Distributed collaborative beamforming designs for real-world applications in relayed and cooperative communications

Three main distributed collaborative beamforming (DCB) designs based on different channel models could be employed in real-world applications where scattering and implementation imperfections might exist: the monochromatic (i.e., single-ray) DCB (M-DCB), the bichromatic (i.e., two-ray) DCB (B-DCB), and the polychormatic (i.e., multi-ray) DCB (P-DCB). In this paper, we perform an analytical comparison, under practical constraints, between these DCB designs in terms of achieved signal-to-noise ratio (SNR) as well as achieved throughput. Assuming the presence of scattering and accounting for implementation errors incurred by each DCB design, we derive closed-form expressions of their true achieved SNRs. Excluding exceptional circumstances of unrealistic low quantization levels (i.e., very large quantization errors) hard to justify in practice, we show that B-DCB always outperforms M-DCB as recently found nominally in ideal conditions. We also show that for low AS B-DCB and P-DCB achieve almost the same SNR while for high AS the latter outperforms the first. Furthermore, this work pushes the performance analysis of DCB to the throughput level by taking into account the feedback overhead cost incurred by each design. We prove both by concordant analysis and simulations that the P-DCB's throughput gain against B-DCB reduces as the channel Doppler frequency increases.