Advances in MIMO Techniques for Mobile Communications—A Survey <s> Iterative Linear MMSE Precoding <s> We address the problem of Mean Square Error (MSE) transceiver design for point-to-multipoint transmission in multi-user Multiple-Input-Multiple-Output (MIMO) systems. We solve the problem of minimizing the downlink sum MSE under a sum power constraint by jointly optimizing the linear transmitters and receivers. Our result is based on a "duality" between downlink and uplink MSE regions. It states that downlink and uplink share the same achievable MSE region under a sum power constraint. Thus, the problem of downlink design can be solved efficiently by focusing on an equivalent uplink problem. <s> BIB001 </s> Advances in MIMO Techniques for Mobile Communications—A Survey <s> Iterative Linear MMSE Precoding <s> In this paper, the multi-user MIMO downlink channel is considered, where a single transmitter (base station) sends data to several users within the same resource unit. Assuming perfect channel state information (CSI) at the transmitter, different linear precoding schemes are studied, aiming at mean square error minimizing transmission to all users. The exact MMSE solution can be obtained by exploiting up-link/downlink duality. A suboptimal solution based on necessary conditions for MMSE optimality may also be computed directly in the downlink domain. Our results indicate that the performance difference between the direct and duality-based method that is visible in uncoded BER curves vanishes when channel coding is introduced to the system. We also compare the MMSE-optimal approaches to other existing linear precoding schemes (BD, S-MMSE). <s> BIB002
Two iterative linear MMSE precoding schemes are discussed in BIB002 for users with multiple antennas. Consider the system model of Figure 50 where P is the combined precoding matrix at the BS and V is the block-diagonal combined decoding matrix consisting of the decoding matrices of all the users. BIB001 to obtain the ue MMSE solution using an iterative algorithm. The resulting objective function is convex in this case. Detailed description as well as a practically implementable algorithm for this duality-based scheme is presented in  . The uncoded BER performance of BD, SMMSE, direct optimization and the duality-based scheme is compared in Figure 57 for {1, 2, 3} u 6 antenna configuration. The bit error rates are averaged over all users. DET is applied for BD and SMMSE while single stream (SS) transmission (consisting of a single data stream per user) is used for direct optimization and the duality-based scheme based on the algorithm from  . Independent Rayleigh fading channel perturbed by complex Gaussian noise is considered and QPSK modulation is used for transmission. Both iterative linear MMSE schemes outperform the other two by a large margin. The duality-based scheme shows slightly better performance than solution can also be used as an initial guess but that would result in slower convergence. The other scheme exploits t tr interesting MU-MIMO downlink transmission scheme ased solely on instantaneous channel norm feedback is proposed in  . MU-MIMO configuration with multiple base station (BS) antennas and a single antenna at each UE is considered. The proposed scheme can provide high multiuser diversity gain by optimizing resource allocation at the BS while simply utilizing the instantaneous channel norm feedback from the UEs. Figure 59 shows the operation of the proposed system at the transmitter (BS). The BS initially transmits orthogonal pilot signals on all transmit antennas which are used by each UE to estimate the received signal energy i.e. the squared norm of the channel vector given by direct optimizati . This d nce is due to the nonx objective function used for direct optimization which occasionally causes the optimization routine to undesired minima. BD provides the worst performance because of the zero-forcing constraint. Figure 58 shows the coded BER performance of these precoding schemes. A rate 1/2 turbo code is used for error correction. OFDM based transmission is considered where the precoding is applied on a per-subcarrier basis. The ITU Vehicular A channel model is used. Direct optimization and the duality-based scheme provide almost identical performance in this case, far better than BD and SMMSE.