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In this chapter, we have introduced a systematic framework [20] to investigate the spacetime coding and constellation design for MIMO channels with imperfect CSIR. In particular, we considered the asymptotically optimal spacetime coding and constellation design in the absence of perfect CSIR. With channel estimation errors, constellations that are designed according to the statistics of the CSI error are more desirable than those designed for perfect CSIR. Using Stein s lemma, the conditional pairwise error probability can be approximated by exp(-D(pi||pj)), where D(pi||pj) is the KL distance between the like lihood functions pi = p(y|xi, h ) and pj = p(y|xj, h ). Hence, the constellation and code design for MIMO fading channels with imperfect CSIR can be expressed as the optimization problem to select the codewords {xi} so as to maximize the minimum average KL distance D (xi; xj) (which is the expectation of the exponential error bound over the CSIR estimation error D). We applied the design criterion (D (xi; xj)) to the constellation design so as to optimize the uncoded MIMO performance with imperfect CSIR. To restrict the search space, we consider optimization over all unitary constellations. We found that the uncoded performance gains of the optimal design based on the average KL distance deliver substantial performance gains over the regular constellations designed for perfect CSIR. Next, we extended the design framework to consider coded modulation design for MIMO with imperfect CSIR. For simplicity, we considered block fading MIMO channels. Similarly, the pairwise error probability can be
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Figure 5.10. Performance comparison between the partially coherent design and the coherent 2 2 design in the presence of imperfect CSIR: (a) s e = 0.01; (b) s e = 0.05. [20]
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bounded with the exponent of the bound given by the average KL distance between the vector codewords xi and xj. More interestingly, the overall average KL distance has similar additive property of the conventional Euclidean distance, which is the design criterion for coded modulation with perfect CSIR. Hence, similar techniques of set partitioning can be applied in our case except using the average KL distance rather than the Euclidean distance. The performance of the coded modulation with imperfect CSIR designed based on the KL distance is compared with that for the coded modulation schemes designed for perfect CSIR. It is shown that substantial SNR gain can be achieved with the coded modulation designed with reference to KL distance and the gain increases as the CSIR error s 2 increases. e
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6.1 OVERVIEW
Traditionally, the achievable bit rate of a communication link is limited by the available bandwidth and power. Given a xed power budget, the only way to increase the bit rate is to increase the bandwidth of transmission. In the previous chapters, we focused on the performance of MIMO point-to-point link with CSI knowledge at the transmitter and the receiver. With multiple transmit and receive antennas, the bit rate can be signi cantly increased without increasing the bandwidth or power budget. This is due to spatial multiplexing over m* = min[nT, nR] spatial channels, where nT is the number of transmit antennas and nR is the number of receive antennas. For the point-to-point link, the performance measure is relatively simple. Speci cally, we would like to optimize the link capacity or reduce the BER of the link. It has been shown in previous chapters that knowledge of CSI at the transmitter can signi cant increase the MIMO link capacity, especially when nT > nR. However, for multiuser systems, optimizing the individual link performance is not always the best approach from a system performance perspective. It is also very important to consider the upper-layer resource allocation together with the adaptive physical layer design so as to completely exploit the temporal dimension (scheduling) and the spatial dimension (multiple antennas) in the resource space to achieve good system-level performance. Two factors are unique to multiuser systems only: multiuser diversity and the distributed spatial multiplexing. When the base station has knowledge of CSI, an extra dimension of adaptation is possible for systems with multiple
Channel-Adaptive Technologies and Cross-Layer Designs for Wireless Systems with Multiple Antennas: Theory and Applications. By V. K. N. Lau and Y.-K. R. Kwok ISBN 0-471-64865-5 2006 by John Wiley & Sons, Inc.