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...

M receiver antennas receive M signals each represented as:

r_m = α_ms + η_m,

where η_m is a white Gaussian noise sample added to the mth copy of the signal. A maximum-likelihood (ML) decoder combines these M received signals to find the most likely transmitted signal.We consider a coherent detection scheme where the receiver knows the channel path gains, α_m. 

Owing to its array gain, MRC typically achieves a few dB better SNR than does SC.

The source of diversity does not affect the method of combination with the exception of transmit antenna diversity. For example, receiving two versions of the transmitted signal through polarization diversity is the same as receiving two signals from two receive antennas for the purpose of combining

 There are two main combining methods that are utilized at the receiver:

•  Maximum Ratio Combining (MRC)
  
• Selection Combining
  

Probability Error for Diversity

P= c₁e^-c2 γ

γ –snr

in fading without diversity

In fading with diversity of N_txN_r=N_d

Probability Error for Array Gain

The replica of the transmitted signal can be sent through different means [99]. For example, it can be transmitted in a different time slot, a different frequency, a different polarization, or a different antenna. The goal is to send two or more copies of the signal through independent fades. Then, since it is less likely to have all the independent paths in deep fades, using appropriate combining methods, the probability of error will be lower.

•  Time slot – repetition
  
• Frequency – fdd
  
• Pol...

The main idea behind “diversity” is to provide different replicas of the transmitted signal to the receiver. If these different replicas fade independently, it is less probable to have all copies of the transmitted signal in deep fade simultaneously. Therefore, the receiver can reliably decode the transmitted signal using these received signals. This can be done, for example, by picking the signal with the highest SNR or by combining the multiple received signals. As a result, the probabi...