Diversity Analysis of a Randomized Distributed Space-Time Coding in an Amplify and Forward Relay Channel

This paper considers a cooperative communications system where a single relay aids a point-to-point transmission using an amplify and forward configuration. The relay linearly encodes the K received symbols into N new ones by means of a matrix multiplication, and the destination employs a LMMSE filter to estimate the information originally transmitted. A large- SNR approximation of the outage probability P_out is derived for this system. The analysis of P_out shows that the diversity order of the system depends on the ratio K/N: if such a ratio is too high (the relay excessively compresses the information), no diversity is added by introducing the relay. Conversely, if this ratio is smaller than a certain quantity, diversity order 2 is ensured. The derived expressions are finally used to establish the diversity-multiplexing tradeoff of the system.