MIMO Systems: Principles, Iterative Techniques, and Advanced Polarization - Adaptive Signal Processing in Wireless Communications - page 105

1

x 1

Channel
coding
C

b c s

Bit/symbol
mapping

Π STC

M T

x M T

FIgure 4.7 Block diagram of the BICM transmission scheme.

of transmit antennas. Moreover, full-rate OSTBCs exist only for a restricted number of
transmit antennas and modulations [50]. Nonorthogonal schemes, on the other hand,
offer higher coding rates, but their optimal decoder becomes prohibitively complex for a
large number of transmit antennas and large signal constellation sets. This is especially
the case for STTC schemes that, although offering high rates and good diversity gains,
are complex to decode and, moreover, suffer from long decoding delays.
For nonorthogonal schemes, instead of performing complex optimal decoding, we
may use suboptimal decoding based on simple linear-algebraic techniques such as sphere
decoding [55] or interference-cancelling-based decoding [28, 48]. For either solution,
the Rx performance can be improved considerably by performing iterative detection.

4.4.1.1 ST Coding, Tx Scheme
In addition to using a special ST scheme, we usually perform channel coding at the
Tx. Let us consider bit-interleaved coded modulation (BICM) [56] for which a typical
scheme is shown in Figure 4.7. The advantage of BICM is its flexibility regarding the
choice of the code and the bit-symbol mapping, as well as its conformity to iterative
detection. In Figure 4.7, the binary data b are encoded by a channel code C, before being
interleaved (the block Π). The output bits c are then mapped to symbols according to a
given constellation set. We will mostly consider QAM modulation with B bits per sym-
bol. Power-normalized symbols s are next combined according to a given ST scheme and
then transmitted on M T antennas.

4.4.2 General Formulation of LD Codes

Before talking about ST decoding, let us present the general formulation of the LD codes
from [54] that can be equally used for other ST schemes as well. Let S of dimension
( Q × 1) be the vector of data symbols prior to ST coding:

t

  …  

S = ss , , , s Q , (4 .11)

12

where . t denotes transposition. By ST coding, these symbols are mapped into a ( M T × T )
matrix X , where T is the number of channel uses. We define the ST coding rate as R STC =
Q / T . Corresponding to an encoded matrix X , we receive the ( M R × T ) matrix Y . We sepa-
rate the R and F parts of the entries of S and X and stack them row-wise in vectors S of
dimension (2 Q × 1) and X of dimension (2 M T T × 1), respectively. For instance,