SPACETIME CODING AND LAYERED SPACETIME CODING FOR MIMO WITH PERFECT CSI

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Figure 4.6. Block diagram of the D-BLAST transmitter: (a) D-BLAST transmitter architecture; (b) D-BLAST signal matrix.

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Figure 4.7. Spatial interleaving of hybrid H-BLAST/D-BLAST.

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DESIGN OF MIMO LINKS WITH PERFECT CSIR

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Figure 4.8. Illustration of threaded LST design.

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where N is the total number of channel uses for the D-BLAST codeword. Note that the spectral ef ciency is slightly smaller than that of the V-BLAST or HBLAST because of the overhead of zero padding but as N , the spectral ef ciency approaches that of the V-BLAST or H-BLAST. 4.2.2.4 Threaded Layered Spacetime Code. The transmitter design of threaded layered spacetime coding (TLST) [45] is similar to the format in Figure 4.6a. The only difference is the way spatial interleaver operates. In TLST, we have a generalized notion of layer called thread. A generalized layer is de ned by an index set L = {(a, t ) : a [1, nT ], t [1, N ]} such that if (a1, t1) L and (a2, t2) L, then either a1 = a2 or t1 t2; that is, at any given time, no symbols from the same layer occupy more than one antenna. A generalized layer is called a thread if

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Each layer is active during the entire transmission interval. Over time, each layer uses the nT transmit antennas equally often.

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For example, the generalized layers {L1, . . . , LnT} de ned below are threads: Li = {(a, t ) : a = [(i + t - 2) mod nT ] + 1}. This is illustrated in Figure 4.8 for nT = 3. Unlike D-BLAST, the encoded symbols from the ith thread is distributed to the transmit antenna a and time t according to the thread index Li without the need for zero padding. In addition, the encoded block length can be longer than nT. Since the encoded symbols from each thread are delivered to the receiver through different transmit antennas, the TLST architecture allows full diversity within each codeword and is therefore outage-optimal in slow MIMO fading channels as will be shown in Section 4.2.5. Yet, TLST design requires more sophisticated receive processing. The spectral ef ciency of the TLST design is given by rb = rc log2(M)nT bits per channel use. 4.2.3 Receiver Designs for Layered Spacetime Codes

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In this section, we shall consider the receiver structures for layered spacetime architectures. The received signal is given by

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SPACETIME CODING AND LAYERED SPACETIME CODING FOR MIMO WITH PERFECT CSI

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y = hx + z =

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where hk is the kth column of the nR nT channel matrix h and xk is the transmitted symbol from the kth transmit antenna. Hence, the LST receiver is in general very similar to a multiuser detector in which the number of transmit antennas is equal to the number of users. Hence, the optimal receiver for uncoded LST systems is a ML multiuser detector [136] operating on a trellis and it has a complexity that is exponential in the number of transmit antennas nT and modulation throughput log2(M). For coded LST systems, the optimal receiver performs joint ML detection and decoding over the entire spatial domain and the entire temporal domain. It has an overall complexity given by the number of transmit antennas nT, modulation throughput log2(M), as well as the channel code memory order. For a moderate number of transmit antennas, modulation level, and code memory, the optimal receiver becomes impractical. Hence, in this section, we shall discuss various reducedcomplexity receiver structures. 4.2.3.1 Zero-Forcing Receiver. Since a special layering structure is introduced at the transmitter in various LST designs, the receiver can exploit this layering structure to simplify the processing complexity. Figure 4.9a illustrates a linear receiver structure based on the zero-forcing (ZF) technique. At the kth receive branch, the received vector y is projected onto the orthogonal subspace spanned by vectors {h1, . . . , hk-1, hk+1, . . . , hnT} (denoted byVk). Mathematically, the projected received vector vk is given by vk = Pk y = Pk h k xk + Pk z (4.15)

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Suppose that the dimension of the orthogonal subspace Vk is dk, which is given by dk = nR - min[nR, (nT - 1)]. The projection matrix is thus a dk nR linear matrix with rows forming an orthonormal basis of Vk. For dk 1, we must have nR nT. After the zero-forcing processing, the equivalent channel between the information xk and the observation vk has the SNR given by 2 P0 Pk h k . The ergodic capacity (fast fading channels) is given by 2 nT s z