Diversity analysis of single and multiple beamforming

In this letter, we study two techniques, known as single and multiple beamforming, to exploit the perfect channel state information (CSI) available both at the transmitter and the receiver of a multiantenna wireless system. Assuming N and M are the number of antennas at the transmitter and the receiver, respectively, we show that single beamforming (transmission of a single symbol from all transmit antennas at the same time, employing the best subchannel) can achieve the maximum spatial diversity order in the channel (NM). We extend our analytical results to multiple beamforming (transmission of S symbols simultaneously, S > 1) and calculate that the diversity order achievable for this system is (N - S + 1)(M - S + 1). Index Terms--Beamforming, diversity, multi-input multi-output (MIMO) systems, pairwise error probability (PEP).