A 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) systems regardless of the frequency selectivity severity of the channel comprising the steps of; For channel estimatiation; In the tranceiver; 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 Inverse discrete Fourier transform (IDFT), Out of the 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 M-block IDFT to the M subsymbols, Applying Parallel to serial, Adding of cyclic prefix (CP), Passing to transmitter through channel, For enhanced channel estimation; In the tranceiver, 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 discrete Fourier transform (DFT), to the received signal y.sub.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 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.sub.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 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, Demodulating the symbols.

Description

DEFINITION OF THE FIGURES

[0026] 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:

[0027] FIG. 1: Proposed transceiver design

[0028] Some definitions in FIGURE:

[0029] Cyclic prefix (CP),

[0030] Channel impulse response (CIR),

[0031] Inverse discrete Fourier transform (IDFT),

[0032] Transmitter (Tx),

[0033] Receiver (Rx),

[0034] Serial (S),

[0035] Parallel (P),

[0036] Serial to parallel S/P,

[0037] Data symbols,

[0038] Demodulated symbols.

DETAILED DESCRIPTION OF THE INVENTION

[0039] 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.

[0040] Transmitter Design:

[0041] 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.

[0042] 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.{Ntap}].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:

[00001]$\begin{array}{cc}{H}_c=\left[\begin{array}{ccccccccc}& h_1& 0& 0& .Math.& h_{N_{\mathrm{tap}}}& h_{N_{\mathrm{tap}}-1}& .Math.& h_2\\ & & .Math.& & & & .Math.& & \\ 0& .Math.& 0& h_{N_{\mathrm{tap}}}& .Math.& & h_1& & \end{array}\right]& \left(3\right)\end{array}$

[0043] Z denotes the noise vector. The channel matrix H.sub.c can be expressed a circulant matrix of

[00002]$\frac{K}{K_p}\frac{K}{K_p}$

sub-matrices; then, H.sub.c can be rewritten as:

[00003]$\begin{array}{cc}{H}_c=\left[\begin{array}{ccccccc}{H}_1& O& O& .Math.& & H_2& \\ & .Math.& & & & .Math.& \\ & O& & .Math.& O& H_2& H_1\end{array}\right]& \left(4\right)\end{array}$

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:

[00004]$\begin{array}{cc}{H}_1=\left[\begin{array}{c}\begin{array}{c}{h}_{1}00\\ .Math.\end{array}\\ h_{N_{\mathrm{tap}}}.Math.h_1\end{array}\begin{array}{c}\begin{array}{c}.Math.\\ \end{array}\\ .Math.\end{array}\begin{array}{c}\begin{array}{c}0\\ .Math.\end{array}\\ 0\end{array}\right],H_2=\left[\begin{array}{c}\begin{array}{c}0\\ \end{array}\\ \end{array}\begin{array}{c}\begin{array}{c}0h_{N_{\mathrm{tap}}}\\ .Math.\end{array}\\ 0.Math.0\end{array}\begin{array}{c}\begin{array}{c}.Math.\\ \end{array}\\ .Math.\end{array}\begin{array}{c}\begin{array}{c}{h}_2\\ .Math.\end{array}\\ 0\end{array}\right]& \left(5\right)\end{array}$

[0044] 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 .

[0045] 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.

[0046] 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.}.

[0047] 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)

[0048] where x=[F.sub.N.sup.1p.sup.T, F.sub.N.sup.1s.sub.1.sup.T, . . . , F.sub.N.sup.1s.sub.M1.sup.T].sup.T and F.sub.N.sup.1 is the NN inverse DFT matrix.

[0049] Receiver Design:

[0050] 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)

[0051] 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)

[0052] Note that since H.sub.c is circulant, then H.sub.D is diagonal matrix given by:

[00005]$\begin{array}{cc}{H}_D=\left[\begin{array}{ccc}{H}_{D_1}& .Math.& O\\ .Math.& & .Math.\\ O& .Math.& H_{D_N}\end{array}\right],& \left(9\right)\end{array}$

[0053] where H.sub.D.sub.1==H.sub.1+H.sub.2.

[0054] 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.1

P.sub.N+F.sub.Nz.sub.1,(10)

[0055] where z.sub.1 contains the first N samples of B.sub.Mz. 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)

[0056] Channel Estimation Scheme:

[0057] 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)

[0058] 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

[0059] where {tilde over (z)}.sub.1=DFT(F.sub.N.sup.1p.sup.1F.sub.Nz.sub.1, K).

[0060] 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;

[0061] For channel estimatiation;

[0062] In the transmitter; [0063] Converting M OFDM symbols as S.sub.m(k), k=1, . . . , N, m=1, . . . , M [0064] Comprising of each comprising N orthogonal subcarriers from frequency-domain to x.sub.m(n), n=1, . . . , N in time-domain using the IDFT, [0065] Out of the 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, [0066] Applying block IDFT to the M subsymbols as given in equation (6) {umlaut over (x)}=B.sub.M.sup.1x, [0067] Aligning the data from parallel to serial, [0068] Adding of cyclic prefix, [0069] Passing to transmitter through channel,

[0070] For enhanced channel estimation;

[0071] In the receiver, [0072] Discarding of the CP, [0073] 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, [0074] 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, [0075] 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 [0076] 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). [0077] where {tilde over (z)}.sub.1=DFT(F.sub.N.sup.1p.sup.1F.sub.Nz.sub.1, K). [0078] Applying of equalization process (equalization is well known in the literature and it is done via many algorithms), [0079] Demodulated symbols.