We highlight some issues in the design of beamformers for transmission and reception in communications systems with antenna arrays at the base stations. We assume a radio channel characterized by frequency flat Rayleighfading which is correlated (but not coherent) from antenna element to antenna element. Different design criteria are considered and we show the relationship between downlink and uplink formulations and solutions. The resulting beamformers are typically given by quadratically constrained optimization problems which could be expected to give increased robustness to signal cancellation. Unfortunately, signal cancellation is still present, but diagonal loading can be introduced to minimize the problem.