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This paper studies fixed wideband beamforming with consideration of realistic channels. There has been a perception that nice beam patterns can always be formed with advanced optimization techniques. This is mostly true if the channels are ideal. But in reality it is not always true. Indeed, achieving a desirable beam pattern with an actual beamforming system can be very difficult, and this might be responsible by the fact that the channel transfer functions are neither spectrally flat nor identical across channels. Therefore, unique issues and countermeasures have to be considered in design phase. In this paper we identify the problems and find solutions via comparison study. Performance and computational load are two major issues. New architectures with parallel processing and off-board computing engines are proposed to reduce the computational pressure as well as run time and improve the performance. Both least-square minimization and convex optimization are used to synthesize the beamformer coefficients. Performance requirements like side-lobe suppression, notch/nulling and frequency invariance have to be jointly considered. Different optimization formulations are proposed to achieve a balance among these requirements. It is found that, with the measured channel data (500-MHz bandwidth, centered at 5.25 GHz), the convexoptimization beamformer can achieve 19 dB side-lobe suppression and a 59-dB notch, but this beamformer does not always turn out a feasible and/or acceptable solution. In contrast, the leastsquare beamformer is more robust to different parameters. It also observed that frequency invariance beamforming is not a feasible requirement for a realistic wideband beamformer. Overall speaking, the convex-optimization beamformer combined with frequency-interleave (parallel processing) offers the best beamforming performance at a reduced computational cost.

Robust wideband beamforming with a real-time array testbed will be studied in this paper. For the practical consideration of uncertainty, channel impulse responses or channel transform functions of RF chains can not be obtained exactly due to the limitation of sounding and calibration procedure. Thus robust optimization will be applied to wideband beamforming. It is assumed that the uncertainty will be bounded and the worst case performance can be guaranteed by robust optimization. Finally, the optimal coefficients for a 2-dimensional filter bank to perform wideband beamforming will obtained.

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