Fast Algorithms for Time Domain Broadband Adaptive Array Processing

Recursive algorithms are presented for time domain, broadband, adaptive beamforming. The algorithms are rapidly converging and can be computationally efficient for a certain range of array processor parameters. The algorithms are presented for two forms of array processor. One form is a Frost-type structure in which explicit constraints are required for defining the array-look direction and also to control the sensitivity of the array processor to implementation errors. The other form is a partitioned array processor in which constraints are built into the processor and the adaptive weight control algorithm is therefore unconstrained. The two processors presented are both element-space processors but the algorithms can be applied also to beam-space processors.     

Error Analysis of the Optimal Antenna Array Processors

The optimal weights of an antenna array processor, which maximizes the output signal-to-noise ratio (SNR) in the absence of errors, are computed using the noise-alone matrix inverse (NAMI) and the steering vector in the look direction or the signal-plus-noise matrix inverse (SPNMI) and the steering vector. In practice the estimated steering vector as well as the estimated optimal weights are corrupted by random errors. This paper has analyzed the effects of these errors on the performance of the NAMI processor and the SPNMI processor by deriving analytic expressions for the output signal power, output noise power, output SNR, and the array gain as a function of the error variance. The treatment is for a general array configuration and no assumption about a particular array geometry is made.