The Distribution of the Bit Error Rate for an M Branch Antenna with N Interferers

Given an antenna with M branches, the bit error rate (BER) and mean squared error (MSE) for choosing the antenna weights (to approximately cancel M − 1 interferers), are given by $$ \mathit{BER} \approx C \;\exp \left(-\alpha-\alpha Z_N\right) \mbox{ and } \mathit{MSE}=1/\left(1+Z_N\right), $$ where Z N is the signal-to-interference plus noise ratio and C, α are some fixed parameters. So, obtaining the distribution of Z N allows one to obtain the distribution of the MSE and to approximate that of the BER. Three cases are presented: the case of fixed powers for the interferers, say Q 1, ..., Q N , and for the wanted signal, say Q 0; the case of fixed power for the wanted signal and random powers for the interferers; the case of random powers for both the wanted signal and the interferers. We assume that Q 0,...,Q N are independent with different distributions. We show that to magnitude 1/N, the distribution of Z is just that of Q 0 g M /T, where g M is a gamma random variable with mean M and T is the average of the total interferer power: $$ T = \mathbb{E} \ \left\{ \sum\limits_{j=1}^N Q_j\right\}. $$ We also show how to obtain an expansion in powers of 1/N for the distribution of $\mathit{TZ}$ about that of Q 0 g M . For example, to get the distribution of $\mathit{TZ}$ up to magnitude 1/N 2, one requires only the means of Q 1,...,Q N and $Q_1^2,\ldots,Q_N^2$ and the distribution of Q 0.