BER Analysis for Distributed Beamforming With Phase Errors

The probability of error for distributed transmit beamforming with phase errors is not available in closed form in the literature. This paper presents an investigation into the bit error ratio (BER) of distributed transmit beamforming with phase errors for equal power transmission in wireless sensor networks. We derive two distinct formulas to approximate the error probability performance for binary phase-shift keying (BPSK) over Rayleigh fading channels that correspond to small numbers of nodes (e.g., N ≤ 10) and large numbers of nodes (e.g., N ≥ 20), respectively. Simulation results show a good match with the analytical results. The effects of the phase errors on the beamforming performance are examined for various numbers of nodes and different levels of total transmit power.