Classifications

• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L25/00—Baseband systems
  • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
  • H04L25/0202—Channel estimation
  • H04L25/0204—Channel estimation of multiple channels
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L25/00—Baseband systems
  • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
  • H04L25/0202—Channel estimation
  • H04L25/024—Channel estimation channel estimation algorithms
  • H04L25/025—Channel estimation channel estimation algorithms using least-mean-square [LMS] method
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04B—TRANSMISSION
  • H04B1/00—Details of transmission systems, not covered by a single one of groups H04B3/00 - H04B13/00; Details of transmission systems not characterised by the medium used for transmission
  • H04B1/69—Spread spectrum techniques
  • H04B1/707—Spread spectrum techniques using direct sequence modulation
  • H04B1/7097—Interference-related aspects
  • H04B1/7103—Interference-related aspects the interference being multiple access interference
  • H04B1/7105—Joint detection techniques, e.g. linear detectors
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04B—TRANSMISSION
  • H04B17/00—Monitoring; Testing
  • H04B17/30—Monitoring; Testing of propagation channels
  • H04B17/391—Modelling the propagation channel
  • H04B17/3913—Predictive models, e.g. based on neural network models
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L25/00—Baseband systems
  • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
  • H04L25/0202—Channel estimation
  • H04L25/0212—Channel estimation of impulse response

Definitions

• the present invention relates to DS-CDMA (direct sequence- code division multiple access) systems. More specifically, the present invention is concerned with method and system for multi-user channel estimation in DS-CDMA systems.
• CDMA code- division multiple access
• some receivers utilize multiuser channel estimation approach, [1], [2], [3], [4], [5] and [6], to combat multiple access interference (MAI) along with the intersymbol interference (ISI).
• MAI multiple access interference
• ISI intersymbol interference
• [10] use the interference cancellation and the minimum mean squared error (MMSE) approach, respectively, and assumes perfect knowledge of the spreading sequences, channel estimates and bits of the interfering users.
• MMSE minimum mean squared error
• an acquisition scheme for a single user entering the system is devised using the knowledge of the spreading sequence and delays of the interfering users, who have already been acquired, without using their bit decisions.
• Blind estimation on the complex channel amplitudes is studied in [11] and [12] assuming knowledge of the delays of the various propagation paths for the interferers and [10] develops channel estimation algorithms for synchronous downlink channels.
• a maximum likelihood (ML) channel estimation [13] operates on an averaged decision statistic over successive (windowed) matched-filters' outputs for all users.
• Bhashyam and Aazhang in [13] designed an ML approach for long codes, applying gradient-based methods to approximate the ML solution and evenly distribute the computational burden over each sample, and thereby offering good tracking capabilities for slow channel variations.
• This method can be viewed as an iterative search for the composite channel impulse response of all users that minimizes a gradient with an "identity implementation law.”
• Implementation complexity remains the driving factor for preferring one channel estimation algorithm over another, as long as performances are satisfactory.
• the correlator because of the simple complexity it offers, is a good candidate.
• the channel impulse response obtained is further processed by employing a low pass filter, called a channel estimation filter (CEF) (correlator-CEF).
• CEF channel estimation filter
• Wiener filter is optimal as the CEF in a stationary channel in the minimum mean square error (MMSE) sense.
• a Wiener filter To design a Wiener filter, however, it is essential to know the power spectrum of the channel and noise, which may not be obtainable in real time. Moreover, a large implementation complexity is required.
• the Doppler spectrum is usually spread to the maximum Doppler frequency of an experiencing channel.
• a brick-wall type lowpass filter such as the CEF, whose cut-off frequency is equal to the maximum Doppler frequency of the channel.
• Such a CEF may not be practical, however, owing to the difficulty of implementation using a small number of filter taps.
• the CEF is realized in the form of a conventional lowpass filter like the finite impulse response (FIR) filter, or infinite impulse response (IIR) filter.
• FIR finite impulse response
• IIR infinite impulse response
• a multiuser-LMS-like structure along with smoothing and perdition filters to improve tracking quality applied to the received signal before despreading is provided.
• the choice for such an adaptation family stems from its low computational complexity and its regular structure, which is favourable for an efficient VLSI (Very Large Scale Integration) implementation where parallelism and wave pipelining, among other techniques, are easily applied. They are computationally effective due to the even distribution of the computation load over each symbol duration; no extra computation is required at the end of the processing window or preamble.
• VLSI Very Large Scale Integration
• an autoregressive stochastic model of correlated Rayleigh fading processes is used but indirectly embedded into the design.
• the attractive property of the proposed structure is the unique filter settings used for a large range of mobile speeds and for all users accessing the system.
• the design process is based on the following methodology: first, a p-order autoregressive stochastic model is designed for an average Doppler profile; second, the resulting model along with the admissible parameter-drift-to-noise floor ratio [39] are used to design the smoothing/prediction coefficients using Wiener LMS design methodology [39]; finally, a multiuser-LMS structure is augmented with an extra smoothing/prediction procedure.
• the LMS structure takes into account all users' contributions simultaneously and delivers a composite channel impulse response, as in [13], at each symbol.
• the composite channel impulse response is defined to be at least an (N+ * )K column vector, whose content provides the information about the multipath delays and time varying attenuations simultaneously.
• K represents the number of users and Nthe pilot (in case of cdma2000 and WCDMA) spreading factor.
• a unique smoothing/prediction filter is designed based on a single p-order AR model over an averaged Doppler profile for all users.
• the adaptation step is dynamically examined at each iteration using the same approach as in steepest descent based methods.
• the multiuser-LMS structure are chosen so as to provide: o An e ven d istribution o f t he c omputational b urden o ver a training window or a preamble; o No extra heavy computation required at the end of a training window or a preamble; and o A regular structure for an efficient VLSI implementation.
• a method for multi-user channel estimation in a multi-access network comprising: a) providing a communication signal (r.) corresponding to instant i; b) providing an estimated communication signal (f.); c) comparing the communication signal (r,. ) to the estimated communication signal (r.) to provide an error signal ( ⁇ , ); and d) generating an estimated composite channel impulse response signal (z.) using the error signal.
• the proposed method is an efficient and low complexity method allowing estimating and tracking even fast times varying multipath channels.
• the composite channel impulse response is computed and estimates of all possible path energies (rather than the tap itself) are computed to be used as an indicator of the significant paths (delays).
• the proposed method makes use of a model allowing applying a LMS-like structure.
• the composite channel impulse response is sought as a solution to an optimization criteria based on minimizing the "tracking error" (rather than a gradient) using an LMS like implementation law endowed with a prediction/smoothing filter for tracking.
• a prediction/smoothing filter for tracking.
• Such algorithm uses prior information on the hypermodel the channel may assume and the designer may estimate. These priors information are imbedded in the prediction/smoothing filter.
• the proposed method offers a considerable tracking performance at still low computational complexity close to LMS algorithm. More than that its computation load is evenly distributed over each bit (symbol).
• the proposed method can be used in a multi-stage method for channel estimation in a multi-access network to provide path attenuation or delay signal some of the users K; and where the method is repeated at least one time using selected components of the resulted estimated composite channel impulse response signal.
• a channel estimation method allows to estimate the composite channel impulse response for all users simultaneously, rather than single user attenuation, by assuming perfect acquisition. This is done by processing the received signal before dispreading.
• a channel estimation method according to the present invention is less dependent on speed variations and does not assume any Doppler estimation, as it uses the average autocorrelation function over the entire range of Doppler frequency of interest.
• an adaptive channel estimation processing module providing a plurality of estimated receiver's antennas composite channel impulse response signals for each communication channel signal of a transmitted communication signal in a multi-access network, comprising a processor receiving the transmitted communication channel signal and providing the plurality of estimated composite channel impulse response signals in accordance with control parameters being modified by an error feedback signal having a plurality of components, each of the plurality of components being related to the estimated received signal antennas and a feedback unit receiving the estimated composite channel impulse response and providing the plurality of estimated received signals for each channel antennas and providing the error feedback signal to the processor.
• an equalizer/detection unit for a multi-user access network system comprising: a channel estimation module from the present invention; and a data detection unit coupled to the channel estimation module to receive the plurality of estimated composite channel impulse response signals form the channel estimation module to use the plurality of estimated composite channel impulse response signals to provide estimated transmitted binary data.
• a multi-antenna system for a multi-access network comprising: a plurality of receiving antennas, each having an antenna output; a plurality of channel estimation modules from the present invention, each coupled to a respective of the plurality of receiving antennas so as to receive the transmitted communication channel signal from the antenna output; and a finger management unit coupled to the plurality of channel estimation modules for receiving the plurality of estimated composite channel impulse response signals therefrom and for using the plurality of estimated composite channel impulse response signals to provide at least one of path attenuation and delay signal corresponding to each of the plurality of receiving antennas.
• Figure 1 i s a b lock d iagram of a communication system incorporating an equalization/detection unit according to an illustrative embodiment of the present invention
• Figure 2 is a block diagram illustrating the equalizer/detection unit from Figure 1 ;
• Figure 3 is a flowchart illustrating a method for multi-user channel estimation in a multi-access system according to a first illustrative embodiment of the present invention
• Figure 4 is a block diagram of the method from Figure 3, illustrating the iterative nature of the method
• FIG. 5 is a block diagram detailing the composite channel impulse response prediction step illustrated in Figure 4.
• Figure 6 is a block diagram detailing the smoothing and prediction finite impulse response substeps from the composite channel impulse response prediction step illustrated in Figure 5;
• Figure 7 is a block diagram a method for multi-user channel estimation in a multi-access system according to a second illustrative embodiment of the present invention
• Figure 8 is a block diagram of a multi-antenna receiving system for DS-CDMA systems according to an illustrative embodiment of the present invention
• Figure 9 is a block diagram illustrating a multi-stage method for channel estimation in DS-CDMA systems using the channel estimation method from Figure 3 according to a more specific illustrative embodiment of the present invention
• Figures 10A-10B are graphs illustrating the loss obtained through simulations using the method from Figure 3, corresponding respectively to a mobile speed of 3km/h and 50km/h;
• Figures 11A-11B are graphs illustrating the MMSE obtained through the simulations resulting in Figures 10A-10B, corresponding respectively to a mobile speed of 3km/h and 50km/h;
• Figures 12A-12B are graphs illustrating the Bit Error Rate
• the system 10 inputs the transmitted binary data b k and outputs the estimated transmitted binary data b k .
• DS- CDMA Direct-Sequence Code Division Multiple Access
• equalizers such as unit 12, consist in removing intersymbol interference (ISI) from data received through a telecommunication channel 14 as well as Multiple Access Interference (MAI). Since DS-CDMA communication channels are believed to be well known in the art, and for concision purposes, only the equalization/detection unit 12 will be described herein in more detail.
• the transmitted sequence defined by correspond to pilot (control) sequence and data sequence respectively.
• the role of equalizer 12 is to detect or estimate data bits transmitted for each user k from the received sequence ⁇ r ; ⁇ ,.
• the data detection module 19 uses the estimation of
• the spreading sequence corresponding to b k l , the -"' bit of the k' h user, is denoted by c k i (t) and consists of N chips, where N is the spreading gain.
• T is the bit duration and E k ⁇ s the transmitted power of the user.
• the channel be a multipath channel with P k paths for the k th user and let the complex attenuation and delay with respect to the timing reference at the receiver of the p th path of the k th user be denoted by w p and ⁇ ktP respectively.
• the received signal may be represented as
• n(t) is the additive white Gaussian noise 16 (see Figure 2)
• the received signal is discretized at the receiver by sampling the output of a chip-matched filter at the chip rate [1], [4], [14].
• the observation vectors are formed by collecting N successive outputs of the chip-matched filterrfn].
• the observation vectors correspond to a time interval equal to one symbol period and start at an arbitrary timing reference at the receiver.
• r is the Nxl observation vector
• C is N ⁇ 2K(N + ⁇ ) spreading code matrix
• Z. is a 2K(N + 1) x 2K channel response matrix
• b is a 2K ⁇ l symbol vector
• n is a Nxl complex Gaussian zero-mean random vector with independent elements each of variance ⁇ 2 .
• the spreading waveform matrix, C ; is constructed using the shifted versions of the spreading codes corresponding to the ' ⁇ h and i + V h symbols of each user in the observation window.
• C,. is of the form
• the channel response matrix Z is of the form diag(x ,z .,z 2 .,z 2ti ,...,z K ,z K ) where z k . is the (N + l) ⁇ l channel response vector for the k th user in instant i.
• the q p and q kp +l"' element of z k are used.
• the symbol vector b ; . [b u b u+1 b 2( . b 2 ⁇ ••b ⁇ i b K has two symbols (chosen to be binary information bits ⁇ 1) for each user.
• Equation (3) is used to represent the received vector for detection
• z,. [z z • ⁇ • z ⁇ ⁇ (Equation 9)
• Equation 10 is a .&:(N+l) ⁇ l channel response vector and B ( . is a 2K(N + ⁇ ) ⁇ K(N+l) matrix defined as (Equation 10)
• N+l channel parameters are estimated for each user.
• the number of non-zero coefficients in this effective channel response vector is determined by the number of paths and delays as in Equation 7. It was first mentioned in [16] that the estimation of channel coefficients is equivalent to carrier phase tracking, and more work, such as in [17] and [18], was devoted to applying the Kalman filter to channel estimation. In most of these studies the fading channel was modeled as an autoregressive (AR) process in order to apply the Kalman filter. It has been shown that a second order AR process (AR2) may approximate the Jakes model [19] and may be used as a hyper model embedded into Kalman filter. It was observed in [20] that the spectral peak frequency of
• AR2 process should be adjusted by a factor of 2 from the maximum Doppler frequency.
• N rf is the number of distinct oscillators (the total number of
• f d is the spectral peak frequency
• T is the symbol period
• r d is the pole radius which corresponds to the steepness of the peaks of the power spectrum. It has been shown in [22] that f d the maximum Doppler frequency.
• the above-described AR2 model was motivated by the fact that the design based on Kalman filtering would not be complex insofar as a higher order is not used. Unfortunately, the AR2 model is far from being a good approximation as it has been demonstrated by Baddour and Beaulieu [28], who show that an AR model order of at least 100 is sometimes required.
• the methodology proposed in [28] is used herein to compute the AR coefficients.
• M (Equation 17); 106 - comparing the communication signal ) to the estimated communication signal (r ⁇ ) to provide an error signal ⁇ . r. -r.
• Equation 18 108 - generating an estimated and predicted composite channel impulse response signal (z ; . and z.
• a communication Nx1 vector signal (r.) is received at a base station or at a mobile station (both not shown). It is reminded that the received signal (r t ) at the base station is a superposition of the attenuated and delayed signals transmitted by all K users (see Equation 2).
• an estimated communication signal (r.) is generated using a spreading code signal (C ( ), an information sequence signal (B.) and a predicted composite channel impulse response signal
• step 108 the predicted composite channel impulse response signal (z.
• or simply R I for some cases and the parameter ⁇ will be described furtherin.
• M is the prediction of z at instant i tanking into account all data until instant t-1 and z m
• Step 108 further includes the substeps 112, where the one
• step prediction ,+1 i' is computed as (see Figure 6) ⁇ prediction , ⁇ smoothing * + ⁇ - * , , (Equation 20);
• FIG. 7 a method 200 for multi-user channel estimation in multi-access systems according to a second illustrative embodiment of the present invention will now be described. Since the method 200 is very similar to the method 100, and for concision purposes, only the differences between the two methods will be described herein. The method 200 is based on the AR2 model described hereinabove.
• steps 202-204 differ respectively from steps 114 and 116:
• Equation 13 Equation 13
• Step 110 is a finger management step, which includes extracting the delays and path attenuation values for each users from the vector z.
• the estimated composite channel impulse response signal (z ; ) When the estimated composite channel impulse response signal (z ; ) is available, it can be used to compute the iT(N+1 )x1 vector variance, which can be expressed as:
• ⁇ is a constant integer that can be set to ensure that ⁇ t ⁇ 1
• the Multi-user Steepest Wiener LMS (Multi-user S-WLMS) can also be used for setting shows stable and suitable solution for setting ⁇ , however at an additional computational cost compare to using Equation 27.
• the design of prediction/smoothing filter coefficients for a general ARn channel model (corresponding to step 112 on Figure 5) can be achieved via computer search so that the MMSE (Minimum Mean
• time-saving methodology can be devised offline: a) p is set at a given desired value, such as 6; b) ⁇ is varied along a range of discrete values sweeping the continuous range, for example [0,001 0,5]; c) as Equation (15) is solved, the filters' smoothing/prediction coefficients are deduced using a Wiener LMS method; d) finally, the entire design is used along with a detector.
• the BER performance allows dictating the appropriate range of ⁇ . This value can be used to make the appropriate final design settings. The process is iterated a few times to determine approximately the desired range of ⁇ . This has shown appropriate results in simulation in both cdma2000 and WCDMA environments.
• the adaptive channel estimation processing module 18 providing a plurality of estimated receiver's antennas composite channel impulse response signals for each communication channel signal of a transmitted communication signal in a multi-access network, comprises a processor receiving the transmitted communication channel signal 102 and providing the plurality of estimated composite channel impulse response signals 109 in accordance with control parameters being modified by an error feedback signal having a plurality of components, each of the plurality of components (not shown) being related to the estimated received signal antennas (not shown) and a feedback unit (not shown) receiving the estimated composite channel impulse response and providing the plurality of estimated received signals for each channel antennas and providing the error feedback signal to the processor.
• the channel estimation module 18 may take many forms accordingly to systems with one transmitting antenna-one receiving antenna to systems with muti-transmitting-multi-receiving antennas as will now be described in more detail.
• a multi-antenna system 300 for DS-CDMA systems according to an illustrative embodiment of the present invention will now be described with reference to Figure 8.
• the multi-antenna system 300 comprises a plurality of receiving antennas / to L, which output is processed by a separate channel estimation module 18 as described hereinabove after baseband conversion through respective baseband conversion units 302. All the units 18 will be sharing the same information, namely Xi.
• the output of each channel estimation module 18 is feed to a finger management unit 110.
• the channel estimation module 18 sees a new Xi which is, relatively to one-transmitting antenna case, augmented by a factor of Q to account for the spreading codes of all transmitting antennas. This can be view as replacing K by QK in the over all dimensions, which can be seen as every transmitting antenna represent a single user, hence facing a system with QK users.
• the transmitting antennas are, of course, endowed with different spreading codes.
• the method does include over-sampling case where r t is of dimension NOs, where Os is the over sampling rate.
• a multi-stage method 400 for channel estimation in DS-CDMA systems using the channel estimation method 100 according to a more specific illustrative embodiment of the present i nvention.
• the first stage i s p rovided by the above described channel estimation method 100 without a priori knowledge about the delays (paths positions), so the only known information is the received signal r t and the pilot spread information (Xi).
• a rough estimate is available at output of the first stage for each time instant / " .
• %i , k ' p and k ' p are feed to the second channel estimation stage.
• X X '> 2 is an N ⁇ K(L2+1) matrix where L2 is less than N, i.e. '> 2 has less
• the columns are selected according to suggested delays from the previous stage.
• the block 402 suggests for each user k, L2 columns around the suggested delays from the previous stage, Here L2 is greater than P, the number of possible paths, but less than N.
• the process is carried over certain number G of stages.
• the last stage G delivers the final channel estimates, namely the paths' delays and attenuations that can be used by a detector/equalizer.
• the last stage sees r X « , and ,,G with very reduced number of columns as its inputs.
• the multi-stage configuration can be implemented in three modes:
• Mode 1 at this operational mode, stage G starts processing instantaneously at each iteration i. So that at each iteration all stages are functional.
• Mode 2 stage g starts processing after a certain number of pilots, for example M, or slots/frames as needed. So that one stage is function for M pilots (slots/frames), the next stage will follow and so on.
• the second mode incurs some delay but offers reliable inputs to each stage. While mode 1 , offer some pipelining aspects, reducing the processing delay, but inputs are not that reliable as in mode 2.
• Mode 3 it works in one of the modes stated above (mode 1 or 2), with an exception of using a Correlator at the first stage where the Correlator suggests more than P delays let say L1 where L1 is less than N but a lot bigger than P. (P for some reference takes values between 4 and 6 in WCDMA and cdma2000 systems)
• Equation 29 the estimate Z ML M ) that uniquely maximizes this likelihood function is the ML estimate and it satisfies Equation 29
• the rank of R M increases by N with each additional term
• any linear transformation Tr, of r is also jointly Gaussian random vector with mean T J BJZ and covariance matrix ⁇ TT ⁇ '
• Z ML( ) is also jointly Gaussian with mean z and covariance matrix
• the single user (correlator) channel estimate given by 1 M ⁇ .
• Z SU ⁇ - NM j ⁇ w M" Equation 31
• a direct computation of the exact ML channel estimate involves the computation of the correlation matrix R M and then the computation of R ' yTM a the end of the preamble.
• the direct computation of the inverse of the correlation matrix at the end of the preamble is computationally intense and could delay the channel estimation process beyond the preamble duration and limit the information rate.
• the simplest gradient descent algorithm performs the following computations during the f h bit duration.
• the estimate of the channel is updated by taking a step along the gradient vector.
• the ML estimate for a preamble of length i is approximated as soon as the i bit is received.
• the updating step (step 3) may be repeated to improve accuracy. It may be repeated as many times as allowed by the available computational resources. It will be assumed that this updating is done only once per bit. Therefore, the number of iterations is equal to the preamble length.
• the step size is chosen to be constant for all the iterations.
• the step size may be chosen optimally for each iteration to minimize the squared error achieved by the updating step (step 3 which updates the channel estimate along the direction opposite to the gradient).
• Equation 36 ⁇ .-
• the optimal step size can be calculated using the knowledge of Ri and the gradient. Therefore, the steepest descent algorithm may be implemented with the same information needed for the constant step size algorithm. Further speed up in convergence may be achieved by choosing the search directions in addition to choosing the step size for each iteration. This may be done by the conjugate gradient algorithm [25].
• the search direction in any iteration is chosen to be orthogonal to the search directions used in the previous iterations.
• the steepest descent algorithm does not ensure this since it uses the gradient directly as the search direction.
• the implementation of the conjugate gradient algorithm would require significant additional computation to obtain the search directions.
• the iterative channel estimation algorithm scheme may be easily extended to track time variations in the channel after the preamble.
• the channel is assumed to be approximately constant over the preamble duration and the tracking is performed by sliding the estimation window and using data decisions instead of training sequences.
• the past channel estimates are used to detect the data in the payload which will be used in turn for channel estimation, till the next preamble.
• the correlation matrix R M and the matched filter outputs y M are averaged over a sliding window of length M. The tracking is done as follows: 1. Detecting bits using multi-shot multistage detection with previous channel estimate; 2.
• the updating step may be repeated to improve estimation accuracy. Since the channel is assumed to be roughly constant over the window length, the ML channel estimate for the new window should be very close to the previous ML estimate. Therefore, in practice, it is noticed that one iteration per bit is sufficient, i. e., the channel estimate from the previous window is a very good initialization for both the simple gradient descent with constant step size and the steepest descent algorithm to estimate the new channel estimate. Reduced size channel estimation
• the channel could have any number of paths with delays lying within o ne symbol period. All of these paths will be captured in the channel response vector z. It w ill b e a ppreciated t hat n o p arametric m odel i s a ssumed o n t he number of paths.
• the whole z vector may not be needed. For example, when there are just 2 paths for a user and the chip waveform is rectangular, the number of non-zero elements in z corresponding to that user is at most 4.
• the support of the autocorrelation r_ ⁇ ⁇ ⁇ ⁇ function is only over the interval L c cJ . If such information about the pulse shape and paths are available at the receiver, the iterative estimate obtained earlier may be further improved by using this knowledge. This information may be used to reduce the size of the estimated channel response vector z .
• One simple ad-hoc method to reduce the size of the estimated channel vector z is to choose a few large coefficients of z . In particular, a few large coefficients, say L, for each user, are chosen which results in a smaller vector of size LK. If the elements that were truly zero were dropped by this procedure, the error in estimation of the zero elements would be made zero and the total squared error in the estimate will be lower. Once the LK significant elements are chosen, the error in these LK elements may be improved by repeating the estimation schemes with a new reduced model of the discrete received signal.
• N 16 has been used.
• the delays of all the users were assumed uniformly distributed in [1 N) chips.
• our method is labeled WLMS. Since a large number of the interdependent parameters are being estimated, it is not very revealing to determine or calculate the estimation error for each individual parameter. It is rather more appealing to look at the loss in dB calculated as follows:
• Figures 1 OA a nd 10B show the efficiency of the present method compared to Steepest decent ML and the SU methods.
• Figures 11A-11B illustrate the MMSE in dB. It can be seen from Figures 11 A-11 B that the proposed method outperforms largely the SU and slightly the Steepest Decent ML methods.

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