Method for pilot-aided channel estimation in ofdm systems regardless of the frequency selectivity severity of the channel

Abstract

Disclosed is a method pilot-aided channel estimation in Orthogonal Frequency Division Multiplexing (OFDM) systems regardless of the frequency selectivity severity of the channel is proposed.

Claims

1. A method for pilot-aided channel estimation in orthogonal frequency division multiplexing (OFDM) system regardless of frequency selectively severity of a channel, the method comprising: estimating the channel in a transceiver by the step of: converting M OFDM symbols as S.sub.m(k), k=1, . . . , N, m=1, . . . , M; inverse discrete Fourier transforming N orthogonal subcarriers from a frequency-domain to x.sub.m(n), n=1, . . . , N in time-domain; using a first symbol of the M OFDM symbols containing N known pilots for channel estimation; using a remainder of the N orthogonal subcarriers for data transmission; applying M-block inverse discrete Fourier transforms (DFT) to M subsymbols; applying parallel to serial; adding a cyclic prefix (CP); and passing to a transmitter through the channel; enhancing channel estimation in the transceiver by the steps of; discarding the CP; writing the received signal as: y=H.sub.c{circumflex over (x)}+z=H.sub.cB.sub.M.sup.1x+z, wherein y is the received signal after discarding the cyclic prefix, H.sub.c is a circulant channel matrix of MNMN size representing the channel, {circumflex over (x)} is a transmitted data vector stacked from all OFDM symbols after an M-point block-IDFT operator, z=an additive white Gaussian noice vector, B.sub.m.sup.1 is an inverse block-discrete Fourier transform; applying the M-block discrete Fourier transform (DFT) to a received signal (y.sup.1 wherein $y^1=B_M{H}_c{B}_M^{-1}x+B_{M}z$ $=H_{D}x+B_{M}z,$ where B.sub.M is an M-point block DFT operator, H.sub.D is a block-diagonalized channel matrix after applying the block-DFT transform; applying an N-DFT process to a first subsymbol (y.sub.1) in accordance with, y.sup.2=F.sub.NF.sub.N.sup.1p+F.sub.Nz.sub.1, where y.sup.2 is an output after applying the N-point DFT on the first subsymbol, F.sub.N is an N-point DFT matrix, is a time domain circulant channel matrix of size NN, F.sub.N.sup.1 is an inverse N-point DFT matrix, p is a pilot vector of the first subsymbol, z.sub.1 is a noise vector corresponding to the first subsymbol after block DFT; estimating the channel using:
=DFT(F.sub.N.sup.1P.sup.1y.sub.2,K)=DFT(F.sub.N.sup.1P.sup.1(P.sub.N+F.sub.Nz.sub.1),K)=DFT(F.sub.N.sup.1.sub.N+F.sub.N.sup.1P.sup.1F.sub.Nz.sub.1,K)=.sub.N+{tilde over (z)}.sub.1 where {tilde over (z)}.sub.1=DFT(F.sub.N.sup.1p.sup.1F.sub.Nz.sub.1,K). where {tilde over (z)}.sub.1=DFT(F.sub.N.sup.1p.sup.1F.sub.Nz.sub.1, K), where is a channel frequency response of MN1 length, K is NM, P is a pilot-symbol diagonal matrix where known pilot symbols are inserted, h.sub.N is a channel impulse response of N1 length; {tilde over (z)}.sub.1 is an equivalent noise after pilot-based channel estimation; applying an equalization process; and demodulating the symbols.

Description

DEFINITION OF THE FIGURES

(1) The FIGURES have been used in order to further disclose a method for pilot-aided channel estimation in orthogonal frequency division multiplexing (OFDM) systems regardless of the frequency selectivity severity of the channel developed by the present invention which the FIGURES have been described below:

(2) FIG. 1: Proposed transceiver design

(3) Some definitions in FIGURE: Cyclic prefix (CP), Channel impulse response (CIR), Inverse discrete Fourier transform (IDFT), Transmitter (Tx), Receiver (Rx), Serial (S), Parallel (P), Serial to parallel S/P, Data symbols, Demodulated symbols.

DETAILED DESCRIPTION OF THE INVENTION

(4) The novelty of the invention has been described with examples that shall not limit the scope of the invention and which have been intended to only clarify the subject matter of the invention. The present invention has been described in detail below.

(5) Transmitter Design:

(6) At the t-th symbol time, the MSE-OFDM transmitter converts M OFDM symbols S.sub.m(k), k=1, . . . , N, m=1, . . . , M comprising N orthogonal subcarriers from frequency-domain to x.sub.m(n), n=1, . . . , N in time-domain using the IDFT. The first symbol out of the M symbols contains N known pilots used for channel estimation, where the rest (M1)N subcarriers are used for data transmission. To combat ISI, CP is appended to the signal and then it is transmitted as depicted in FIG. 1.

(7) The wireless channel is assumed to be slow time-varying, i.e., CIR is invariant for each MSE-OFD symbol with N.sub.tap path components. Also,
y[n]=h[n].Math.x[n]+z[n],(1)
where x[n] is the OFDM modulated signal and z[n] denotes the zero-mean AWGN with variance .sub.2. To cast (1) from serial to matrix-vector form, we define y=[y(1), . . . , y(K)].sup.T, x=[x(1), . . . , x(K)].sup.T and z=[z(1), . . . , z(K)].sup.T to be the .sup.K1 vectors, and h=[h.sub.1, . . . , h.sub.{N.sub.tap.sub.}].sup.T to be the .sup.N.sup.tap.sup.1 channel vector. Therefore, (1) is rewritten as:
y=h.Math.x+z=H.sub.cx+z,(2)
where H.sub.c denotes the circulant channel matrix which is given as:

(8) $\begin{array}{cc}{H}_c=\left[\begin{array}{ccccccccc}& h_1& 0& 0& .Math.& h_{N_{\mathrm{tap}}}& h_{N_{\mathrm{tap}}-1}& .Math.& h_2\\ & & .Math.& & & & .Math.& & \\ 0& .Math.& 0& h_{N_{\mathrm{tap}}}& .Math.& & h_1& & \end{array}\right]& \left(3\right)\end{array}$

(9) Z denotes the noise vector. The channel matrix H.sub.c can be expressed a circulant matrix of

(10) $\frac{K}{K_p}\frac{K}{K_p}$
sub-matrices; then, H.sub.c can be rewritten as:

(11) $\begin{array}{cc}{H}_c=\left[\begin{array}{ccccccc}{H}_1& O& O& .Math.& & H_2& \\ & .Math.& & & & .Math.& \\ & O& & .Math.& O& H_2& H_1\end{array}\right]& \left(4\right)\end{array}$
where OC.sup.{K.sup.p.sup.K.sup.p.sup.} denotes the zeros matrix, and H.sub.1.sup.{K.sup.p.sup.K.sup.p.sup.} and H.sub.2.sup.{K.sup.p.sup.K.sup.p.sup.} are given by:

(12) $\begin{array}{cc}{H}_1=\left[\begin{array}{c}\begin{array}{c}{h}_{1}00\\ .Math.\end{array}\\ h_{N_{\mathrm{tap}}}.Math.h_1\end{array}\begin{array}{c}\begin{array}{c}.Math.\\ \end{array}\\ .Math.\end{array}\begin{array}{c}\begin{array}{c}0\\ .Math.\end{array}\\ 0\end{array}\right],H_2=\left[\begin{array}{c}\begin{array}{c}0\\ \end{array}\\ \end{array}\begin{array}{c}\begin{array}{c}0h_{N_{\mathrm{tap}}}\\ .Math.\end{array}\\ 0.Math.0\end{array}\begin{array}{c}\begin{array}{c}.Math.\\ \end{array}\\ .Math.\end{array}\begin{array}{c}\begin{array}{c}{h}_2\\ .Math.\end{array}\\ 0\end{array}\right]& \left(5\right)\end{array}$

(13) It should be noticed that =H.sub.1+H.sub.2 is also a circulant matrix and it contains all non-zero values of the matrix H.sub.c, thus, it is a smaller representation of the channel matrix H.sub.c. Therefore, fully estimating H.sub.c is equivalent to only estimating .

(14) Differently from the conventional MSE-OFDM transceiver, in the proposed design, MM block-DFT and its inverse process are introduced at the receiver and the transmitter sides, respectively, as depicted in FIG. 1. The added DFTs are block-based DFTs i.e., each submatrix in H.sub.c is treated as one single element and the DFT matrix F.sub.M serves to block-diagonalize H.sub.c.

(15) Let B.sub.M denote the block-DFT process which is a DFT process that takes complex vectors as an input instead of complex values. It can be explicitly represented in terms of DFT process as B.sub.M=F.sub.M.Math.I.sub.N, where I.sub.N represents the N\times N identity matrix, F.sub.M.sup.{K.sup.p.sup.K.sup.p.sup.} and B.sub.M.sup.{K.sup.p.sup.K.sup.p.sup.}.

(16) Let the unmodulated transmitted signal be s=[P.sub.1, . . . , P.sub.N, S.sub.1, . . . , S.sub.K-N].sup.T=[p.sup.T, s.sub.1.sup.T, . . . , s.sub.M-1.sup.T].sup.T, where p.sup.N1 is the first sub-symbol containing the pilots, and s.sub.i.sup.N1 denotes the i-th data sub-symbol. Then, transmitted signal is found as:
{circumflex over (x)}=B.sub.M.sup.1x,(6)
where x=[F.sub.N.sup.1p.sup.T, F.sub.N.sup.1s.sub.1.sup.T, . . . , F.sub.N.sup.1s.sub.M-1.sup.T].sup.T and F.sub.N.sup.1 is the NN inverse DFT matrix.
Receiver Design:

(17) At the receiver side, after discarding the CP, the received signal is written as:
y=H.sub.c{circumflex over (x)}+z=H.sub.cB.sub.M.sup.1x+z,(7)

(18) As shown in FIG. 1 (b), there are two DFT processes at the receiver side after discarding the CP. Let y.sup.1 and y.sup.2 be the output of the first and second process, respectively. y.sub.1 is the output of the block DFT, then:
y.sup.1=B.sub.MH.sub.cB.sub.M.sup.1x+B.sub.Mz=H.sub.Dx+B.sub.Mz,(8)

(19) Note that since H.sub.c is circulant, then H.sub.D is diagonal matrix given by:

(20) $\begin{array}{cc}{H}_D=\left[\begin{array}{ccc}{H}_{D_1}& .Math.& O\\ .Math.& & .Math.\\ O& .Math.& H_{D_N}\end{array}\right],& \left(9\right)\end{array}$
where H.sub.D.sub.1==H.sub.1+H.sub.2.

(21) In order to estimate the channel, only the first N samples of y.sub.1 (i.e., the first sub-symbol H.sub.D.sub.1F.sub.N.sup.1p) are considered for the second process. Then, the output of the second process is given by:
y.sup.2=F.sub.NF.sub.N.sup.1p+F.sub.Nz.sub.1=.sub.Dp+F.sub.Nz.sub.1=.sub.Np+F.sub.Nz.sub.1P.sub.N+F.sub.Nz.sub.1,(10)
where z.sub.1 contains the first N samples of B.sub.M z. P is the diagonal matrix having p as a diagonal and .sub.D is the diagonal matrix containing the N point CFR .sub.N of the wireless channel given by
.sub.N=diag(.sub.D)=DFT(h,N)=F.sub.Nh,(11)
Channel Estimation Scheme:

(22) At the receiver side the pilots are recovered without any interference from the data. Therefore, conventional OFDM channel estimation algorithms can be applied, such MMSE and LS estimators. the LS estimation is used for the estimation. Least-square (LS), Minimum mean squared error (MMSE)

(23) Let .sub.N=[H(1), . . . , H(K)].sup.T be the CFR vector, then the estimated channel is readily found as:
=DFT(F.sub.N.sup.1P.sup.1y.sub.2,K)=DFT(F.sub.N.sup.1P.sup.1(P.sub.N+F.sub.Nz.sub.1),K)=DFT(F.sub.N.sup.1.sub.N+F.sub.N.sup.1P.sup.1F.sub.Nz.sub.1,K)=.sub.N+{tilde over (z)}.sub.1
where {tilde over (z)}.sub.1=DFT(F.sub.N.sup.1p.sup.1F.sub.Nz.sub.1, K).

(24) A method for pilot-aided channel estimation in orthogonal frequency division multiplexing (OFDM) systems regardless of the frequency selectivity severity of the channel comprising the steps of;

(25) For channel estimation;

(26) In the transmitter; Converting M OFDM symbols as S.sub.m(k), k=1, . . . , N, m=1, . . . , M Comprising of each comprising N orthogonal subcarriers from frequency-domain to x.sub.m(n), n=1, . . . , N in time-domain using the IDFT, Out of the first symbol of M symbols contains N known pilots used for channel estimation, where the rest (M1)N subcarriers are used for data transmission, Applying block IDFT to the M subsymbols as given in equation (6) {umlaut over (x)}=B.sub.M.sup.1x, Aligning the data from parallel to serial, Adding of cyclic prefix, Passing to transmitter through channel,

(27) For enhanced channel estimation;

(28) In the receiver, Discarding of the CP, After discarding the CP, the received signal is written as:
y=H.sub.c{circumflex over (x)}+z=H.sub.cB.sub.M.sup.1x+z, Applying the M-block DFT to the received signal y.sup.1,
y.sup.1=B.sub.MH.sub.cB.sub.M.sup.1x+B.sub.Mz=H.sub.Dx+B.sub.Mz, Applying N-DFT (N is the DFT(FFT) size that is given as 2{circumflex over ()}B, where b is a positive integer.) process to the first subsymbol y.sub.1.
y.sup.2=F.sub.NF.sub.N.sup.1p+F.sub.Nz.sub.1 Estimating the channel by using
=DFT(F.sub.N.sup.1P.sup.1y.sub.2,K)=DFT(F.sub.N.sup.1P.sup.1(P.sub.N+F.sub.Nz.sub.1),K)=DFT(F.sub.N.sup.1.sub.N+F.sub.N.sup.1P.sup.1F.sub.Nz.sub.1,K)=.sub.N+{tilde over (z)}.sub.1 where {tilde over (z)}.sub.1=DFT(F.sub.N.sup.1p.sup.1F.sub.Nz.sub.1,K). where {tilde over (z)}.sub.1=DFT(F.sub.N.sup.1p.sup.1F.sub.Nz.sub.1, K). Applying of equalization process (equalization is well known in the literature and it is done via many algorithms), Demodulated symbols.