GB2457260A

GB2457260A - Combining MRC and MMSE equalisation techniques for MIMO-OFDM system

Info

Publication number: GB2457260A
Application number: GB0802292A
Authority: GB
Inventors: Kassem Benzair
Original assignee: WIMAX COMM Ltd
Current assignee: WIMAX COMM Ltd
Priority date: 2008-02-08
Filing date: 2008-02-08
Publication date: 2009-08-12
Also published as: GB0802292D0

Abstract

The proposed system is based on Multiple-Input Multiple-Output Orthogonal Frequency Division Multiplexing (MIMO-OFDM) with two transmit and three receive antennas and uses two diversity modes. The Transmit Diversity mode consists of transmitting the same signal stream on both transmit antennas with a phase delay factor and provides a robust radio link against fading and frequency selective channels and increases the communication range. The Maximum Ratio Combining (MRC) equalization technique used in this mode gives very good results in terms of calculation complexity and performance. The Spatial Multiplexing mode consists of transmitting two different signal streams in each transmit antenna and provides a high throughput for a given bandwidth compared with normal communication systems using single input and single output antennas. The Minimum Mean Square Error (MMSE) equalization technique used in this mode gives very good results in term of calculation complexity reduction and throughput performance.

Description

The proposed system is based on MIMO-OFDM with two transmit and three receive antennas and uses two diversity modes.

The Transmit Diversity mode allows us to have a robust radio link against fading and frequency selective channels and increase the communication range. It consist of transmitting the same signal stream on both transmit antennas with a phase delay factor. The MRC equalization technique used in this mode gives very good results in term of calculation complexity and performance.

The Spatial Multiplexing mode allows us to have a high throughput for a given bandwidth compared with normal communication systems using single input and single output antennas. Tt consist of transmitting two different signal streams in each transmit antenna. The MMSE equalization technique used in this mode gives very good results in term of calculation complexity reduction and throughput performance.

There are S independent streams of information transmitted, S �= R where R is the number of receive antennas. At the receiver, channel estimates from each transmitted signal to each receive antenna are available from the channel id block. Let H,. 5(k) denote the channel from transininer s to receiver r for tone k, where s = 1,K 5, r = IX R, k = O,K,1023. For each tone k, the received vector is Y(k)=[Y(k) A}R(k)] = lk)X(k) + k) the RxS channel mauix is H11(k) A H15(k) H(k)= M 0 M HRI (k) A HRS (k) and the transmitted signal vector is X(k) = (X1 (k) A X5 (k)]T. For convenience, ignore the tone index k from here on.

MMSE Solution The MMSE solution is given as R=(H'H+o2151'HY (I) Where I. is SxS identity matrix, and a2 is the noise power per receive antenna. It can be shown that (H*H +0.2 Is)1H* = H*(HH* +G21R)1 so that X can also bc computed as X =H(HH +2iy'y (2) which is the standard MMSE formulation. We will use the formulation in (1) for Avido since it has lower complexity for the baseline case: S = 2 and R =3 (two strewns and three receive antennas). Note that this formulation is solving the "regularized" least-squares (LS) problem. It is well-known that a numerically stable approach to solve a LS problem is using the QR-decomposition. We are interested to convert (1) into a LS problem, which we know how to solve robustly. Consider minimizing 1!IR 1 IYR 12 mink I IX I TI [a Ij [0 J, (3) mink 1(Ri-S) xS'.SxI -R+S) xI 2 where -rHxsl -rYKIl H(R+S)S R+S)xI (4) L0.' scJ L'sti J The solution for (3) can be given by the standard normal equations ) =(H*HJIH*y =(Hii +a2I5)1HY which is exactly (1).

Numerical Implementation: Numerically, the MMSE solution is computed as follows: 1. Form the augmented matrices "(R+S)rS' (R+sJ given in (4) 2. Compute an "economy" QR-decomposition of = QR+ R. where Q is a matrix of orthonormal vectors spanning the column-space of H, and R is an upper triangular matrix.

3. Compute V51 = QXR+S R+StI 4. Use back-substitution to compute an estimate of XSrI by solving the system of equations RcsXsTI SXI SNR Weighting: The MMSE output can be written as X =WY, where W* =(/J*ff +ô215)1H*. The error variance in each element of the MMSE output, corresponding to each transmitted signal, is passed to the convolutional decoder so that tones with large error variance are given less importance in the decoding process. This allows improved performance in a frequency selective channel. We can write the error vector E= X-X =w*Y-x =W(HX+N)-X =(W*H_I)X+W*N The covanance of the error vector is RE= LIEE] = (WH _1)ETXX*](W*H -I) �(WH -I)EIXN']W+WE[NX]O4'H -1) +WEINN]W Assuming that a) signals are independent with unit energy, E[XX] = I b) single and noise are uncorrelated, EIXN I = 0 c) noise is white with variance a2, E[NN'] = c21, the covariance can be written as R = (W*H -I)(W*H -l) + a2W*W.

The expression above can be futher simplified to RE = o2(HH +o2l)1 (5) so that there is no explicit dependence on the weight matrix W. The error variance for each element of the signal vector is X is given by the corresponding diagonal element of R. Numerical Implementation: The expression for RE in (5) can he written in terms of H which is defined in Eqn. (4) = Given that we compute the QR decomposition of HR+)X = QR+L R to compute the MMSE solution, we can rewrite RE in terms of the upper triangular matrix Rçç only * -l RE = o(R5 R) Since S= 2 for the Avido system, the elements of RE can be computed explicitly. Note that we are only interested in the diagonal entries of RE. Let us denote [r r ssI L0 r21 Then, the error variance for signal 1 can be written as: 2 Ij2I +Ir2I 2 -, (6) I Ir,2 and the error variance for signal 2 is II2 1 �72 �7 2 =o. (7) Ir I Ira, 1r11 Interference Cancellation The above discussion assumes that only additive white noise is present at the receiver output. There may also be additional interference from users in adjacent bands or adjacent cells, which is not white. The data model for this scenario is Y=HX+N+J where I is the interference term. Let us denote RN as the noise and interference covariance matrix, ie R, = E[(N + 1)(N + J)*] Assuming that this covariance is known at the receiver, the MMSE solution is =H'(HH +RJ'Y.

The noise-plus-interference covariance matrix may be estimated by subtracting the estimated channel matrix times the estimated signal vector from the received vector for previous OFDM symbols or neighboring tones which have the same interference present. Compute the Cholesky decomposition of

RN

R, =R,2R,2, so that X can be rewritten as X = H(HH + R2R2)1Y = H*(R.J2 (R112HHR72 + I)R2 i1Y = H*R 2(R,,"2HHR72 + Ii'R72Y -H(HNH., +JY'Yv where H,,, = R)'2H, and Y,,. = R"2Y. Noting that 1J (H,H + = (H H. + Jy H, the final MMSE solution is given by K =(HH, +IY'HYN. (8)

C

Numerical Implementation: 1) Estimate RN using decision-directed approach --, 1/2.

2) Compute the Cholesky decomposition of RN = R. RN', where RN is lower triangular 3) Solve system of equations R2H = H for H using forward-substitution 4) Solve system of equations R2YN = Y for YN using forward-substitution 5) Form augmented matrices -IN,1 -ry,1 =[ ], Y L i (9) SxS 6) Solve for X using the QR based approach described earlier SNR Weighting: The covariance of the error vector E = X -X is given by RE= AETEE] = (WH -1)(WtH -+ WRNW where it follows from Eqn. (8) that W =(H,H, +!)H,R"2 = (H*RIH + JY' HR' Using the above weight vector, we can write WR,,,,W = (H*RI H + I) H*RIH(H* R' H + and we can write W*H I =(H*R;IH + iy' H*R;IH -J = (H*R)H J)_I [(H*R)H +1)-I]-I = !(H*R)H+IyI -! = -(HR'H +I) Using the above 2 expressions. the error covariance can be simplified to RF = (HR)H + Jy [HR'H + + J)l (10) = (H*RIH + Numerical Implementation: The expression for RE in (10) can be written in terms of Hv which is defined in Eqn. (9) R =(HHN)'.

Given that we compute the QR decomposition of HN = QR+SXS to compute the MMSE solution, we can rewrite RE in terms of the upper triangular matrix Rr only. As before, denoting i2 R-l L0 r2., the error variance for signal I can be written as: Ir 12 +Ir,,12 12 2 (II) hi r,2 I and the error variance for signal 2 is 2 1 02 = (12) MRC solution * The H matrix is reformatted, so we convert the original 3x2 into a 3x 1 matrix by adding column 2 of H matrix to column I. The second column is zeroed out.

* H'* H forms a 2x2 matrix. Only element [0, 0] needs to be calculated.

* H inverses the H* H matrix and forms the 2x2 matrix.

* R the "Reciprocal Noise Enhancement Factor" for the "TD" tone is element [0,0] of the H'* H matrix, * X = H*(Y[OJ�Y(1])