core network 150), and the femtocell 110 may allow restricted access by UEs having association with the femtocell (e.g., UEs in a Closed Subscriber Group (CSG), UEs for users in the home, etc.). In one example, femtocell 110 can be installed in a user residence 130 or other small scale network environment.

[0034] As used herein, the term "user equipment" refers to any portable computer or other hardware designed to communicate with an infrastructure device over an air interface through a wireless channel. User equipment is "portable" and potentially mobile or "nomadic" meaning that the user equipment can physically move around, but at any given time may be mobile or stationary. User equipment can be one of any of a number of types of mobile computing devices, which include without limitation, mobile stations (e.g. cellular telephone handsets, mobile radios, mobile computers, hand-held or laptop devices, and personal computers, personal digital assistants (PDAs), or the like), access terminals, subscriber stations, wireless computing devices, or any other devices configured to communicate via wireless communications.

[0035] The macrocell BS 160 may provide communication coverage for a relatively large geographic area (e.g., several kilometers in radius) and may allow unrestricted access by UEs with service subscriptions. In this regard, the macrocell BS 160 defines a cell or coverage area 170 and can service UEs, such UE 120, within its coverage area 170 offering services related to a particular service location. The cell 170 may be divided into multiple sectors, where a sector refers to a physical coverage area within the cell 170. In 3GPP, the term "cell" can refer to a coverage area of the macrocell BS 160 and/or a subsystem of the macrocell BS 160 serving this coverage area, depending on the context in which the term is used.

[0036] In the example illustrated in FIG. 1, the macrocell BS 160 can communicate with UE 120 (and other UEs). A communication link used for transmission from the macrocell BS 160 to the UE 120 may be referred to as a downlink (DL), and a communication link used for transmission to the macrocell BS 160 from the UE 120 may be referred to as an uplink (UL). Alternatively, a downlink may be referred to as a forward link or a forward channel, and an uplink may be referred to as a reverse link or a reverse channel. The macrocell BS 160 may transmit data and signaling/control information on the downlink to the UE 120, and may receive data and signaling/control information on the uplink from the UE 120. In one non- limiting implementation, signals may be sent and received between the macrocell base station 160 and the UE 120 in accordance with OFDM/OFDMA techniques.

[0037] The femtocell 110 can communicate with UE 120 using similar technology (e.g., modulation and coding scheme) to that of the macrocell BS 160. Depending on the implementation, the femtocell 110 can be deployed on a single frequency or on multiple frequencies, which may overlap with respective macro cell frequencies. The femtocell 110 may have lower transmit power levels (e.g., 1 Watt) than the macrocell BS 160 (e.g., 20 Watts), different coverage areas, and a different impact on interference in the system 100.

[0038] Receivers of the femtocell 110 and UE 120 should ideally be time and frequency synchronized with the transmitter of the macrocell BS 160. As will be described below with reference to FIGS. 5-9, the femtocell 110 and/or UE 120 can employ the frequency offset estimation and cancellation techniques to reduce carrier frequency offset between the macrocell BS 160 and the femtocell 110 and/or UE 120. Prior to describing some of the disclosed embodiments for estimating CFO and using the estimated CFO to cancel/reduce CFO, a description of LTE downlink radio frame structures will be provided with reference to FIGS. 2A and 2B, and a description of a primary synchronization channel (P-SCH) used in that downlink radio frame structure will be provided with reference to FIGS. 3 and 4.

LTE Downlink Radio Frame Structure [0039] Per the 3GPP LTE specification, downlink transmissions are organized into radio frames. Each radio frame is 10 ms in duration. The LTE specifications define two radio frame structures: frame structure type 1, which uses both frequency division duplexing (FDD) and time division duplexing (TDD), and frame structure type 2, which uses TDD.

[0040] FIG. 2A illustrates a radio frame structure type 1 200 for a Frequency Division Duplex (FDD) implementation. As illustrated, radio frame structure type 1 is used for the downlink and is optimized to co-exist with 3.84 Mcps UMTS Terrestrial Radio Access (UTRA) systems. In the LTE frame structure type 1, downlink transmission is partitioned into units of radio frames 200 each having a predetermined duration (e.g., 10 milliseconds

(ms)). Each radio frame 200 is partitioned into 10 subframes (1 10), and each subframe

(1...10) has two consecutive 0.5 ms slots. Thus, each downlink radio frame 200 includes 20 slots.

Slot and Symbol Structure.

[0041] Each slot includes a number of OFDM/OFDMA symbols in the time-domain, and each OFDM/OFDMA symbol in that slot is preceded by a cyclic prefix (CP). The number of OFDM/OFDMA symbols in each slot varies depending on whether the base station is operating in a "normal" or "extended" cyclic prefix (CP) mode. As is known to those skilled in the art, a CP is a guard interval that is prefixed to a symbol that is a repetition of the end of that symbol. The CP extends the symbol so that is separated from adjacent symbols. Within the CP, it is possible to have distortion for the preceding symbol. However, if the CP is of sufficient duration (e.g., the duration is greater than the maximum channel delay), then preceding symbol will not spill over into the current symbol, and inter-symbol interference (ISI) caused by multi-path delay can be reduced/eliminated. Thus, to be effective, the length of the CP must be at least equal to the anticipated length of the multipath channel.

[0042] In LTE, normal and extended CP modes can be used in different radio environments depending on the expected multipath delays. The CP mode that is set varies depending on different coverage areas, channel conditions, or any other performance affecting variables. For a "reliable" communication link, the LTE specification suggests a long or extended CP mode, and for less reliable communication links a short or normal CP mode can be used. The number of OFDM/OFDMA symbols in each slot varies depending on a CP mode that is implemented. In the long or extended CP mode each slot has six (6) OFDM/OFDMA symbols, whereas each slot has seven (7) OFDM/OFDMA symbols in short or normal CP mode. For instance, FIG. 2A illustrates alternative slot structures 230/240 that can be used for a downlink channel in normal/extended CP modes, respectively, in a frame structure type 1 200. During normal CP mode, each slot 230 includes seven symbols (and therefore each sub-frame/TTI consists of 14 symbols). By contrast, in extended CP mode, each slot 240 consists of 6 symbols (and therefore each sub-frame/TTI consists of 12 symbols). Regardless of the mode, orthogonality is achieved by making the symbol length equal to the reciprocal of the sub-carrier spacing (Δί), which is 15 kHz, which means that the symbol length is 66.7 μβ.

Time-Frequency Resource Grid and Resource Elements

[0043] Each downlink slot corresponds to a time-frequency resource grid. FIG. 2B depicts an example of a downlink slot 230 (in normal CP mode) and its corresponding time- frequency resource grid of subcarriers and OFDM/OFDMA symbols. Data that are to be transmitted are mapped to basic elementary units called resource elements. Each resource element is a modulation symbol that is uniquely identified by a transmit antenna, a sub- carrier position, and the OFDM/OFDMA symbol index within a radio frame. Each resource element can be used to send one modulation symbol, which may be a real or complex-valued. A resource element may cover one subcarrier in one symbol period and is the smallest time- frequency unit for downlink transmission. As illustrated in FIG. 2B, the available time frequency resources may be partitioned into resource blocks. A resource block is defined as N^„_b consecutive OFDM/OFDMA symbols in the time-domain and consecutive subcarriers in the frequency-domain. Thus, a resource block consists of N^_b x

N w resource elements, corresponding to one slot in the time-domain and 180 kHz in the frequency-domain.

[0044] In the particular example illustrated in FIG. 2B that corresponds to a frame structure type 1 that implements a normal CP, a RB includes a group of 12 contiguous sub- carriers in frequency and one slot in time forms a resource block (RB) (i.e., each resource block may cover 12 subcarriers in one slot). Stated differently, a RB spans 12 consecutive sub-carriers at a sub-carrier spacing of 15 kHz, and 7 consecutive symbols over a slot duration of 0.5 ms. (Although not illustrated in FIG. 2B, a CP is appended to each symbol as a guard interval.) Thus, in this example, a RB has 84 resource elements (12 sub-carriers x 7 symbols) corresponding to one slot in the time-domain and 180 kHz (12 sub-carriers x 15 kHz spacing) in the frequency-domain. The size of a RB is the same for all bandwidths, therefore, the number of available physical RBs depends on the transmission bandwidth. In the frequency-domain, the number of available RBs can range from 6 (when transmission bandwidth is 1.4 MHz) to 100 (when transmission bandwidth is 20 MHz).

LTE Synchronization Channel

[0045] In an LTE network, a UE seeking to access a cell performs a cell search procedure that allows the UE to identify different types of information including: symbol and radio frame timing, frequency, cell identification, overall transmission bandwidth, antenna configuration, and cyclic prefix length. Synchronization signals are used during cell search to perform a series of synchronization stages that allow the UE to determine time and frequency parameters that are necessary to demodulate the downlink signals and to transmit uplink signals with the correct timing.

[0046] More specifically, two synchronization signals that are transmitted in each cell: the Primary Synchronization Signal (PSS) and the Secondary Synchronization Signal (SSS). The PSS and SSS correspond to a primary synchronization channel (P-SCH) and the secondary synchronization channel (S-SCH), respectively.

[0047] As illustrated in FIG. 2A, the SSS 210/212 and PSS 220/222 are downlink physical signals that are transmitted or broadcast two times per radio frame. Specifically, the SSS 210/212 and PSS 220/222 are both periodically transmitted once every 5 ms using the last two OFDM/OFDMA symbols of the first slot of the first sub-frame (sub-frame index 0) and in the last two OFDM/OFDMA symbols of the first slot of the sixth sub-frame (sub- frame index 5). In one implementation, applicable to an FDD cell, the SSS is located in the symbol immediately preceding the PSS.

[0048] The 3GPP standard specifies use of multiple (three) P-SCH signals to support the OFDM/OFDMA symbol timing synchronization at the UE. The three P-SCH signals are tied to the cell identities within a cell identity group. Having provided a description of the basic DL radio frame structure and the P-SCH, a description will now be provided of code sequences used to generate the P-SCH.

Constant Amplitude Zero Auto Correlation (CAZAC) sequence [0049] A Constant Amplitude Zero Auto Correlation (CAZAC) sequence is a periodic complex-valued mathematical sequence with modulus one and out-of-phase periodic (cyclic) autocorrelation equal to zero. Well-known examples of CAZAC sequences include: Chu sequences, Frank-Zadoff sequences, and Zadoff-Chu (ZC) sequences. Zadoff-Chu sequences (ZCS) (also known as Generalized Chirp-Like (GCL) sequences) are one type of CAZAC waveform with special properties. A ZCS is a complex -valued mathematical sequence that has a constant amplitude and flat frequency-domain response. In addition, the circular cross- correlation between two ZCSs is low with constant magnitude for prime number lengths. A ZCS also exhibits zero or nearly zero circular autocorrelation meaning that the correlation with the circularly shifted version of itself is a delta function. The average and peak values of the cross-correlation are low relative to the autocorrelation, and therefore any residual cross- correlation signal can be considered as white noise with low variance. This nearly ideal cyclic autocorrelation property is important when the received signal is correlated with a reference sequence and the received reference sequences are misaligned. When each cyclic shift (viewed within the time-domain of the signal) is greater than the combined propagation delay and multi-path delay-spread of that signal between the transmitter and receiver, cyclically-shifted versions of the ZCS remain orthogonal to one another. As such, when a ZCS is used to generate a radio signal, cyclically shifted versions of the ZCS sequence do not cross-correlate with each other when the signal is recovered at the receiver. ZCSs also have a low-frequency offset sensitivity, which can be defined as the ratio of the maximum undesired autocorrelation peak in the time-domain to the desired correlation peak computed at a certain frequency offset. The flat frequency-domain autocorrelation property and low frequency offset sensitivity allows for the PSS to be easily detected during the initial synchronization (e.g., PSS detection with a frequency offset up to ±7.5 kHz).

[0050] In the 3 GPP LTE standards, ZCSs are used to define the PSS and P-SCH as will now be described with reference to FIG. 3.

PSS Sequences

[0051] In the 3 GPP LTE standards, the P-SCH signals are OFDM signals with up to 72 active subcarriers, centered around the DC subcarrier. As will now be described, the active subcarriers are modulated with the elements of a cell-specific P-SCH sequence, d„(n), selected from a set of three different ZCSs with root indices u=ul, u2, and u3. [0052] FIG. 3 is diagram 300 that schematically illustrates a mapping of an example Zadoff-Chu sequence (ZCS) d„(n) to available subcarriers in the frequency-domain used in accordance with some of the disclosed embodiments. This mapping is used to generate a primary synchronization signal (PSS) sequence that is modulated according to the ZCS, and eventually transmitted as the P-SCH twice in each downlink radio frame.

[0053] In this particular embodiment, the P-SCH occupies 62 center sub-carriers located symmetrically around a DC sub-carrier (sub-carrier index of zero) that is left unused to avoid transmitting on the DC-subcarrier. The last five resource elements (not shown) at each extremity of each synchronization sequence (-36, -35, -34, -33, -32, 32, 33, 34, 35, 36) are not used and therefore not illustrated in FIG. 3. This structure enables the UE to detect the PSS using a size-64 FFT and a lower sampling rate than would be necessary if all 72 subcarriers in the central resource block were used.

[0054] A generated ZCS that has not been shifted is known as a "root sequence." In LTE within each group of cells, three ZCSs are generated that correspond to a particular root sequence index (u) of the ZCS sequence. The Zadoff-Chu root sequence indices ( u ) are specified in Table 1 , which shows a cell-identity group ( N ) in the first column, and a corresponding Zadoff-Chu root sequence index (u) that can be used for the P-SCH signal in the second column.

Table 1

[0055] This set of roots (u = 29, 34, 25) for the ZC sequences was chosen for its good periodic autocorrelation and cross-correlation properties.

[0056] Per the 3GPP LTE standard section that describes cell searching, the frequency- domain ZCS that is used to generate the primary synchronization channel (P-SCH) signal can be specified according to equation (1) as follows:

₉ ¹ 63 0,1,...,30

d_u (n) . aM(n+l)(n+2) Equation (1)

1 63 [0057] In equation (1), the sequence length (Nzc) of the ZCS is 63, n is an index that ranges from 0 to 61 or (between 0 and N_zc.-1), and u is the Zadoff-Chu root sequence index ( u ), where the selected roots for the three ZCSs are u = 25, 29, 34, as described above. The three ZCSs that are generated are of length 62 and are orthogonal to each other.

[0058] To generate the PSS sequences, the elements of sequence (d„(0). .. d_«(61 )) that are generated via equation (1) can be mapped to resource elements (¾_,/.) according to equation (2) as follows:

a_{k l} = d{n),

n = 0,...,61, Equation (2) k = n - 31 H

2

[0059] where a_{k l} is a resource element (k,l), k is sub-carrier index corresponding to one subcarrier (k) that ranges from -31 to +30, / is a symbol index corresponding to one particular OFDM/OFDMA symbol period (/), n is a sequence index that ranges from 0 to 61 , N_syj_nb is the number of consecutive time-domain OFDM/OFDMA symbols in the resource block, and is the number of consecutive frequency-domain subcarriers in the resource block. The sequence indices n = -5, -4, -3, -2, -1, 62, 63, 64, 65, 66 are reserved and not used for generation of the P-SCH signals.

[0060] The three resulting P-SCH signals are tied to the cell identities (V_/z>) 0, 1 , or 2 within a cell identity group. The BS selects one of the three primary synchronization sequences (PSSs) that is linked to a particular sector or cell identifier, and can transmit the selected PSS in the P-SCH.

Periodic Autocorrelation Characteristic of P-SCH

[0061] Autocorrelation is the cross-correlation of a signal with itself. The P-SCH signals generated through mapping illustrated in FIG. 3 exhibit a high degree of autocorrelation. For example, FIG. 4 is a graph that illustrates a periodic autocorrelation property of P-SCH signals generated in FIG. 3 when it is assumed that there is no interference or fading. In this particular example, the periodic autocorrelation is shown for an FFT size (N) of 1024. In the autocorrelation graph or "correlogram," the vertical axis represents the autocorrelation values (from zero to one) that are computed using FFT techniques. The horizontal axis represents the time delay index, which ranges between 0 and 1023, and represents the 1024 possible unique offsets between two copies of the same sequence of 1024 values. The time delay index is a delayed sampling number (or end-around shift number) needed for autocorrelation for N equal to 1024. FIG. 4 demonstrates that the sequences used to generate the P-SCH signals (e.g., generated through mapping illustrated in FIG. 3) have very good/strong periodic autocorrelation properties as the peak autocorrelation values are located near the extreme time delay indices of 0 and 1024. As will be described below, these strong periodic autocorrelation properties help cancel or reduce the impact of multipath interference when estimating FCFO thus improving the accuracy of the FCFO estimate.

[0062] FIG. 5 is a block diagram of a portion of a wireless receiver 500 in accordance with one exemplary implementation of the disclosed embodiments. In one implementation, the wireless receiver 500 can be implemented in a wireless communication device such as user equipment or a femtocell that that is in communication with a macrocell base station in a LTE system, and thus needs to maintain time and frequency synchronization with the macrocell base station.

[0063] The wireless receiver 500 includes an antenna 502, an analog front end module 504, an analog-to-digital converter (ADC) 505, a frequency correction module 510, a time synchronization and carrier frequency offset estimator module 580, a Fast Fourier Transform (FFT) module 590, channel estimation and equalization modules 592, and demodulation and forward error correction (FEC) modules 596. Those skilled in the art will appreciate that the wireless receiver 500 can include other conventional receiver modules that are not illustrated for sake of brevity.

[0064] The wireless receiver 500 receives a RF signal 503 with modulated OFDM/OFDMA symbols from a transmitter (not shown) via antenna 502.

[0065] The wireless receiver 500 communicates RF signal 503 to analog front end module 504. As is well-known to those skilled in the art, the analog front end module 504 includes various components (e.g., filters, low-noise amplifiers (LNAs), automatic gain control (AGC) circuitry, down-conversion mixer(s), and associated local oscillator(s) for driving the mixer(s), etc.) for processing the modulated RF signal 503 to generate an analog baseband waveform (with the downconverted OFDM/OFDMA symbols) suitable for input into the analog-to-digital converter (ADC) 505. [0066] For example, in one embodiment, after the radio frequency signal 503 is received via an antenna 502, the desired signal is selected and downconverted to an intermediate frequency, filtered, and then downconverted with an IQ demodulator and filtered again to generate an analog baseband (or passband at much lower frequency than the original radio frequency) signal. The analog front end 504 may optionally include automatic gain control (AGC) circuitry (not illustrated) for varying the gain of the received signal such that all signals at the output of the AGC circuit may have the same amplitude. As feedback and control for the AGC circuit, the analog front end module 504 may include a power measuring circuit to measure power of the gain-controlled signals from the output of the AGC circuit. The various processing steps performed at the analog front end module 504 to generate the analog baseband signal vary depending on the particular implementation, and are well-known in the art. For sake of clarity these processing steps will not be described further herein.

[0067] The analog-to-digital converter (ADC) 505 performs analog-to-digital (A/D) conversion on the analog baseband waveform (with the downconverted OFDM/OFDMA symbols) to generate a digital baseband signal 506 that includes digitized time-domain OFDM/OFDMA symbols.

[0068] In one embodiment, the frequency correction module 510 includes at least a multiplier 512 and a numerically controlled oscillator (NCO) 575. At the multiplier 512 the digital baseband signal 506 is multiplied with a digital output signal 582 from the NCO 575 to generate a frequency compensated baseband signal 514 at a frequency that is controlled by the NCO 575. As will be described in greater detail below, the digital output signal 582 is at a reference frequency that corrects CFO between the wireless receiver 500 and the transmitter that transmitted the modulated RF signal 503.

[0069] The time synchronization and carrier frequency offset (CFO) estimator module 580 performs various timing and frequency synchronization operations that will now be described below. In one embodiment, the time synchronization and carrier frequency offset (CFO) estimator module 580 includes a symbol timing synchronization module 520, a Fractional CFO (FCFO) estimation module 530, a compensation module 540, an Integer CFO (ICFO) estimation module 560, and an adder module 570.

[0070] The baseband signal 514 is sent to both the symbol timing synchronization module 520 and the fractional CFO (FCFO) estimation module 530. [0071] Due to multipath fading, the baseband signal 514 will include multiple transmission streams due to different transmit/receive paths. FIG. 6 is timing diagram illustrating a plurality of multipath-affected versions of a received OFDM/OFDMA symbol 600. Each multipath-affected version of the particular OFDM/OFDMA symbol 600 includes a cyclic prefix (CP) 610 and a FFT portion 620 (i.e., portion within an FFT window 625). In this embodiment, the FFT portion 620 corresponds to a P-SCH symbol described above. One property of the P-SCH symbol shown in FIG. 6 is that because it is generated using a CAZAC sequence it has a distinct pattern. The P-SCH symbol 620 can be divided into a first part 630 and a second part 640 that exhibit time-domain symmetry. As will be described further below, this pattern of the PSS sequence allows a Fractional Carrier Frequency Offset (FCFO) to be accurately estimated over a wide estimation range using only single P-SCH symbol.

[0072] As such, the wireless receiver 500 must time align the OFDM/OFDMA symbol boundaries. To do so, the symbol timing synchronization module 520 includes a time synchronization (TS) module 522 that that receives a plurality of multipath copies of the OFDM/OFDMA symbol, detects OFDM/OFDMA symbol boundaries in each of the plurality of multipath copies of the OFDM/OFDMA symbol to determine a correct start position of the OFDM/OFDMA symbol, identifies a fast Fourier transform (FFT) window size and a cyclic prefix (CP) length, and synchronizes timing of the start position of the OFDM/OFDMA symbol with the FFT window before FFT processing takes place. The TS module 522 may employ any known timing synchronization methods to detect the OFDM/OFDMA symbol boundaries and determine the correct start position of each symbol. In one embodiment, the TS module 522 correlates the incoming OFDM/OFDMA symbols with a known sequence to detect the OFDM/OFDMA symbol boundaries and determine the correct start position of each symbol.

[0073] When the OFDM/OFDMA symbols are time-synchronized, the TS module 522 sends the OFDM/OFDMA symbols to the CP removal (CPR) module 525. The CPR module 525 removes the CP that precedes (or is prepended to) each time-synchronized OFDM/OFDMA symbol, and outputs a time-domain signal 526 having OFDM/OFDMA symbols with their respective CPs removed. The TS module 522 also sends timing offset information 524 regarding the location of OFDM/OFDMA symbol boundaries to the FCFO estimation module 530 and to the Serial-to-Parallel (S/P) Converter module 527. As the S/P converter module 527 receives the symbol stream of the time-domain OFDM/OFDMA symbols from the CPR module 525, the S/P converter module 527 uses the timing offset information 524 to generate N parallel streams of time-domain OFDM/OFDMA symbols, where each stream corresponds to one of the N orthogonal subcarriers. The N parallel time- domain OFDM/OFDMA symbol streams are eventually sent to the FFT module 590.

Fractional Carrier Frequency Offset (FCFO) Estimation

[0074] The FCFO estimation module 530 performs time-domain fractional CFO estimation on an individual OFDM/OFDMA symbol basis using a single OFDM/OFDMA symbol. The FCFO estimation module 530 uses timing information 524 to determine boundaries of each time-domain OFDM/OFDMA symbol, and then computes, based on a particular time-domain OFDM/OFDMA symbol, an estimated FCFO value ( S_f ) 534 that provides an estimate of the FCFO between the wireless receiver 500 and the transmitter. The estimated FCFO value ( S_f ) 534 that estimates a fractional part of the carrier frequency offset to within +/- one sub-carrier spacing (+/- 15 kHz in a 3 GPP LTE network).

[0075] In one embodiment that will now be described with reference to FIG. 7, the estimated FCFO value ( S_f ) 534 can be computed by determining a differential phase of cross-correlation between the first-half and second-half of the P-SCH based on equation (3) as follows:

S_f = + η)χ (η) (Δ/) Equation (3)

[0076] where n is a sample index that ranges from 0 to N-l , where N is the sample size of the FFT window, Δ/is the sub-carrier spacing (e.g., 15 kHz), 6^ is a timing offset { 6_Time ) information corresponding to the symbol timing point for a start of the FFT window that is provided from the symbol timing synchronization module 520, r(n) is a discrete function representing the received time-domain P-SCH sequence (after transmission over the multipath fading channel), r{6_Time + ri) is a discrete function representing a time-shifted version of the received time-domain P-SCH sequence after timing offset ( 6_Time ) information has been applied to r(n) , x(n) is a discrete function representing the originally transmitted time-domain P-SCH sequence, and x * (n) is a discrete function representing the complex conjugate of the originally transmitted time-domain P-SCH sequence.

[0077] The sample index (n) may vary depending on the sample size (N) of the FFT window. For example, when the FFT window is 512 samples (i.e., N = 512), the index will range from 0 to 51 1 , the first-half of the P-SCH includes samples 0 to 255, and the second- half of the P-SCH includes samples 256 to 51 1. By contrast, when the FFT window is 1024 samples (i.e., N = 1024), the index will range from 0 to 1023, the first-half of the P-SCH includes samples 0 to 51 1 , and the second-half of the P-SCH includes samples 512 to 1023. The estimated range of Equation (3) is between ± subcarrier spacing (± Δ/) .

[0078] FIG. 7 is a block diagram that illustrates a Fractional Carrier Frequency Offset (FCFO) estimator for estimating a FCFO in accordance with some of the disclosed embodiments.

[0079] One characteristic of a P-SCH sequence ( x{n) ) that is generated based on a Zadoff-Chu sequence like that described above, is that the original transmitted time-domain P-SCH sequence ( x(n) ) of a transmitted OFDM/OFDMA symbol and the received time- domain P-SCH sequence ( r(n) ) can both be divided into a first-half 630 and a second-half 640. At block 710, samples of the received time-domain P-SCH sequence ( r(n) ) (after transmission over the multipath fading channel) are split into two parts that will be referred to herein as a first-half that corresponds to the sample range n = 0. ..(N/2)-l , and a second- half that corresponds to the sample range n =(N/2). ..N-l . Similarly, at block 715, samples of the originally transmitted time-domain P-SCH sequence ( x(n) (before transmission over the multipath fading channel) are split into two parts that will be referred to herein as a first-half that corresponds to the sample range n = 0. ..(N/2)-l , and a second-half that corresponds to the sample range n =(N/2). ..N-1. Thus, the first-half of r(n) and x(n) correspond to the sample range n = 0. ..(N/2)-l , and the second-half of r(n) and x(n) correspond to the sample range n = N/2. .. N-l . In both cases, the sample index (n) varies depending on the sample size (N) of the FFT window that is defined by the time synchronization module.

[0080] At block 720, the FCFO estimator module 530 computes a first cross-correlation between the first-half of the received time-domain P-SCH sequence ( r(n) ) and the first-half of the original transmitted time-domain P-SCH sequence ( x(ri) ) for samples 0 to (N/2)-l , and determines a complex conjugate (*) of the first cross-correlation. Block 720 represented in expression (3 A) as follows:

- n)x^* (n) Expression (3 A)

[0081] At block 720, the FCFO estimator module 530 includes a cross-correlator module 722 that computes the first cross-correlation based on a summation of the product of (1) samples of a first-half of a time-shifted received time-domain P-SCH sequence ( r(6_Time + n) ) (i.e., the first-half of the received time-domain P-SCH sequence ( r(n) after a timing offset ( Time ) ^nas been applied), and (2) corresponding samples of a first-half of a complex conjugate ( x * (n) ) of the original transmitted time-domain P-SCH sequence over the sample range n = 0 . .. (N/2)-l . Block 720 also includes a complex conjugate computation module 724 that operates on the output of the cross-correlator module 722 to compute a complex conjugate of the first cross-correlation.

[0082] Similarly, at block 730, the FCFO estimator module 530 includes another cross- correlator module that computes a second cross-correlation between the second-half of the received time-domain P-SCH sequence ( r(n) ) and the second-half of the original transmitted time-domain P-SCH sequence ( x(n) ) for samples N/2 to N-l . The processing performed at block 730 can be represented in expression (3B) as follows: + n)x^* (n) Expression (3B)

[0083] At block 730, the FCFO estimator module 530 computes second cross-correlation based on a summation of the product of (1) samples of a second-half of a time-shifted received time-domain P-SCH sequence ( r(0_Time + w) )over the sample range n = N/2. .. N-l , and (2) corresponding samples of a second-half of a complex conjugate ( x * (n) ) of the originally transmitted time-domain P-SCH sequence. Expression (3B) provides a measure of similarity of the two discrete functions ( x{ri) , r(n) ) as a function of a time-lag ( 6_Time ) applied to the second-half of the received time-domain P-SCH sequence ( r(n) ).

[0084] At block 740, the FCFO estimator module 530 computes the product of: (1) the complex conjugate of the first cross-correlation (i.e., the output of block 724), and (2) the second cross-correlation (i.e., the output of block 730) to generate a value. The processing performed at block 740 can be represented in expression (3C) as follows: +n)x^*(n) Expression (3C)

[0085] The computation in expression 3C extracts the phase offset from the received time-domain P-SCH sequence ( r(n) ) since the expression 3A will have a constant phase offset comparedin comparison to expression 3B. To explain further, if the FCFO is / , the channel tap response is h , the original transmitted time-domain P-SCH sequence is ( x(n) ) 0≤ n < N - 1 , the sampling interval is At , and AWGN is ignored, then the received time- domain P-SCH sequence ( r(n) ) can be expressed in equation 4 as follows:

r{n) = h * e^" * [x(0), x(l) * e¹²*^*1" , x(2) * e^j2*'^2&t ,A ,x(N/2-l)* _en4*(Ni 2-

= {A*e *[x{Q),x{\)*e^{j24* t} ,x{2)*e^{j24*2 t} ,A ,x(JV/2-l)*e^w*(i"^H)4'] __ . , _Λ.

, , , , , , Equation (4)

,h*e^]*° *[x(NI2)*e^j2^^{NI2^ ^t,x(NI2 + \)*e^J2^^{NI2^ ^T,A ,x(N -1)* e^J2^^N^ ^t]}

= {h * e^j,p° * [x(0), x(l) * e^j24*M , x(2) * _E ^J24*2AT ,A,x{NI2- 1) *_e ^{i2 *}(^N ' ^2~ι)Δί ]

, h * β>^φ° * [x(N 12), x(N 12 + 1) * e^^*At ,A , x(N - 1) * e¹²**^ ' ^2~ι)Δί ] * e¹²**^ ' ^{2) t} }

[0086] The cross correlation with the first-half and the second-half can be expressed in equation (5) as follows:

Equation (5)

[0087] The P-SCH is CAZAC sequence in frequency domain. In the time domain the P- SCH still has a constant amplitude. If the constant amplitude square is C, equation (5) can be re-written as equation (6) as follows: w , , , , Equation (6)

,h*e^j,po *[C,C*e^{j24* t} ,A ^ * e^j24^^{N l2}^ ^t * e^j24^^{N l2) t})

[0088] When the initial phase (<p₀) of the received P-SCH signal is equal to the product of the 2π x FCFO (f) x the timing offset (0_Time) (i.e., when eⁱⁿ = _ε ^}24θτ™^< ), expression 3C can be equated in equation (7) to the product of the π x FCFO (f) x the number of samples (N) x the sampling interval (Δί) as follows: 2nf * {N 12)At =

Equation (7)

Tjf * NAt = angle {n)

[0089] The FCFO (f) can be defined in as the product of a factor ( S_f ) and the sub-carrier spacing ( Δ/ ), which is 15kHz for LTE, and equation (7) can be re-written as: πδ_ί * Af * NAt = angle Equation (8)

[0090] In addition, in an OFDM system, the sub-carrier spacing ( Af ) is inversely proportional to the product of the number of samples (N) and the sampling interval ( At ) (i.e., Af = l /(NAt) ), which allows e uation (8) to be rewritten in equation (9) as follows: + n)x^* (n) Equation (9)

[0091] As such, the factor ( S_f ) can be re-written as equation (10) as follows:

Sf = angle Ιπ (Af)

Equation (10)

[0092] At block 750, the FCFO estimator module 530 computes a complex phase angle of the value that was generated at block 740. In equation (3), the complex phase angle is represented in expression (3D) as follows: angle < + n)x^* (n) Expression (3D) [0093] At block 760, the FCFO estimator module 530 scales the complex phase angle based on a scaling factor to generate the estimated FCFO value (S_f ) 534. In one non-limiting embodiment, the scaling factor is the ratio of subcarrier spacing to pi (-^- ).

π

[0094] Returning to FIG. 5, the estimated FCFO value 534 can then be sent to the adder module 570 and the compensation module 540.

[0095] The estimated FCFO value 534 may then be the fractional CFO estimation used for the correction, and for some embodiments, may be stored until a corresponding integer CFO estimation is computed.

[0096] In some embodiments, the compensation module 540 outputs a compensation signal 536, based on the estimated FCFO value 534. The compensation signal 536 is applied to the time-domain OFDM/OFDMA symbol(s) 529 to compensate for the estimated FCFO. As a result, a compensated time-domain OFDM/OFDMA symbol 538 is generated with reduced error (i.e., because it has been compensated based on the estimated FCFO value 534).

[0097] A time-domain-to-frequency-domain transformation may then be performed. In this embodiment, the Fast Fourier Transform (FFT) module 590 transforms the N parallel (compensated) time-domain OFDM/OFDMA symbol streams 538 from the time-domain to the frequency-domain and outputs N parallel frequency-domain symbol streams 591.

[0098] As will now be described, in accordance with some of the disclosed embodiments, after FCFO has been canceled and compensated for in time-domain, the auto correlation feature of Zadoff-Chu sequence in frequency-domain can be used to compute an estimated

ICFO value ( k ) 562.

Integer Carrier Frequency Offset (ICFO) Estimation

[0099] The Integer CFO (ICFO) estimation module 560 generates an estimated ICFO value 562 based on the frequency-domain OFDM/OFDMA symbol 591. The estimated

ICFO value 562 that estimates an integer part ( k ) of the CFO to within an integer number of sub-carrier spacings n (Δ/) (e.g., 15 kHz) that its carrier frequency is offset from that of the transmitter. In one embodiment, the estimated ICFO value ( k ) 562 is computed by determining a maximum absolute value of the correlation between a received frequency- domain P-SCH sequence ( Z . ) and a complex conjugate of a frequency shifted version of the original frequency-domain P-SCH sequence ( d_j ), as will now be described below with reference to FIG. 8.

[00100] FIG. 8 is a block diagram that illustrates an Integer Carrier Frequency Offset (ICFO) estimator for estimating ICFO in accordance with some of the disclosed embodiments. In the following description, d is the original frequency-domain P-SCH sequence, and Z is the received frequency-domain P-SCH sequence.

[00101] At block 810, over the possible range of ICFO values (_φ ), samples (Z . ) of the received frequency-domain P-SCH sequence ( Z ) are correlated against corresponding samples ( d ^* ) of a frequency shifted version of the original frequency-domain P-SCH sequence ( d ) with a shift value g to generate correlation values (φ(#)). Each j^th. correlation value is computed between: (1) a j^th sample of the received frequency-domain P-SCH sequence (Z . ) and (2) a j^th sample of the complex conjugate of a frequency shifted version of the original frequency-domain P-SCH sequence ( <i^* ) with a shift value g. In this embodiment, the calculated correlation value (Φ(#)) can be expressed in Equation (11) as follows: φ = ∑^Zj ' ^dL Equation (l l)

[00102] where <i^* _s is a j^th. sample of the complex conjugate of a frequency shifted version of the original frequency-domain P-SCH sequence with a shift value g, Z . is a j^th. sample of the received frequency-domain P-SCH sequence at the j^th sampling point, and where _φ is the possible range of ICFO values. Each shift value (g) is a particular, possible value of the ICFO.

[00103] At block 820, the estimated ICFO value ( k ) 562 is determined to be the maximum calculated correlation value (Φ(#)) observed when a shift value (g) of the ICFO is varied over a possible range of ICFO values (_φ ). This can be expressed in equation (12) as follows:

k = arg max(abs( (g ))) Equation (12) CFO Correction

[00104] The adder module 570 can then add the estimated FCFO value ( S_f ) 534 and the estimated ICFO value ( k ) 562 to generate a total estimated CFO value 572 that provides an estimate of the CFO between the wireless receiver 500 and the transmitter. The total estimated CFO value 572 is then fed forward to the NCO 575 to adjust the reference frequency of its digital output signal 582. The reference frequency of the digital output signal 582 is used to adjust the baseband signal 506 to correct for CFO between the receiver 500 and the transmitter. The multiplier 512 multiplies the baseband signal 506 with digital output signal 582 to generate a frequency compensated baseband signal 514 (i.e., the baseband signal 506 converted to a frequency that is controlled by the digital output signal 582 from NCO 575 and having reduced CFO).

[00105] Meanwhile, the channel estimation and equalization modules 592 receive the CFO compensated (frequency-domain) OFDM/OFDM A symbols 591 that are output by FFT module 590. For example, in one implementation, the frequency-domain OFDM/OFDMA symbols 591 output by the FFT block 590 may be sent to channel estimation (CE) module 592, which may estimate the channel for corresponding subcarriers and symbols. The output of the CE module and the output of the FFT module 590 can then be passed to an equalization module 592 in an effort to remove the effects of the channel from the received signal. The equalization module 592 processes these inputs to generate an equalized signal output 594. The equalized signal output 594 can be passed to the demodulation and forward error correction (FEC) modules 596. The FEC decoding module 596 can decode the frequency-domain OFDM/OFDMA symbols in accordance with known techniques and output a stream of digital data generated based on the decoded symbols. Those skilled in the art will appreciate that various additional processing steps (e.g., bit level de-interleaving, inner decoding, symbol level de -interleaving, outer decoding, and other higher level processing, etc.) can be performed on the output signal generated by the forward error correction (FEC) module 596. In this regard, the processing performed at blocks 592, 596 is conventional and well-known to those skilled in the art. Thus, for sake of brevity, it will not be described in further detail herein. [00106] FIG. 9 is a simulated graph that illustrates periodic autocorrelation property of P- SCH signals generated in FIG. 3 after transmission over a multipath fading channel. In this particular example, the periodic autocorrelation is shown for an FFT size (N) of 1024. As in FIG. 3, the vertical axis of the autocorrelation graph represents the autocorrelation values (from zero to one) and the horizontal axis represents the time delay index, which ranges between 0 and 1023, and represents the 1024 possible unique offsets between two copies of the same sequence of 1024 values. The time delay index is a delayed sampling number (or end-around shift number) needed for autocorrelation for N equal to 1024. In the 3 GPP LTE standard, the maximum multipath delay is less than the length of Cyclic Prefix (CP), which is not more than 1/8 of FFT size. The simulation results show that the auto correlation values between the original P-SCH sequence and a multipath delayed version of original P-SCH sequence are small compared with the maximum correlation value during the multipath delay range. The P-SCH signal (e.g., generated through mapping illustrated in FIG. 3) still exhibit relatively strong periodic autocorrelation properties as the peak autocorrelation values are located near the extreme time delay indices of 0 and 1024. Although the autocorrelation graph includes other peaks (e.g., located near time delay index values of 200, 400, 600 800), these periodic autocorrelation property of the P-SCH remains adequate to help cancel or reduce the impact of multipath interference when estimating FCFO. The multipath delayed versions of P-SCH sequence have nearly no impact on the performance of the proposed FCFO estimation technique.

[00107] In addition, because the P-SCH signal is transmitted two times in one frame, the estimated FCFO can be averaged over the two P-SCH signals thus providing a measure of time diversity in the estimate.

Conclusion

[00108] In summary, embodiments of the present disclosure have been presented including a base station transmitter, a user equipment receiver, and methods of synchronizing a base station transmitter and a user equipment receiver.

[00109] While the methods and apparatus disclosed herein have been described and shown with reference to particular steps performed in a particular order, it will be understood that these steps may be combined, subdivided, or reordered to form an equivalent method without departing from the teachings of the present disclosure. Accordingly, unless specifically indicated herein, the order or the grouping of the steps is not a limitation of the present disclosure.

[00110] It should be appreciated that the exemplary embodiments described with reference to FIGS. 5-9 are not limiting and that other variations exist. It should also be understood that various changes can be made without departing from the scope of the invention as set forth in the appended claims and the legal equivalents thereof. For example, although FIG. 1 describes an environment in which it is desirable to time and frequency synchronize femtocell 110 or UE 120 with macrocell BS 160, those skilled in the art will appreciate that the disclosed embodiments can be used to time and frequency synchronize a picocell, a relay node, or any other wireless communication device with macrocell BS 160.

[00111] Although some of embodiments of the present disclosure have been described in which primary synchronization sequences are based on frequency-domain Zadoff-Chu sequences, those skilled in the art will appreciate that the disclosed embodiments are equally applicable to other types of CAZAC sequences or near-CAZAC sequences, in the time or frequency-domain. The only requirement is that the CAZAC sequences have a constant amplitude in time-domain and good auto correlation properties.

[00112] Those of skill will appreciate that the various illustrative logical blocks, modules, circuits, and steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or combinations of both. Some of the embodiments and implementations are described above in terms of functional and/or logical block components (or modules) and various processing steps. However, it should be appreciated that such block components (or modules) may be realized by any number of hardware, software, and/or firmware components configured to perform the specified functions. As used herein the term "module" refers to a device, a circuit, an electrical component, and/or a software based component for performing a task. To clearly illustrate this interchangeability of hardware and software, various illustrative components, blocks, modules, circuits, and steps have been described above generally in terms of their functionality. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the overall system. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present invention. For example, an embodiment of a system or a component may employ various integrated circuit components, e.g., memory elements, digital signal processing elements, logic elements, look-up tables, or the like, which may carry out a variety of functions under the control of one or more microprocessors or other control devices. In addition, those skilled in the art will appreciate that embodiments described herein are merely exemplary implementations.

[00113] The various illustrative logical blocks, modules, and circuits described in connection with the embodiments disclosed herein may be implemented or performed with a general purpose processor, a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic device, discrete gate or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. A general-purpose processor may be a microprocessor, but in the alternative, the processor may be any conventional processor, controller, microcontroller, or state machine. A processor may also be implemented as a combination of computing devices, e.g., a combination of a DSP and a microprocessor, a plurality of microprocessors, one or more microprocessors in conjunction with a DSP core, or any other such configuration.

[00114] The steps of a method or algorithm described in connection with the embodiments disclosed herein may be embodied directly in hardware, in a software module executed by a processor, or in a combination of the two. A software module may reside in RAM memory, flash memory, ROM memory, EPROM memory, EEPROM memory, registers, hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor such that the processor can read information from, and write information to, the storage medium. In the alternative, the storage medium may be integral to the processor. The processor and the storage medium may reside in an ASIC. The ASIC may reside in a user terminal. In the alternative, the processor and the storage medium may reside as discrete components in a user terminal.

[00115] Furthermore, the connecting lines or arrows shown in the various figures contained herein are intended to represent example functional relationships and/or couplings between the various elements. Many alternative or additional functional relationships or couplings may be present in a practical embodiment. [00116] In this document, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Numerical ordinals such as "first," "second," "third," etc. simply denote different singles of a plurality and do not imply any order or sequence unless specifically defined by the claim language. The sequence of the text in any of the claims does not imply that process steps must be performed in a temporal or logical order according to such sequence unless it is specifically defined by the language of the claim. The process steps may be interchanged in any order without departing from the scope of the invention as long as such an interchange does not contradict the claim language and is not logically nonsensical.

[00117] Furthermore, depending on the context, words such as "connect" or "coupled to" used in describing a relationship between different elements do not imply that a direct physical connection must be made between these elements. For example, two elements may be connected to each other physically, electronically, logically, or in any other manner, through one or more additional elements.

[00118] While at least one exemplary embodiment has been presented in the foregoing detailed description, it should be appreciated that a vast number of variations exist. It should also be appreciated that the exemplary embodiment or exemplary embodiments are only examples, and are not intended to limit the scope, applicability, or configuration of the invention in any way. Rather, the foregoing detailed description will provide those skilled in the art with a convenient road map for implementing the exemplary embodiment or exemplary embodiments. It should be understood that various changes can be made in the function and arrangement of elements without departing from the scope of the invention as set forth in the appended claims and the legal equivalents thereof.

Claims

CLAIMS What is claimed is:

1. A method for synchronizing a wireless receiver (500) with a transmitter, the method comprising:

receiving an Orthogonal Frequency Division Multiplexing (OFDM)/Orthogonal Frequency Division Multiple Access (OFDMA) symbol that has a primary synchronization channel (P-SCH) sequence ( x(n) ) that is generated based on a constant amplitude zero autocorrelation (CAZAC) sequence;

computing a differential phase of a cross-correlation between a first part of the OFDM/OFDMA symbol (630) and a second part of the OFDM/OFDMA symbol (640) to generate an estimated fractional carrier frequency offset (FCFO) value ( S_f ) (534) of a FCFO between the wireless receiver (500) and the transmitter.

2. A method according to claim 1 , wherein a transmitted time-domain P-SCH sequence ( x(n) ) of the OFDM/OFDMA symbol comprises a first-half and a second-half, and wherein the received OFDM/OFDMA symbol comprises a received P-SCH sequence ( r{n) ) having a first-half and a second-half, and wherein the step of computing comprises:

computing a first cross-correlation between the first-half of the received P-SCH sequence ( r{n) ) and the first-half of the transmitted P-SCH sequence ( x(n) );

determining a complex conjugate of the first cross-correlation;

computing a second cross-correlation between the second-half of the received P-SCH sequence ( r(n) ) and the second-half of the transmitted P-SCH sequence ( x{n) );

computing a product of the complex conjugate of the first cross-correlation and the second cross-correlation to generate a value; and

computing a complex phase angle of the value; and

scaling the complex phase angle via a scaling factor to generate the estimated FCFO value ( S_f ) (534).

3. A method according to claim 2, wherein the step of computing a first cross- correlation comprises:

computing the first cross-correlation based on a summation of the product of (1) samples of a first-half of a time-shifted received time-domain P-SCH sequence ( r{6_Time + n) ) after a timing offset ( 6_Time ) has been applied to the first-half of the received P-SCH sequence ( r(n) , and

(2) corresponding samples of a first-half of a complex conjugate of the transmitted P-SCH sequence ( x * (n) )over the sample range n = 0 . .. (N/2)-l .

4. A method according to claim 2, wherein the step of computing a second cross- correlation comprises:

computing the second cross-correlation based on a summation of the product of (1) samples of a second-half of a time-shifted received P-SCH sequence ( r(6_Time + n) ) after a timing offset ( 0_Time ) has been applied to the second-half of the received P-SCH sequence ( r(n) , and (2) corresponding samples of a second-half of a complex conjugate of the transmitted time-domain P-SCH sequence ( x * (n) ) over the sample range n = N/2. ..N-1.

5. A method according to claim 2, wherein the transmitted time-domain P-SCH sequence ( x{n) ) is generated based on a frequency-domain Zadoff-Chu sequence mapped to sub-carriers.

6. A method according to claim 1 , further comprising:

receiving a plurality of multipath copies of the received OFDM/OFDMA symbol;

detecting symbol boundaries in each of the plurality of multipath copies of the received OFDM/OFDMA symbol to determine a start position for the received OFDM/OFDMA symbol; identifying a fast Fourier transform (FFT) window size and a cyclic prefix (CP) length; synchronizing timing of the start position of the received OFDM/OFDMA symbol with the FFT window; and

generating timing offset ( 6_Time ) information.

7. A method according to claim 1 , further comprising:

generating a compensation signal (536) based on the estimated FCFO value (534);

applying the compensation signal (536) to the received OFDM/OFDMA symbol (529) to generate a compensated received OFDM/OFDMA symbol (538); and

transforming the compensated received OFDM/OFDMA symbol (538) from the time- domain to the frequency-domain to generate a frequency-domain OFDM/OFDMA symbol (591).

8. A method according to claim 7, further comprising:

generating, based on the frequency-domain OFDM/OFDMA symbol (591), an estimated integer carrier frequency offset (ICFO) value ( k ) (562) that estimates an integer part of a carrier frequency offset (CFO) to within an integer number of sub-carrier spacings n (Δ/) that a carrier frequency of the wireless receiver (500) is offset from that of the transmitter.

9. A method according to claim 8, wherein the step of generating an estimated integer carrier frequency offset (ICFO) value ( k ) (562), comprises:

determining a maximum absolute value of a correlation between a received frequency- domain P-SCH sequence ( Z . ) and a complex conjugate of a frequency shifted version of the transmitted frequency-domain P-SCH sequence ( d^* ) to compute the estimated ICFO value ( k ) (562).

10. A method according to claim 9, wherein the step of determining a maximum absolute value of a correlation comprises:

correlating, over a possible range of ICFO values ( _φ ) as a shift value (g) of the ICFO is varied over the possible range of ICFO values ( _φ ), samples ( Z . ) of the received frequency- domain P-SCH sequence ( Z ) against corresponding samples ( d^* ) of a complex conjugate of the frequency shifted version of the original transmitted frequency-domain P-SCH sequence ( d ) to generate correlation values ( <I>(g) ; and

determining a maximum absolute value of the correlation values ( Φ(#) to generate the estimated ICFO value ( k ) (562).

1 1. A method according to claim 10, further comprising:

adding the estimated FCFO value ( S_f ) (534) and the estimated ICFO value ( k ) (562) to generate a total estimated CFO value (572) that provides an estimate of the CFO between the wireless receiver (500) and the transmitter;

adjusting a reference frequency based on the total estimated CFO value (572); and generating a digital output signal (582) at the reference frequency;

multiplying a digital baseband signal (506) by the digital output signal (582) to adjust the frequency of the digital baseband signal (506) based on the reference frequency.

12. A wireless receiver (500) configured for communication with a transmitter, the wireless receiver (500) comprising:

a synchronization module (580) designed to receive an Orthogonal Frequency Division Multiplexing (OFDM)/Orthogonal Frequency Division Multiple Access (OFDMA) symbol transmitted by the transmitter, wherein the OFDM/OFDMA symbol has a transmitted time- domain primary synchronization channel (P-SCH) sequence ( x(n) ) that is generated based on a constant amplitude zero auto-correlation (CAZAC) sequence, wherein the synchronization module (580) comprises:

a fractional carrier frequency offset (FCFO) estimator module (530) that computes a differential phase of a cross-correlation between a first part of the received OFDM/OFDMA symbol (630) and a second part of the received OFDM/OFDMA symbol (640) to generate an estimated FCFO value ( S_f ) (534) of the FCFO between the wireless receiver (500) and the transmitter.

13. A wireless receiver (500) according to claim 12, wherein the transmitted OFDM/OFDMA symbol includes a transmitted P-SCH sequence ( x(n) ) that has a first-half and a second-half, and wherein the received OFDM/OFDMA symbol includes a received P-SCH sequence ( r{n) ) that includes a first-half and a second-half, and wherein the FCFO estimator module (530) comprises: a first cross-correlator module (722) that computes a first cross-correlation between the first-half of the received P-SCH sequence ( r(n) ) and the first-half of the transmitted P-SCH sequence ( x{ri) ), and a complex conjugate computation module (724) that then determines a complex conjugate of the first cross-correlation;

a second cross-correlator module (730) that computes a second cross-correlation between the second-half of the received P-SCH sequence ( r{n) ) and the second-half of the transmitted P- SCH sequence ( x{ri) );

a product computation module (740) that computes the product of the complex conjugate of the first cross-correlation and the second cross-correlation to generate a value; and

a complex phase angle computation module (750) that computes a complex phase angle of the value, and scales the complex phase angle via a scaling factor to generate the estimated FCFO value ( ^ ) (534).

14. A wireless receiver (500) according to claim 13, wherein the FCFO estimator module (530) computes the first cross-correlation based on a summation of the product of (1) samples of a first-half of a time-shifted received P-SCH sequence ( r(6_Time + n) ) after a timing offset ( 0_Time ) has been applied to the first-half of the received P-SCH sequence ( r(n) ), and (2) corresponding samples of a first-half of a complex conjugate of the transmitted P-SCH sequence ( x * (n) ) over the sample range n = 0 . .. (N/2)- 1.

15. A wireless receiver (500) according to claim 13, wherein the FCFO estimator module (530) computes second cross-correlation based on a summation of the product of (1) samples of a second-half of a time-shifted received P-SCH sequence ( r(6_Time + n) ) after a timing offset ( 0_Time ) has been applied to the second-half of the received P-SCH sequence ( r(n) ), and (2) corresponding samples of a second-half of a complex conjugate of the transmitted P-SCH sequence ( x * (n) ) over the sample range n = N/2. ..N- 1.

16. A wireless receiver (500) according to claim 12, wherein the FCFO estimator module mputes an equation as follows: to generate the estimated FCFO value (S_f ) (534), wherein n is a sample index that ranges from 0 to N-1 , N is a sample size of an FFT window, Δ/ is the sub-carrier spacing, 6^ is the timing offset ( 0_Time ) information corresponding to the symbol timing point for a start of the FFT window, r(n) is a discrete function representing the received P-SCH sequence, r{6_Time + ri) is a discrete function representing the received P-SCH sequence after the timing offset ( 6_Time ) information has been applied, x(n) is a discrete function representing the transmitted P-SCH sequence, and x * (n) is a discrete function representing the complex conjugate of the transmitted P-SCH sequence.

17. A wireless receiver (500) according to claim 12, wherein the synchronization module (580) further comprises:

a time synchronization module (522) that receives a plurality of multipath copies of the received OFDM/OFDMA symbol, detects symbol boundaries in each of the plurality of multipath copies of the received OFDM/OFDMA symbol to determine a start position of the received OFDM/OFDMA symbol, identifies a fast Fourier transform (FFT) window size and a cyclic prefix (CP) length, synchronizes timing of the start position of the received OFDM/OFDMA symbol with the FFT window; and generates timing offset ( 0_Time ) information; and

a compensation module (540) that generates a compensation signal (536) based on the estimated FCFO value (534), wherein the compensation signal (536) is applied to the received OFDM/OFDMA symbol (529) to generate a compensated received OFDM/OFDMA symbol (538) that has been compensated based on the estimated FCFO value (534).

18. A wireless receiver (500) according to claim 17, further comprising: a Fast Fourier Transform (FFT) module (590) that transforms the compensated received OFDM/OFDMA symbol (538) from the time-domain to the frequency-domain to generate a frequency-domain symbol (591),

wherein the synchronization module (580), further comprises:

an integer carrier frequency offset (ICFO) estimator module (560) that generates an estimated ICFO value ( k ) (562) based on the frequency-domain OFDM/OFDMA symbol (591), wherein the estimated ICFO value ( k ) (562) estimates an integer part of a carrier frequency offset (CFO) to within an integer number of sub-carrier spacings n (Δ/) that a carrier frequency of the wireless receiver (500) is offset from that of the transmitter.

19. A wireless receiver (500) according to claim 18, wherein the ICFO estimator module (560):

a correlator module (810) that correlates, over a possible range of ICFO values ( _? ) as a shift value (g) of the ICFO is varied over the possible range of ICFO values ( _φ ), samples ( Z . ) of the received frequency-domain P-SCH sequence ( Z ) against corresponding samples ( d^* ) of a complex conjugate of a frequency shifted version of the original transmitted frequency-domain P-SCH sequence ( d ) to generate correlation values ( <I>(g) ; and

a selector module (820) that generates the estimated ICFO value ( k ) (562) by determining a maximum absolute value of the correlation values ( Φ(#) .

20. A wireless receiver (500) according to claim 18, further comprising:

an adder module (570) designed to add the estimated FCFO value ( S_f ) (534) and the estimated ICFO value ( k ) (562) to generate a total estimated CFO value (572) that provides an estimate of the CFO between the wireless receiver (500) and the transmitter;

a frequency correction module (510) communicatively coupled to the adder module (470), the frequency correction module (510) comprising:

a numerically controlled oscillator (NCO) (575) that adjusts a reference frequency based on the total estimated CFO value (572), and generates a digital output signal (582) at the reference frequency that is designed to adjust a digital baseband signal (506) to correct for CFO between the wireless receiver (500) and the transmitter; and

a multiplier (512) that multiplies the digital baseband signal (506) and the digital output signal (582) to generate a frequency compensated baseband signal (514) at the reference frequency that is controlled by the NCO (575).