Beamforming is a fundamental technique in array signal processing. Many existing approaches are based on second-order statistics. However, their performance degrades significantly due to outliers in the received signal. In this letter, we propose an outlier-resistant beamformer design criterion based on minimizing the expectation of the modulus of the array output with an${\ell _1}$-regularization term being added for sidelobe suppression. By using the${\ell _1}$-modulus of complex numbers instead of the standard modulus, the resulting optimization problem can be efficiently solved by a simple iterative algorithm or linear programming. Simulation results in the presence of impulsive signals are provided to demonstrate its robustness and accuracy compared to existing techniques.

This paper is concerned with communication over a multiple-input multiple-output channel. In the first reference, a lower bound on the bit-error rate of a pre- and postequalized communication system was derived for uniform bit loading. Here, we extend the lower bound to nonuniform bit loading. The lower bound applies to communication systems for which: 1) the cascade of the pre-equalizer, (noise-free) channel, and postequalizer is a diagonal matrix (a generalized zero-forcing condition satisfied by many designs in the literature); and 2) the encoding/modulation (decoding/demodulation) is done independently over the dimensions of the pre-equalizer input (postequalizer output). The lower bound is stated as a function of the bit loading, channel, and transmitter power only, and applies to uncoded, as well as coset-coded, systems. Toward deriving the lower bound, we minimize a weighted average of the noise variances at the postequalizer output.