The Effect of a Pulsed Interference Signal on an Adaptive Array

The performance of a least mean square (LMS) adaptive array in the presence of a pulsed interference signal is examined. It is shown that a pulsed interference signal has two effects. First, it causes the array to modulate the desired signal envelope (but not its phase). Second, it causes the array output signal-to-interferenceplus-noise ratio (SINR) to vary with time. The desired signal modulation is evaluated as a function of signal arrival angles, powers and interference pulse-repetition frequency (PRF) and pulsewidth. It is shown that the signal modulation is small except when the interference arrives close to the desired signal. To evaluate the effect of the time-varying SINR, it is assumed that the array is used in a differential phase-shift keyed (DPSK) communication system. It is shown that the SINR variation causes a noticeable but not disastrous increase in the bit error probability.     

Adaptive Array Bandwidth with Tapped Delay-Line Processing

The bandwidth of adaptive arrays with tapped delay lines behind the elements is examined. Such processing offers improved bandw over that attainable with quadrature hybrid processing. The performance of a two-element array with four types of processing (equarature hybrids, single delay lines, 3-tap delay lines, and 5-tap delay lines) is compared. It is shown that with half-wavelength element spacing, a quadrature hybrid and single delay-line processor are inadequate at 10-percent bandwidth. A 3-tap processor is adeq however, up to 40-percent bandwidth.     

Improved Feedback Loop for Adaptive Arrays

This paper is concerned with the problem of time constants in adaptive arrays. The paper presents a improved form of an adaptive array feedback loop, which has the property that its time constants are fixed. This property is an advantage over the well-known least mean square (LMS) loop, for which time constants depend on received signal power. Fixed time constants are of interest because they simplify dynamic range problems for adaptive arrays in communication and radar systems.     

The Effect of Differential Time Delays in the LMS Feedback Loop

The effect of differential time delay in the feedback loops of an LMS adaptive array is examined. Differential time delay is shown to have two effects on array performance. First, it causes the weights to oscillate during weight transients. Second, it degrades the output signal-to-interference-plus-noise ratio (SINR) from the array. Weight oscillation occurs when the phase shifts in the LMS loop are not matched at the signal carrier frequency. SINR degradation depends on signal bandwidth: the wider the bandwidth, the larger the degradation.     

The Effect of Random Steering Vector Errors in the Applebaum Adaptive Array

The effect of random errors in the steering vector of an Applebaum adaptive array is examined. Each component of the steering vector is assumed to have a random error component uncorrelated between elements. The array output signal-to-interferenceplus-noise ratio (SINR) is computed as a function of the error variance. It is shown that the array output SINR becomes more sensitive to steering vector errors as more elements are added to the array and as the received desired signal power becomes larger. The variance of the steering vector error that may be tolerated depends on the required desired signal dynamic range. The larger the dynamic range that must be accommodated, the smaller the error variance must be.     

Angle and polarization estimation in a coherent signal environment

It is shown how a uniform linear array of crossed dipoles may be used with the ESPRIT algorithm and spatial smoothing techniques to estimate the arrival directions and polarizations of incoming coherent plane waves. Some examples showing typical performance are presented. One method of smoothing can be used where it is necessary to estimate both the arrival angles and polarizations of signals. Two other methods can be used when only the arrival angles are of interest     

Reference Loop Phase Shift in Adaptive Arrays

Adaptive arrays for use in communication systems require the generation of a so-called reference signal, which is usually derived from the array output. A particular problem associated with this technique, the problem of reference loop phase shift, is discussed. It is shown that phase shift in the reference loop causes the array weights to cycle, and also causes the array to frequency-modulate the signal. In spite of this frequency change, the array maintains a maximum SNR at the output.     

Multiplier Offset Voltages in Adaptive Arrays

The effects of multiplier offset voltages in adaptive arrays are examined. Multiplier offset voltages arise when active circuits are used to implement the error-by-signal multipliers required in an array based on the LMS algorithm. These offset voltages are known from experimental work to have a strong effect on array performance. It is first shown how multiplier offset voltages may be included in the differential equations for the array weights. Then their effect on weight behavior is studied. It is found that the offset voltages affect the final values of the weights, but not the time constants. Furthermore, the effect they have is influenced by the amount of element noise in the array. An adequate amount of noise is necessary to minimize weight errors due to offset voltages. An example is treated to show the effect of offset voltages on the final array weights and the output signal-to-noise ratio (SNR). With offset voltages present, it is found that there is a maximum SNR that can be obtained from the array. A specific input SNR is required to obtain this maximum output SNR. Finally, it is shown that a finite operating range for the weights places a further restriction on the acceptable values of offset voltages and noise.     

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.     

Pointing Accuracy and Dynamic Range in a Steered Beam Adaptive Array

The performance of a steered beam adaptive array as a function of the beam pointing error is examined. The purpose is to determine how close the steered beam has to be to the actual desired signal arrival angle for good performance. It is shown that the beam pointing error that can be tolerated is essentially a question of dynamic range. The greater the desired signal dynamic range that must be accommodated by the array, the more accurate the beam pointing angle must be.