Lal C. Godara

Uniqueness and linear independence of steering vectors in array space

The study of array processing often involves the manipulation of steering vectors defined in array space. The question of uniqueness and linear independence of steering vectors often arises in the analysis of array processing algorithms and in their formulation. The paper examines the effect of array geometry on the mapping between directions in three‐dimensional space and steering vectors in array space. Conditions on array geometry for uniqueness and linear independence of steering vectors are established for linear, planar, and general arrays.

Application of the fast Fourier transform to broadband beamforming

The processing of broadband signals using an array of sensors is normally carried out in a time domain using a tapped delay line filter or in a frequency domain where each frequency channel is weighed by complex weights and no tapped delay line filter is required. The time domain implementation of the broadband structure is important in the area of communication where the frequency domain implementation may not be suitable due to its associated delay. This paper derives relationships between the weights, the array correlation matrices, and the constraints on the weights of the two structures to produce identical results. These relationships are then used to update the weights of the tapped delay line filter structure using narrow‐band techniques. The method has potential for computational saving to estimate weights of the broadband structure, for a large bandwidth signal requiring a long tapped delay line filter.

Postbeamformer interference canceler with improved performance

A postbeamformer interference canceler (PIC) processes the signals derived from an antenna array by forming two beams using fixed beamforming weights. The weighted output of one beam, referred to as the interference beam, is subtracted from the other beam, referred to as the target beam. In a conventional beamforming method, both beams are formed using equal weighting on each element. For this case the PIC processor suppresses a substantial amount of the signal; its output contains a large amount of residual interference when the weight of the interference channel is adjusted to minimize the mean output power of the PIC. This article presents and analyzes two methods to reduce the signal suppression by the PIC. The analysis shows that in one case the signal suppression has been completely eliminated, while in the second case the output of the PIC does not contain any residual interference. The examples presented show that the output signal to noise ratio (SNR) of the PIC using these beamforming methods is...

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.

Performance of a postbeamformer interference canceller in the presence of broadband directional signals

A Postbeamformer Interference Canceller, PIC, is essentially a single‐channel noise canceller. Two beams are formed; one in the target direction and another in the interference direction. The interference direction beam is processed with a tapped delay filter before being subtracted from the target beam to yield the system output. A detailed analysis of PIC is presented in the paper. The performance which can be achieved with PIC is shown to depend critically on the input signal to interference ratio and the tapped delay line length.

The effect of bandwidth on the performance of a postbeamformer interference canceller

A postbeamformer interference canceller, PIC, processes the signals derived from an antenna array by forming two beams using fixed beamforming weights. The weighted output of one beam, referred to as the interference beam, is subtracted from the other beam referred to as the target beam. This paper analyzes the performance of PIC in the presence of narrow‐band directional interference by deriving the analytical expressions for the output signal power, the output interference power, and the output signal to interference ratio, and presents the results of a computer study showing how the performance of PIC varies as a function of bandwidth of the directional sources.

Adaptive postbeamformer interference canceler with improved performance in the presence of broadband directional sources

A postbeamformer interference canceler (PIC) is a beam space processor that processes the signals derived from an antenna array by forming two beams using fixed beamforming weights. One beam, referred to as the signal beam, is formed to have a fixed response in the known signal direction. The processed output of the second beam, referred to as the interference beam, is subtracted from the output of the signal beam to form the output of the PIC. In the presence of broadband directional sources, the formation of a beam is usually carried out by a set of steering delays followed by a weight and sum network. For this case, the processing of the interference beam output is carried out by a tapped delay line filter. When the two beams of the PIC are formed using conventional weights and the tapped delay line filter weights are adjusted to minimize the mean output power of the PIC, a substantial amount of the signal gets suppressed. It is due to the presence of signal component in the interference channel. This ...

Detection of weak stochastic signals in double-sided exponential noise using generalized energy detector

Many locally optimum, suboptimum, and ad hoc detectors exploit knowledge of the noise probability density function (pdf) to obtain their test statistic for the detection of stochastic signals in non‐Gaussian noise. These detectors appear to offer potential for highly improved performance for very small signal to noise ratios (asymptotically approaching zero). This paper studies a locally optimum detector namely the generalized energy detector, by deriving analytical expressions for a performance measure using a double‐sided exponential noise pdf. The paper concludes that the apparently large gains predicted by the asymptotic theory may not be reachable within the practical range of signal‐to‐noise ratios.

Adaptive beamforming in the presence of correlated arrivals

The constrained least-mean-square (LMS) algorithm updates the weights of an antenna array by estimating the gradient of the mean output power surface. In its standard form an estimate of the required gradient is made by multiplying the array output with the sensor outputs. This form of LMS algorithm is not suitable for updating the weights in the presence of correlated arrivals. The correlation between the desired signal and an unwanted interference may exist in situations of multipath and deliberate jamming. This paper investigates the performance of two algorithms, namely, the structured gradient algorithm and the improved LMS algorithm, in the presence of correlated narrow-band arrivals. Theoretical analysis and computer simulation are presented to demonstrate the capability of these algorithms to estimate the weights of a linear array of equispaced elements, to cancel the correlated directional sources.

Analysis of transient and steady‐state weight covariance in an adaptive postbeamformer interference canceler

A postbeamformer interference canceler (PIC) processes the signals derived from an antenna array by forming two beams using fixed beamforming weights. The weighted output of one beam, referred to as the interference beam, is subtracted from the other beam, referred to as the target beam. This article analyzes an algorithm to adjust the complex weight of the interference channel iteratively, studies the transient and steady‐state behavior of the weight covariance, and derives the exact expression for the misadjustment.