TWI396415B - Channel length estimation method and estimator of orthogonal frequency division multiplexing system - Google Patents
Channel length estimation method and estimator of orthogonal frequency division multiplexing system Download PDFInfo
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本發明係有關於一種正交分頻多工系統的通道長度估測方法及其估測器，且特別係有關於全盲式的通道長度估測方法及其估測器。The invention relates to a channel length estimation method and an estimator thereof for an orthogonal frequency division multiplexing system, and particularly relates to a full blind channel length estimation method and an estimator thereof.
現今，正交分頻多工(Orthogonal Frequency Division Multiplexing，OFDM)系統已成為相當成熟的一種通訊技術，且由於OFDM系統具有許多優點，例如高資料傳輸速率(High Data Rate)、高頻譜使用效率(Spectral Efficiency)、抗頻率選擇性衰減(Frequency Selective Fading)等，因而廣泛地應用於各種通訊系統中。Nowadays, Orthogonal Frequency Division Multiplexing (OFDM) systems have become quite mature communication technologies, and because OFDM systems have many advantages, such as high data rate (High Data Rate) and high spectrum use efficiency ( Spectral Efficiency), Frequency Selective Fading, etc., are widely used in various communication systems.
對於OFDM系統，其通道估測係相當重要，由於在無線的環境下傳輸，傳輸的訊號通常會受到通道的影響，而改變其振幅與相位，且無線通道通常亦具有多重路徑效應，而造成符際干擾。因此，若能預先得知通道長度的資訊，則可減低運算複雜度，並增加運作的效能。For OFDM systems, the channel estimation system is quite important. Because it is transmitted in a wireless environment, the transmitted signal is usually affected by the channel, and its amplitude and phase are changed, and the wireless channel usually has multiple path effects. Interference. Therefore, if the channel length information can be known in advance, the computational complexity can be reduced and the operational efficiency can be increased.
在一般OFDM系統的全盲式通道估測中，通常會假設其通道長度已知，或者利用通道長度的資訊來簡化複雜度，但無法在估測通道之前不進行估測就得知通道長度的資訊。在現有的通道估測的研究中，一種方式係假設通道長度直接等於循環字首(Cyclically Prefix，CP)長度來進行運算，但如此會增加計算複雜度。另一種全盲式估測係利用秩數估測的方法，其需先求出特徵值，再計算其個數，然而此方式的效能不佳，其係由於當雜訊大，平均的量不夠多，則精準地分辨秩數係相當困難，且計算特徵值對於接收機的複雜度太高，並不容易實現。又一種方式係利用領航信號(Pilot)的估測方法，然而，需浪費寶貴的頻寬。In the full blind channel estimation of a general OFDM system, it is usually assumed that the channel length is known, or the channel length information is used to simplify the complexity, but the channel length information cannot be obtained without estimating before estimating the channel. . In the existing channel estimation study, one way is to assume that the channel length is directly equal to the length of the Cyclically Prefix (CP), but this will increase the computational complexity. Another type of full-blind estimation uses the method of rank estimation, which needs to first obtain the eigenvalues and then calculate the number. However, the performance of this method is not good, because the noise is large, the average amount is not enough. It is quite difficult to accurately resolve the rank number, and the calculation of the eigenvalue is too high for the receiver to be too easy to implement. Yet another way is to use the Pilot estimation method, however, it is necessary to waste valuable bandwidth.
因此本發明之一方面係在於提供一種正交分頻多工系統的通道長度估測方法及其估測器，藉以估測通道長度，而不需Pilot或通道響應的資訊。Therefore, an aspect of the present invention is to provide a channel length estimation method for an orthogonal frequency division multiplexing system and an estimator thereof, thereby estimating a channel length without requiring information of a Pilot or channel response.
根據本發明之實施例，本發明之正交分頻多工系統的通道長度估測方法包含：根據該接收訊號來取得雜訊功率；根據接收訊號與雜訊功率來設定第一價值函數；將第一價值函數的值代入高斯機率分佈中，以得到第二價值函數；根據第二價值函數來設定第三價值函數；以及根據第三價值函數的最大值，求得通道長度。According to an embodiment of the present invention, a channel length estimation method of the orthogonal frequency division multiplexing system of the present invention includes: obtaining a noise power according to the received signal; and setting a first value function according to the received signal and the noise power; The value of the first value function is substituted into the Gaussian probability distribution to obtain a second value function; the third value function is set according to the second value function; and the channel length is determined according to the maximum value of the third value function.
又，根據本發明之實施例，本發明之正交分頻多工系統的通道長度估測器包含價值函數產生器、高斯分佈單元、連乘單元以及計算單元。價值函數產生器係用以根據接收訊號與雜訊功率來設定第一價值函數。高斯分佈單元係用以將第一價值函數的值代入高斯機率分佈中，以得到第二價值函數。連乘單元係用以對第二價值函數進行連乘步驟，以得到第三價值函數。計算單元係用以根據第三價值函數的最大值來求得通道長度。Further, according to an embodiment of the present invention, the channel length estimator of the orthogonal frequency division multiplexing system of the present invention includes a value function generator, a Gaussian distribution unit, a multiplication unit, and a calculation unit. The value function generator is configured to set the first value function according to the received signal and the noise power. The Gaussian distribution unit is used to substitute the value of the first value function into the Gaussian probability distribution to obtain a second value function. The multiply unit is used to perform a multiplication step on the second value function to obtain a third value function. The calculation unit is configured to determine the channel length based on the maximum value of the third value function.
又，根據本發明之實施例，上述通道長度估測器可設置於正交分頻多工系統的接收器。Further, according to an embodiment of the present invention, the channel length estimator may be disposed in a receiver of an orthogonal frequency division multiplexing system.
又，根據本發明之實施例，上述之方法和通道長度估測器可應用於在同步誤差下進行通道長度估測。Still further in accordance with an embodiment of the present invention, the method and channel length estimator described above can be applied to channel length estimation under synchronization errors.
因此，本發明之正交分頻多工系統的通道長度方法及其估測器可較簡易且較準確地進行通道長度的估測，且不需要Pilot或通道響應的資訊。Therefore, the channel length method and the estimator of the orthogonal frequency division multiplexing system of the present invention can estimate the channel length relatively simply and accurately, and does not require information of Pilot or channel response.
為讓本發明之上述和其他目的、特徵、優點與實施例能更明顯易懂，本說明書將特舉出一系列實施例來加以說明。但值得注意的係，此些實施例只係用以說明本發明之實施方式，而非用以限定本發明。The above and other objects, features, advantages and embodiments of the present invention will become more apparent and understood. It is to be understood that the embodiments are merely illustrative of the embodiments of the invention and are not intended to limit the invention.
請參照圖1，其繪示依照本發明之一實施例之正交分頻多工系統的系統方塊圖。本實施例之正交分頻多工(OFDM)系統100包含發射器110和接收器120，其中接收器120係用以接收發射器110所發射的訊號。接收器120可設有雜訊功率估測器121、訊號功率估測器122及通道長度估測器123，訊號功率估測器122和通道長度估測器123係電性連接於訊號功率估測器122。雜訊功率估測器121係用以估測OFDM系統100的雜訊功率，訊號功率估測器122係用以估測OFDM系統100的訊號功率。通道長度估測器123係用以估測OFDM系統100的通道長度。Please refer to FIG. 1, which is a system block diagram of an orthogonal frequency division multiplexing system according to an embodiment of the present invention. The orthogonal frequency division multiplexing (OFDM) system 100 of the present embodiment includes a transmitter 110 and a receiver 120, wherein the receiver 120 is configured to receive signals transmitted by the transmitter 110. The receiver 120 can be provided with a noise power estimator 121, a signal power estimator 122 and a channel length estimator 123. The signal power estimator 122 and the channel length estimator 123 are electrically connected to the signal power estimation. 122. The noise power estimator 121 is used to estimate the noise power of the OFDM system 100, and the signal power estimator 122 is used to estimate the signal power of the OFDM system 100. Channel length estimator 123 is used to estimate the channel length of OFDM system 100.
請參照圖2，其繪示依照本發明之一實施例之發射器的結構示意圖。本實施例之正交分頻多工(OFDM)系統100可將一寬頻(Wideband)的訊號，分割成數個低速率且窄頻(Narrowband)的訊號，接著將每一子載波(Subcarrier)分別安插在不同的載波頻率上，然後再一起傳送出去。假設此OFDM系統100共有N 個子載波，且實際上調變傳輸訊號的只有D 個子載波，亦即剩下的N -D 個子載波為虛擬子載波，其並未傳輸訊號。此時，定義從第d 0 到第d 0 +D -1係用於傳輸訊號，其中d 0 為第一個子載波。最初的數位訊號位元(Bit)會被映射成數個符元(Symbols)，並使用例如相位偏移鍵移(Phase Shift Keying)或正交振幅調變(Quadrature Amplitude Modulation，QAM)等方式來進行調變，接著，再把這些訊號經由串連轉並聯轉換器(Serial-to-Parallel，S/P)，接著，再經過快速富立葉轉換。一般稱快速富立葉轉換之前的訊號為頻域(Frequency Domain)的訊號，而快速富立葉轉換之後的訊號為時域(Time Domain)的訊號。接著，加入CP來避免碼際干擾(ISI)，此時，假設CP長度為N g ，且定義OFDM符元訊號加上CP的長度為N t =N g +N 。一般而言，通常會假設CP的長度要大於通道長度，以避免ISI，使得所接收的訊號可為一完整的符元周期(Symbol Period)，並可使用簡單的單軌等化器(One-Tap Equalizer)來進行補償通道的作用。接著，將安插了CP的時域訊號傳到並聯轉串連轉換器(Parallel-to-Serial，P/S)，並定義為x (k )。Please refer to FIG. 2, which is a schematic structural diagram of a transmitter according to an embodiment of the present invention. The orthogonal frequency division multiplexing (OFDM) system 100 of this embodiment can divide a wideband signal into a plurality of low-rate and narrow-band signals, and then insert each subcarrier separately. At different carrier frequencies, they are then transmitted together. It is assumed that the OFDM system 100 has a total of N subcarriers, and actually only the D subcarriers of the modulated transmission signal, that is, the remaining N - D subcarriers are virtual subcarriers, which do not transmit signals. At this time, the definition from the d 0th to the d 0 + D -1 is used to transmit a signal, where d 0 is the first subcarrier. The first digit bit is mapped into a number of symbols and is used, for example, by Phase Shift Keying or Quadrature Amplitude Modulation (QAM). Modulation, then, these signals are then passed through a serial-to-parallel converter (S/P), followed by a fast Fourier transform. Generally, the signal before the fast Fourier transform is a frequency domain (Frequency Domain) signal, and the signal after the fast Fourier transform is a time domain (Time Domain) signal. Next, the CP is added to avoid inter-symbol interference (ISI). In this case, the CP length is assumed to be N g , and the length of the OFDM symbol signal plus the CP is defined as N t = N g + N . In general, it is usually assumed that the length of the CP is greater than the length of the channel to avoid ISI, so that the received signal can be a complete symbol period (Symbol Period) and a simple monorail equalizer (One-Tap) can be used. Equalizer) to compensate for the channel. Next, the time domain signal in which the CP is inserted is transmitted to a Parallel-to-Serial (P/S) and is defined as x ( k ).
根據上述以矩陣表示在頻域上傳輸的符元如下：The symbols transmitted in the frequency domain according to the above matrix are as follows:
s (k )=[s k (0),s k (1),s k (2),...,s k (D -1)] T ,........................................(1) s ( k )=[ s k (0), s k (1), s k (2),..., s k ( D -1)] T ,............ ............................(1)
其中，k 指的是第k 區塊(Block)，另外定義一反離散富立葉轉換(Inverse Discrete Fourier Transform,IDFT)的矩陣如下：Where k refers to the kth block, and the matrix defining an Inverse Discrete Fourier Transform (IDFT) is as follows:
其中，又因為此系統100設有虛擬子載波，則可以另定義一個IDFT的矩陣來對應於s (k )：among them, Also because this system 100 is provided with virtual subcarriers, a matrix of IDFTs can be defined to correspond to s ( k ):
因此，Ws (k )等於將s (k )作IDFT轉換，則時域上的訊號即為[x k (0)x k (1)...x k (N -1)]=Ws (k )，其中W為一N ×D 的矩陣。接著，還需在時域上加上CP，因而需再定義一個加上CP的IDFT矩陣。Therefore, Ws ( k ) is equal to s ( k ) for IDFT conversion, then the signal in the time domain is [ x k (0) x k (1)... x k ( N -1)]= Ws ( k ), where W is a matrix of N × D. Next, you need to add the CP to the time domain, so you need to define another IDFT matrix plus the CP.
其中x(k)為要傳送出去時域上的訊號，為加上CP後的新IDFT矩陣。一般來說，通道都有具多重路徑的影響，可定義一個通道向量h =[h (0),h (1),...,h (L -1)]，通道長度為L ，通道與時域訊號作摺積可表示為下式(4)：Where x(k) is the signal on the time domain to be transmitted, To add a new IDFT matrix after the CP. In general, channels have the effect of multiple paths. You can define a channel vector h =[ h (0), h (1),..., h ( L -1)], the channel length is L , and the channel The time domain signal can be expressed as the following formula (4):
接著，收集第k 個無碼際干擾的OFDM的符元訊號，也就是去掉前N g 個取樣點(Samples)，因而接收訊號r (k )為：Then, the symbol signal of the kth inter-symbol-free OFDM is collected, that is, the first N g sample points (Samples) are removed, and thus the received signal r ( k ) is:
其中among them
其中，r (k )為一個N ×1的矩陣，而n(k)為複數可加性高斯白雜訊(Additive White Gaussian Noise,AWGN)，其中假設雜訊功率為σ2 。Where r ( k ) is an N × 1 matrix, and n(k) is an additive additive white Gaussian noise (AWGN), in which the noise power is assumed to be σ 2 .
以下，先討論無載波頻率偏移(Carrier Frequency Offset，CFO)的影響的估測方式，假設同步點落在CP區間內，且為無ISI干擾的區間。首先，由公式(5)可知r (k )等效於，因而可預先對進行奇異值分解(Singular Value Decomposition，SVD)，如下式：In the following, the estimation method of the influence of carrier frequency offset (CFO) is discussed first, and it is assumed that the synchronization point falls within the CP interval and is an interval without ISI interference. First, from equation (5), r ( k ) is equivalent to So that it can be pre- Perform Singular Value Decomposition (SVD) as follows:
其中U n 為IDFT矩陣的雜訊子空間的基底(Orthonormal Basis)，另外[U s U n ]為N ×N 的矩陣，且U n 為N ×N -D 的矩陣，因而可由線性代數中的正交定理得到以下公式：Where U n is the IDFT matrix The Orthonormal Basis, in addition, [ U s U n ] is a matrix of N × N , and U n is a matrix of N × N - D , so the following formula can be obtained from the orthogonal theorem in linear algebra :
由上述公式(9)中，可以看出由於，因而可得到公式(9)。因此，本實施例的雜訊功率估測器可根據以下公式(10)：From the above formula (9), it can be seen that Thus, the formula (9) can be obtained. Therefore, the noise power estimator of this embodiment can be based on the following formula (10):
其中，定義為一個N -D ×N b 的矩陣，另外定義Y為一個收集N b 個OFDM符元的矩陣，且其符元訊號皆無受到ISI影響。其中，Y =[r (k +1),r (k +2),...,r (k +N b )]，假設r (k )=[r (kN t ),...,r ((k +1)N t -1)] T ，接收訊號r (k )包含了CP的部分。另外，為調整功率大小的參數，由(9)式可以看出雜訊受到U n H 的影響而改變了大小，其中[U s U n ]為的行數為N ，U n 的行數為N -D ，因此，要放大回原來的大小則需乘上。Among them, definition For a matrix of N - D × N b , Y is additionally defined as a matrix that collects N b OFDM symbols, and its symbol signals are not affected by ISI. Where Y = [ r ( k +1), r ( k +2),..., r ( k + N b )], assuming r ( k )=[ r ( kN t ),..., r (( k +1) N t -1)] T , the received signal r ( k ) contains the part of the CP. In addition, In order to adjust the power size parameter, it can be seen from equation (9) that the noise is changed by U n H , where [ U s U n ] is the number of rows N and the number of rows of U n is N - D , therefore, to zoom back to the original size, you need to multiply .
在一實施例中，系統100的通道長度超過CP長度。此時，定義一個，其中，以表示所定義的需大於通道長度L 。而雜訊功率估測器可根據以下公式(10)：In an embodiment, the channel length of system 100 exceeds the CP length. At this point, define a ,among them To indicate the definition Need to be greater than the channel length L. The noise power estimator can be based on the following formula (10):
其中，且參數i 會在無ISI的區間中。among them And the parameter i will be in the interval without ISI .
在另一實施例中，此系統100並未具有CP，此時，可直接設N g =0於公式(11)中，藉以避免ISI的影響。In another embodiment, the system 100 does not have a CP. In this case, N g =0 can be directly set in the formula (11) to avoid the influence of the ISI.
在又一實施例中，當取時，可以不必將整個取出來，而可僅取出複數個U n 即可，藉以減低運算時的複雜度，例如，其中。In yet another embodiment, when taken When you don’t have to Take out, but only take a plurality of U n to reduce the complexity of the operation, such as ,among them .
以下，接著說明本實施例的訊號功率估測。Hereinafter, the signal power estimation of the present embodiment will be described next.
首先，由上述可知r (k )等效於，並由公式(8)得到[U s U n ]，假設通道長度短於CP長度，根據線性代數定理可知，因而可得到：First, it can be seen from the above that r ( k ) is equivalent to And obtain [ U s U n ] from the formula (8), assuming that the channel length is shorter than the CP length, according to the linear algebra theorem , thus obtaining:
由上述公式(13)可知訊號受到的影響，但不會改變振幅，然而，雜訊因乘上了而改變了振幅的大小，因而由上述可推導出訊號功率為：According to the above formula (13), the signal is affected. Effect, but does not change the amplitude, however, the noise is multiplied The magnitude of the amplitude is changed, so that the signal power can be derived from the above:
其中，，且為所減除的雜訊項功率。among them, And For the noise power of the subtracted noise .
在另一實施例中，當通道長度超過CP長度時，訊號功率為：In another embodiment, when the channel length exceeds the CP length, the signal power is:
其中的功率。among them Power.
當估測出雜訊功率與訊號功率時，即可使用以下公式(17)來估測訊號雜訊比：When estimating the noise power and signal power, the following equation (17) can be used to estimate the signal noise ratio:
其中，在此所估測的為平均時間的訊號雜訊比，而非瞬時的訊號雜訊比。Among them, the estimated signal-to-noise ratio is the average time, not the instantaneous signal-to-noise ratio.
在又一實施例中，在載波頻率偏移(Carrier Frequency Offset，CFO)情況下，雜訊估測器可根據如下公式：In yet another embodiment, in the case of a carrier frequency offset (CFO), the noise estimator can be based on the following formula:
其中，且如上式(18)可知，其需乘上一個的值，其不同於(D /(N-D ))，原因在於所使用的U n 列數並不相同。值得注意的是，由於所使用的U n 2 列數相較於之前的U n 要少，因而等同於使用較少的取樣點來進行估測。因此，同理，此時訊號功率估測器可根據如下公式：among them And as shown in the above formula (18), it needs to be multiplied by one The value, which is different from ( D /( ND )), because the number of U n columns used is not the same. It is worth noting that since the number of U n 2 columns used is less than the previous U n , it is equivalent to using fewer sampling points for estimation. Therefore, for the same reason, the signal power estimator can be based on the following formula:
其中，。among them, .
請參照圖3，其繪示依照本發明之一實施例之雜訊功率估測器與訊號功率估測器的結構示意圖。本實施例之正交分頻多工(OFDM)系統100的雜訊功率估測器121包含訊號接收單元131、第一乘法器132及第一均方器133。訊號接收單元131係用以接收訊號r (k )，其中一反離散富立葉轉換(IDFT)矩陣係對應於接收訊號r (k )的頻域，此反離散富立葉轉換矩陣包含訊號子空間矩陣和雜訊子空間矩陣。在本實施例中，訊號接收單元131可包括累加器(Accumulator)，用以累加所收集的OFDM符元訊號。第一乘法器132係用以將接收訊號r (k )與雜訊子空間基底進行相乘，以得到此雜訊功率，其中，雜訊子空間基底係對反離散富立葉轉換矩陣進行奇異值分解(SVD)而取得，如公式(8)所示。在一實施例中，第一乘法器132可包括記憶單元(未繪示)，例如記憶體、記憶卡或其他資料儲存裝置，用以記憶此雜訊子空間基底。第一均方器133係用以對第一乘法器132的輸出結果取絕對值平方，因而可得到此雜訊功率σ2 。Please refer to FIG. 3, which is a schematic structural diagram of a noise power estimator and a signal power estimator according to an embodiment of the invention. The noise power estimator 121 of the orthogonal frequency division multiplexing (OFDM) system 100 of this embodiment includes a signal receiving unit 131, a first multiplier 132, and a first mean square 133. The signal receiving unit 131 is configured to receive the signal r ( k ), wherein an inverse discrete Fourier transform (IDFT) matrix corresponds to a frequency domain of the received signal r ( k ), and the inverse discrete Fourier transform matrix comprises a signal subspace matrix And the noise subspace matrix. In this embodiment, the signal receiving unit 131 may include an accumulator for accumulating the collected OFDM symbol signals. The first multiplier 132 is configured to receive the signal r ( k ) and the noise subspace base Multiplying to obtain the noise power, wherein the noise subspace base It is obtained by performing singular value decomposition (SVD) on the inverse discrete Fourier transform matrix, as shown in equation (8). In an embodiment, the first multiplier 132 can include a memory unit (not shown), such as a memory, a memory card, or other data storage device for storing the noise subspace substrate. . The first squarer 133 is configured to take the absolute value squared by the output result of the first multiplier 132, and thus the noise power σ 2 can be obtained.
如圖3所示，本實施例之正交分頻多工(OFDM)系統100的訊號功率估測器122係耦接於雜訊功率估測器121，訊號功率估測器122更包含第二乘法器134、第二均方器135、第三乘法器136及減法器137。第二乘法器134係用以將接收訊號r (k )與訊號子空間基底進行相乘，在一實施例中，第二乘法器134亦可包括記憶單元，例如記憶體、記憶卡或其他資料儲存裝置，用以記憶此訊號子空間基底。第二均方器135係用以對第二乘法器134的輸出結果取絕對值平方，第三乘法器136係用以將雜訊功率σ2 乘上一係數α，在一實施例中，此係數α為(D/N)，因而可得。減法器137係用以將接收訊號r (k )與訊號子空間基底所相乘的結果來減去該雜訊功率，以得到訊號功率，如公式(14)所示。As shown in FIG. 3, the signal power estimator 122 of the orthogonal frequency division multiplexing (OFDM) system 100 of the present embodiment is coupled to the noise power estimator 121, and the signal power estimator 122 further includes a second A multiplier 134, a second mean squarer 135, a third multiplier 136, and a subtractor 137. The second multiplier 134 is configured to receive the signal r ( k ) and the signal subspace base Performing multiplication, in an embodiment, the second multiplier 134 may also include a memory unit, such as a memory, a memory card, or other data storage device for storing the signal subspace base. . The second squarer 135 is configured to take an absolute value squared for the output of the second multiplier 134, and the third multiplier 136 is configured to multiply the noise power σ 2 by a coefficient α. In an embodiment, this The coefficient α is (D/N), so it is available . A subtractor 137 is used to receive the signal r ( k ) and the signal subspace base Subtract the result to subtract the noise power To get the signal power, as shown in equation (14).
本實施例之通道長度的估測方法係利用OFDM的符元後段與CP相同的特性來進行估測，由此可導出：The estimation method of the channel length in this embodiment uses the same characteristics of the OFDM symbol post-segment and the CP to estimate, thereby deriving:
另外，在有ISI的情況下可推得：In addition, in the case of ISI, it can be derived:
其中e k (i )為的k 個符元的第i 個取樣點的ISI干擾量。The amount of ISI interference of the i- th sampling point of k symbols of e k ( i ).
根據公式(20)和(21)，可定義價值函數(Cost Function)為：According to equations (20) and (21), the value function (Cost Function) can be defined as:
一般來說，通道模型的振幅為一個指數下降的型式，因此在越後面之通道路徑的振幅係相對較小，因而造成估測的困難。此時，可利用高斯分佈函數(Gaussian Distribution)來拉開價值函數的差距，因此，將C (i )值代到高斯機率分佈中，且假設平均N b 個接收符元訊號，其中為雜訊功率。如上所述，因而可得到新的價值函數，如下式：In general, the amplitude of the channel model is an exponentially decreasing pattern, so the amplitude of the channel path at a later stage is relatively small, thus causing difficulty in estimation. At this point, the Gaussian Distribution function can be used to open the gap of the value function. Therefore, the C ( i ) value is substituted into the Gaussian probability distribution. Medium, and assume an average of n b received symbol signals, where For noise power. As mentioned above, a new value function is thus obtained , as follows:
其中α i 為峰值。接著，利用連乘的方法來進行估測的動作，藉以形成又一新的價值函數，如下式：Where α i is the peak. Then, using the method of multiplication to estimate the action, to form another new value function, as follows:
由上式(24)可知其為一由左往右乘的系統，其可固定起始點為第一點，然後再依次地往左乘。接著，可找出最大值的位置，即可以估測出所要的通道長度，如下式：It can be seen from the above formula (24) that it is a system that is multiplied by left to right, which can fix the starting point to the first point and then multiply it to the left. Then, you can find the position of the maximum value, that is, you can estimate the length of the desired channel, as follows:
以下，接著說明在同步誤差下的通道長度估測。Hereinafter, the channel length estimation under the synchronization error will be described next.
在本發明的另一實施例中，可同時利用二OFDM的符元訊號來進行估測，且位移N t 次的方法。假設接收訊號為，其中r k 長度為兩個含CP的完整OFDM符元訊號。另外假設同步點的位置為N s ，藉以設定價值函數為：In another embodiment of the present invention, the symbol signal of the two OFDM can be simultaneously used for estimation, and the method of shifting N t times. Suppose the received signal is Where r k is the length of two complete OFDM symbol signals with CP. Also assume that the location of the synchronization point is N s , whereby the value function is set to:
其中公式(26)為假設N s 落在第一個OFDM符元之無ISI干擾之CP區間內所得到的結果，隨著繼續位移，當碰到資料部分時即得到如下式：Equation (26) is the result obtained by assuming that N s falls within the CP interval of the first OFDM symbol without ISI interference. As the displacement continues, the following formula is obtained when the data portion is encountered:
隨著繼續位移，進入第二個OFDM符元的無ISI干擾的區間時，又會出現公式(26)的結果，因而其價值函數為：As the displacement continues, the result of equation (26) appears when entering the interval of the second OFDM symbol without ISI interference, so its value function is:
在本實施例中，CP長度減掉無ISI干擾區間的長度，即可以求得通道長度。In this embodiment, the length of the CP is reduced by the length of the ISI-free interference interval, that is, the channel length can be obtained.
接著，同樣地，代入機率密度函數。假設代到高斯機率密度而出的值為，其中Next, similarly, the probability density function is substituted. . Assume that the value of the Gaussian probability density is ,among them
接著，將價值函數左右兩邊各取CP長度N g ，而可得到，然後再各別進行連乘步驟，如下式：Then, taking the CP length N g from the left and right sides of the value function, and obtaining Then, each step is carried out separately, as follows:
接著，各別取出最大值的位置，如下式：Next, each takes the position of the maximum value as follows:
接著，可估測出通道長度，如下式：Then, the channel length can be estimated , as follows:
請參照圖4，其繪示依照本發明之一實施例之正交分頻多工系統之通道長度估測方法的方法流程圖。當進行本實施例之正交分頻多工系統100的通道長度估測方法時，首先，根據接收訊號r (k )來取得雜訊功率(步驟S201)。接著，根據接收訊號r (k )與雜訊功率，設定第一價值函數C (i )(步驟S202)。接著，將第一價值函數C (i )代入高斯機率分佈中，以得到第二價值函數(步驟S203)。接著，根據第二價值函數，設定第三價值函數c (i )，以進行連乘步驟(步驟S204)。接著，根據第三價值函數c (i )的最大值，來求得通道長度(步驟S205)。Please refer to FIG. 4, which is a flow chart of a method for estimating a channel length of an orthogonal frequency division multiplexing system according to an embodiment of the present invention. When the channel length estimation method of the orthogonal frequency division multiplexing system 100 of this embodiment is performed, first, the noise power is obtained according to the received signal r ( k ). (Step S201). Then, according to the received signal r ( k ) and the noise power The first value function C ( i ) is set (step S202). Next, the first value function C ( i ) is substituted into the Gaussian probability distribution. In order to get the second value function (Step S203). Next, according to the second value function The third value function c ( i ) is set to perform the multiplication step (step S204). Then, according to the maximum value of the third value function c ( i ), the channel length is obtained. (Step S205).
請參照圖5，其繪示依照本發明之另一實施例之正交分頻多工系統之通道長度估測方法的方法流程圖。當進行本實施例之正交分頻多工系統100在同步誤差下的通道長度估測方法時，首先，根據接收訊號r (k )來取得雜訊功率(步驟S301)，其中接收訊號r (k )包含二個OFDM符元訊號，每一OFDM符元訊號包含一循環字首CP。接著，根據接收訊號r (k )與雜訊功率，設定第一價值函數C (i )(步驟S302)。接著，將第一價值函數C (i )代入高斯機率分佈中，以得到第二價值函數(步驟S303)。接著，根據第二價值函數，設定第四價值函數c 1 (i )和第五價值函數c 2 (i )，以進行連乘步驟(步驟S204)。接著，根據四價值函數c 1 (i )的最大值、第五價值函數c 2 (i )的最大值以及循環字首CP的長度N g ，來求得通道長度(步驟S205)。Please refer to FIG. 5, which is a flowchart of a method for estimating a channel length of an orthogonal frequency division multiplexing system according to another embodiment of the present invention. When the channel length estimation method of the orthogonal frequency division multiplexing system 100 of the present embodiment under synchronization error is performed, first, the noise power is obtained according to the received signal r ( k ). (Step S301), wherein the received signal r ( k ) comprises two OFDM symbol signals, and each OFDM symbol signal comprises a cyclic prefix CP. Then, according to the received signal r ( k ) and the noise power The first value function C ( i ) is set (step S302). Next, the first value function C ( i ) is substituted into the Gaussian probability distribution. In order to get the second value function (Step S303). Next, according to the second value function The fourth value function c 1 ( i ) and the fifth value function c 2 ( i ) are set to perform the multiplication step (step S204). Then, the channel length is obtained according to the maximum value of the four-value function c 1 ( i ), the maximum value of the fifth value function c 2 ( i ), and the length N g of the cyclic prefix CP (Step S205).
請參照圖6，其繪示依照本發明之一實施例之通道長度估測器的方塊示意圖。本實施例之正交分頻多工(OFDM)系統100的通道長度估測器123包含價值函數產生器141、高斯分佈單元142、連乘單元143及計算單元144。價值函數產生器141係用以根據接收訊號r (k )與雜訊功率來產生第一價值函數C (i )。高斯分佈單元142係用以將第一價值函數C (i )代入高斯機率分佈中，以得到第二價值函數。連乘單元143係用以對第二價值函數進行連乘步驟，以產生第三價值函數c (i )。計算單元144係用以根據第三價值函數c (i )的最大值來求得通道長度。Please refer to FIG. 6, which is a block diagram of a channel length estimator according to an embodiment of the present invention. The channel length estimator 123 of the orthogonal frequency division multiplexing (OFDM) system 100 of the present embodiment includes a value function generator 141, a Gaussian distribution unit 142, a multiplication unit 143, and a calculation unit 144. The value function generator 141 is configured to receive the signal r ( k ) and the noise power according to To generate the first value function C ( i ). Gaussian distribution unit 142 is used to substitute first value function C ( i ) into Gaussian probability distribution In order to get the second value function . The multiplying unit 143 is used to apply the second value function A multiplication step is performed to generate a third value function c ( i ). The calculating unit 144 is configured to determine the channel length according to the maximum value of the third value function c ( i ) .
在同步誤差下的通道長度估測方法時，上述通道長度估測器123亦可用以對第二價值函數進行連乘步驟，以產生第四價值函數c 1 (i )和第五價值函數c 2 (i )。且計算單元144可根據第四價值函數c 1 (i )的最大值、第五價值函數c 2 (i )的最大值以及循環字首CP的長度N g ，來求得通道長度。The channel length estimator 123 can also be used to the second value function when estimating the channel length under synchronization error. A multiplication step is performed to generate a fourth value function c 1 ( i ) and a fifth value function c 2 ( i ). And the calculating unit 144 can determine the channel length according to the maximum value of the fourth value function c 1 ( i ), the maximum value of the fifth value function c 2 ( i ), and the length N g of the cyclic prefix CP .
由上述本發明的實施例可知，本發明之正交分頻多工系統的通道長度方法及其估測器可利用通道長度的特性和雜訊功率來產生價值函數，並利用高斯機率分佈和連乘方式來求得通道長度，因而可適用於不同的系統，亦可在同步誤差下執行。再者，本發明可較簡易且較準確地進行通道長度的估測，且不需要Pilot或通道響應的資訊。It can be seen from the above embodiments of the present invention that the channel length method and the estimator of the orthogonal frequency division multiplexing system of the present invention can utilize the channel length characteristics and the noise power to generate a value function, and utilize the Gaussian probability distribution and connection. Multiply the way to find the channel length, so it can be applied to different systems, and can also be executed under synchronization error. Furthermore, the present invention makes it easier and more accurate to estimate the channel length without the need for Pilot or channel response information.
綜上所述，雖然本發明已用較佳實施例揭露如上，然其並非用以限定本發明，本發明所屬技術領域中具有通常知識者，在不脫離本發明之精神和範圍內，當可作各種之更動與潤飾，因此本發明之保護範圍當視後附之申請專利範圍所界定者為準。In view of the above, the present invention has been disclosed in the above preferred embodiments, and is not intended to limit the invention, and the present invention may be made without departing from the spirit and scope of the invention. Various modifications and refinements are made, and the scope of the present invention is defined by the scope of the appended claims.
100．．．正交分頻多工系統100. . . Orthogonal frequency division multiplexing system
110．．．發射器110. . . launcher
120．．．接收器120. . . receiver
121．．．雜訊功率估測器121. . . Noise power estimator
122．．．訊號功率估測器122. . . Signal power estimator
123．．．通道長度估測器123. . . Channel length estimator
131．．．訊號接收單元131. . . Signal receiving unit
132．．．第一乘法器132. . . First multiplier
133．．．第一均方器133. . . First squarer
134．．．第二乘法器134. . . Second multiplier
135．．．第二均方器135. . . Second squarer
136．．．第三乘法器136. . . Third multiplier
137．．．減法器137. . . Subtractor
141．．．價值函數產生器141. . . Value function generator
142．．．高斯分佈單元142. . . Gaussian distribution unit
143．．．連乘單元143. . . Multiply unit
144．．．計算單元144. . . Computing unit
S201．．．取得雜訊功率S201. . . Get noise power
S202．．．設定第一價值函數S202. . . Set the first value function
S203．．．將第一價值函數代入高斯機率分佈S203. . . Substituting the first value function into a Gaussian probability distribution
S204．．．設定第三價值函數S204. . . Set the third value function
S205．．．根據第三價值函數的最大值來求得通道長度S205. . . Find the channel length based on the maximum value of the third value function
S301．．．取得雜訊功率S301. . . Get noise power
S302．．．設定第一價值函數S302. . . Set the first value function
S303．．．將第一價值函數代入高斯機率分佈S303. . . Substituting the first value function into a Gaussian probability distribution
S304．．．設定第四價值函數和第五價值函數S304. . . Setting the fourth value function and the fifth value function
S305．．．根據第四價值函數的最大值、第五價值函數的最大值以及循環字首的長度，來求得通道長度S305. . . The channel length is determined according to the maximum value of the fourth value function, the maximum value of the fifth value function, and the length of the loop prefix
為讓本發明之上述和其他目的、特徵、優點與實施例能更明顯易懂，所附圖式之詳細說明如下：The above and other objects, features, advantages and embodiments of the present invention will become more apparent and understood.
圖1繪示依照本發明之一實施例之正交分頻多工系統的系統方塊圖。1 is a system block diagram of an orthogonal frequency division multiplexing system in accordance with an embodiment of the present invention.
圖2繪示依照本發明之一實施例之發射器的結構示意圖。2 is a schematic structural diagram of a transmitter according to an embodiment of the present invention.
圖3繪示依照本發明之一實施例之雜訊功率估測器與訊號功率估測器的結構示意圖。3 is a schematic structural diagram of a noise power estimator and a signal power estimator according to an embodiment of the invention.
圖4繪示依照本發明之一實施例之正交分頻多工系統之通道長度估測方法的方法流程圖。4 is a flow chart of a method for estimating a channel length of an orthogonal frequency division multiplexing system according to an embodiment of the present invention.
圖5繪示依照本發明之另一實施例之正交分頻多工系統之通道長度估測方法的方法流程圖。FIG. 5 is a flow chart of a method for estimating a channel length of an orthogonal frequency division multiplexing system according to another embodiment of the present invention.
圖6繪示依照本發明之一實施例之通道長度估測器的方塊示意圖。6 is a block diagram of a channel length estimator in accordance with an embodiment of the present invention.
S201．．．取得雜訊功率S201. . . Get noise power
S202．．．設定第一價值函數S202. . . Set the first value function
S203．．．將第一價值函數代入高斯機率分佈S203. . . Substituting the first value function into a Gaussian probability distribution
S204．．．設定第三價值函數S204. . . Set the third value function
S205．．．根據第三價值函數的最大值來求得通道長度S205. . . Find the channel length based on the maximum value of the third value function
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| US7027519B2 (en) * | 2001-02-28 | 2006-04-11 | Mitsubishi Electric Research Laboratories, Inc. | Iterative maximum likelihood channel estimation and signal detection for OFDM systems |
| US7355958B2 (en) * | 2002-10-22 | 2008-04-08 | Syracuse University | Blind OFDM channel estimation and identification using receiver diversity |
| US20090046768A1 (en) * | 2007-08-17 | 2009-02-19 | Ralink Technology, Inc | Method and apparatus for adaptive reduced overhead transmit beamforming for wireless communication systems |
-
2009
- 2009-09-15 TW TW98131123A patent/TWI396415B/en not_active IP Right Cessation
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US7027519B2 (en) * | 2001-02-28 | 2006-04-11 | Mitsubishi Electric Research Laboratories, Inc. | Iterative maximum likelihood channel estimation and signal detection for OFDM systems |
| US7355958B2 (en) * | 2002-10-22 | 2008-04-08 | Syracuse University | Blind OFDM channel estimation and identification using receiver diversity |
| US20090046768A1 (en) * | 2007-08-17 | 2009-02-19 | Ralink Technology, Inc | Method and apparatus for adaptive reduced overhead transmit beamforming for wireless communication systems |
Non-Patent Citations (2)
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| D. N. Van, H.-P Kuchenbecker, and M. Patzold, "Estimation of the channel impulse response length and the noise variance for OFDM systems," in Proc. IEEE VTC., Jun. 2005, vol. 1 * |
| X. Wang, H.-C. Wu, S. Y. Chang, Y. Wu, and J.-Y Chouinard, "Analysis and algorithm for non-pilot-aided channel length estimation in wireless communications," in Proc. IEEE GLOBECOM, Dec. 2008 * |
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| TW201110624A (en) | 2011-03-16 |
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