Simplified Gram-Schmidt preprocessor for broadband tapped delay-line adaptive array

The author derives a simplified Gram-Schmidt preprocessor for decorrelating the signals in a broadband tapped delay-line adaptive array. After studying the structure of the covariance matrix at a small bandwidth, a two-stage preprocessing structure is proposed. The first stage of preprocessing is independent of the external noise environment, and thus can be designed a priori and can be easily implemented. The second stage of preprocessing employs a normal Gram-Schmidt preprocessor whose order is only 2M for an M-element L-tap array with ML array signals. Thus, in terms of the number of 2-input adaptive decorrelators needed, the simplified preprocessor is less complex than using the Gram-Schmidt procedure directly by a factor of about (L/2)². Also, it will converge faster by a factor of roughly L/2. Finally, although the simplified preprocessor is derived assuming a small bandwidth, simulation results show that it is effective up to bandwidths of the order of 10%.