The goal of space-time coding is to achieve the maximum diversity of NM, the maximum coding gain, and the highest possible throughput. In addition, the decoding complexity is very important.

Alamouti code

N = 2 M = 1

To transmit b bits/cycle, we use a modulation scheme that maps every b bits to one symbol from a constellation with 2bsymbols

First, the transmitter picks two symbols from the constellation using a block of 2b bits. If s1 and s2 are the selected symbols for a block of 2b bits, the transmitter sends s1 from antenna one and s2 from antenna two at time one. Then at time two, it transmits −s∗2 and s∗1 from antennas one and two,

Respectively



Design Criterion

Codes C1, C2

A(C1,C2) = D(C1,C2)H · D(C1,C2) = (C2 − C1)H · (C2 − C1)

For any two codewordsCi = Cj , the rank criterion suggests that the error matrix D(Ci,Cj ) = Cj − Ci has to be full rank for all i = jin order to obtain full diversity NM. The determinant criterion says that the minimum determinant of A(Ci,Cj ) = D(Ci,Cj )H D(Ci,Cj ) among all i = j has to be large to obtain high coding gains. The determinant of the difference matrix det[D(C,C_)] = |s’1−s1|2 + |s’2− s2|2 is zero if and only if s’1 = s1 and s’2 = s2. Therefore, D(C,C_) is always full rank when C’ = C and the Alamouti code satisfies the determinant criterion. It provides a diversity of 2M for M receive antennas and therefore is a full diversity code.