1. The problem statement, all variables and given/known data Base station transmits signal t which is received by two antennas such that: x = h1t + n1 y = h2t + n2 where n1 and n2 are independent additive white Gaussian noise with variances σ21 and σ22 respectively. h1 is the channel gain between the base station and receive antenna 1 and h2 is the gain between the base station and receive antenna 2. The receive terminal combines the signals x and y as follows: z = αx + βy Find the optimal values of α and β. What is the resulting SNR of z? How does this compare to the SNR of x and y? 2. Relevant equations The only hint given was that k = α/β and that SNRz = f(k) 3. The attempt at a solution I have tried finding the power of each signal since the variance is the power of the noise, and then trying to find a ratio of α/β to give a constant which should allow α and β to be adjusted to find the optimal values. However I haven't come to a solution that actually expresses SNR of z, x or y. Some of the calculations I have made are lengthy and don't arrive at a solution, but I could upload them if you wish. Any help or pointers would be greatly appreciated.