SPACETIME CODING AND LAYERED SPACETIME CODING FOR MIMO WITH PERFECT CSI

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and modulation level adaptation. Therefore, it is important to consider adaptation design issues. Speci cally, three issues need to be addressed in designing a channeladaptive transmitter. 1. How many different adaptation modes Q are needed at the transmitter We may not want to have too many modes because of the nite overhead in the control eld needed to communicate to the receiver on the current transmission mode. 2. Given that the transmitter can support Q different encoding rate and modulation level combinations, what is the best choice of the M transmission modes in terms of encoding rate and modulation level 3. Given a current CSIT, howdoes the transmitter gure out the right transmission mode (out of the F possible modes) to use In regular SISO channels, the adaptation strategy (point 3) is relatively straightforward as the CSIT is a complex value. However, in the MIMO channels, the CSIT is a matrix and therefore, the adaptation strategy is more tricky. Furthermore, there is the issue of power allocation and precoding matrix computation across the spatial channels. In this section, we discuss a systematic design framework to address the abovementioned design issues. In addition, we focus on slow fading (quasistatic fading) channels, which is more challenging due to channel outage. 4.3.1 MIMO Transmitter and Adaptation Designs

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As illustrated in 2, the MIMO channels with perfect CSIT can be decomposed into m* = min[nT, nR] decoupled parallel channels. Hence, the adaptation design problem of the MIMO transmitter can be transformed into the adaptation design problem for m* parallel channels as follows. The received signal y of the original MIMO channels can be expressed as y = hx + z. If the channel matrix h is i.i.d., it will have full rank with probability 1. Applying SVD on h, we have h = ULV*, where U and V are nR nR and nT nT eigenvector matrices of hh* and h*h, respectively, and L is the nR nT diagonal matrix with the diagonal entries given by the eigenvalues of h. Since U and V are nonsingular, there is no loss of information if we premultiply y with U*, as follows y = U*y = Lx + z (4.32)

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where x = V*x is the nT 1 equivalent channel input vector and z = U*z is the transformed noise having the same distribution as the original noise. Figure 4.13 illustrates a generic MIMO transmitter with CSIT based on Equation (4.32). The adaptation parameters include the encoding rates rc = (rc(1), . . . , rc(nT)) (coded bits per channel use), the modulation levels

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SWITCHING THRESHOLD DESIGN FOR MIMO ADAPTATION WITH PERFECT CSIT & CSIR

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CSIT

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Equivalent channel Figure 4.13. Illustration of MIMO transmitter adaptation.

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M = (M1, . . . , MnT), and the power allocation p = (p1, . . . , pnT). For purposes of practical implementation, we can afford to have a total of only Q combinations of the encoding rate and modulation level per spatial channel. With Q transmission modes per spatial channel, we require a total of nT log2(Q) overhead control bits in the frame to indicate the transmission modes in the packet. The qth transmission mode M(q) is a collective description of the encoding rate vector rc(q) and the modulation constellation M(q). Note that if nR < nT such that m* = nR, the observations y do not contain information about the (nR + 1), . . . , (nT)th components of the equivalent-channel input vector x. Hence, the power and rate allocated to these components must be zero. For notation convenience, we assume nT nR such that m* = nT. Since the original channel matrix h is transformed to the space of nT eigenvalues L = {l1, . . . , lnT}, a general adaptation architecture of the MIMO transmitter can be speci ed by the CSIT partition {H(1), R(2), . . . , H(Q)}, where the union of the partition regions gives the entire CSIT space (containing {l1, . . . , lnT}) and the partition regions are mutually disjoint. Given a CSIT L, transmission mode M(q) is selected if L H(q). Our focus is to select the transmission modes {M(1), . . . , M(Q)} and CSIT partition {H(1), . . . , H(Q)} so as to maximize the overall throughput of the MIMO link in slow fading channels. This can be cast into an optimization problem to be elaborated in the next section.

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