Adaptive Array Behavior with Sinusoidal Envelope Modulated Interference

The behavior of a LMS (least mean square) adaptive array with modulated interference is described. An interference signal with sinusoidal, double-sideband, suppressed-carrier modulation is assumed. It is shown that such interference causes the array to modulate the desired signal envelope but not its phase. The amount of the desired signal modulation is determined as a function of signal arrival angles and powers and the modulation frequency of the interference. Such interference also causes the array output signal-to-interference-plus-noise ratio (SINR) to vary with time. However, it is shown that when the desired signal is a digital communication signal, the averaged bit error probability is essentially the same as for continuous wave (CW) interference.     

Adaptive Array Behavior with Periodic Envelope Modulated Interference

A method is presented for determining the effects of envelope modulated interference on a least mean square (LMS) adaptive array. The interference is assumed to have periodic envelope modulation with a bandwidth that is small compared with the carrier frequency. For such interference, the method allows one to calculate the periodic steady-state behavior of the array weights and the resulting array performance. As an example, we compute the effects of an ordinary amplitude modulated (AM) interference signal on the array. It is shown that such interference causes the array to modulate the desired signal envelope but not its phase. With a differential phase-shift-keyed (DPSK) desired signal, AM interference is found to have about the same effect on bit error probability as CW interference.     

Adaptive Array Behavior with Periodic Phase Modulated Interference

We consider a least mean square (LMS) adaptive array [1] receiving a phase modulated interference signal. The phase modulation is assumed to be periodic and to have finite bandwidth. Under these assumptions, we determine the time-varying array weights, the modulation on the array output desired signal, and the time-varying output interference-to-noise ratio (INR) and SINR (signal-to-interference-plus-noise ratio). We present numerical results describing the behavior of a 2-element adaptive array that receives an interference signal with sinusoidal phase modulation. We show how each signal parameter (arrival angle, power, modulation index, and modulation frequency) affects the performance of the array.