Analysis of collaborative beamforming designs in real-world environments

Three main collaborative beamforming (CB) designs based on different channel models could be applied in real-world environments where local scattering and implementation imperfections might exist: the optimal CSI-based CB (OCB), the conventional or monochromatic (i.e., single-ray) distributed CB (M-DCB), and the recently developed bichromatic (i.e., two-ray) distributed CB (B-DCB). In this paper, we perform an analytical comparison, under practical constraints, between these CB designs in terms of achieved signal-to-noise ratio (SNR) as well as achieved throughput. Assuming the presence of local scattering in the source vicinity and accounting for implementation errors incurred by each CB design, we derive for the first time closed-form expressions of their true achieved SNRs. At a low angular spread (AS) where both designs nominally achieve the same SNR in ideal conditions, we show that the B-DCB always outperforms OCB, more so and at larger regions of AS values when errors increase. Excluding exceptional circumstances of unrealistic low quantization levels (i.e., very large quantization errors) hard to justify in practice, we also show that the new B-DCB always outperforms the M-DCB as recently found nominally in ideal conditions. This work is also the first to push the performance analysis of CB 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 B-DCB is able to outperform, even for high AS values, the OCB which is penalized by its prohibitive implementation overhead, especially for a large number of collaborating terminals and/or high Doppler frequencies.