Transmit beamforming for multiple antenna systems with imperfect feedback

Multiple antennas can effectively minimize the negative impact of multiplicative fading in wireless communication systems by providing spatial diversity. In this thesis we consider a spatial diversity scheme with multiple antennas at the base station. In order to achieve the optimum performance gains, i.e., to achieve both the array gain and the diversity gain, the transmitter needs to know channel information. In frequency division duplexing systems the channel information has to be fed back to the transmitter. This feedback requirement leads to various forms of imperfection. A typical practical system has three main sources of feedback imperfection, namely, channel estimation errors, channel quantization, and feedback delay. In this thesis we comprehensively study the impact of feedback imperfections on the performance of multi-antenna systems. We develop a general framework capturing the three forms of feedback imperfection, i.e., estimation errors, quantization, and delay, for both spatially independent and correlated fading scenarios. In the modeling of imperfect feedback, we show that depending on the beamforming vector construction, the feedback delay error term can be known or unknown at the receiver. On the other hand, channel estimation error term is always unknown at the receiver. In a slow fading context, i.e., in scenarios where channel remains constant for the entire packet, we highlight the fact that both the estimation error term and the delay error term remain constant, with estimation error term unknown at the receiver and delay error term known at the receiver, for the entire packet while the thermal noise changes from symbol-to-symbol. For spatially independent channels, with the help of general framework, we then analytically quantify the effect of the three forms of feedback imperfection on the symbol and bit error probabilities of both M-PSK and M-ary rectangular QAM constellations with Gray code mapping. We also derive an analytical expression for the average packet error probability with BPSK signaling. In addition, with channel estimation errors and feedback delay, for spatially correlated channels, we develop codebook design algorithms specific to the modulation format and ergodic capacity. The new optimum codebooks show an improvement in performance compared to the existing set of codebooks available in the literature. Utilizing high resolution quantization theory and assuming perfect channel estimation at the receiver, we analyze the loss in average symbol error probability for spatially independent and correlated finite-rate feedback transmit beamforming multiple input single output systems with M1xM2-QAM constellation. We also address the issue of minimizing the negative impact of feedback delay. A natural way to combat the effect of feedback delay is channel prediction. We study the role of ergodicity in wireless channel modeling and provide an insight into when statistical channel models that employ ensemble averaging are appropriate for the purpose of channel prediction. Simulation results complement the extensive set of analytical expressions derived in the thesi