Paul C. Wei

Adaptive tracking of linear time-variant systems by extended RLS algorithms

We exploit the one-to-one correspondences between the recursive least-squares (RLS) and Kalman variables to formulate extended forms of the RLS algorithm. Two particular forms of the extended RLS algorithm are considered: one pertaining to a system identification problem and the other pertaining to the tracking of a chirped sinusoid in additive noise. For both of these applications, experiments are presented that demonstrate the tracking superiority of the extended RLS algorithms compared with the standard RLS and least-mean-squares (LMS) algorithms.

Adaptive interference suppression for CDMA overlay systems

It has been proposed that CDMA systems can be assigned to spectral bands which are presently occupied by narrowband users to further increase spectral capacity. Such CDMA overlay systems could provide new options for efficient utilization of the spectrum with minimal disruption to existing narrowband users, especially if adaptive interference suppression techniques are utilized in the spread spectrum receiver. Previous studies have defined the SNR improvement ratio which can be achieved for tone interferers and for narrowband interferers for which the center frequency of the interference is at the carrier frequency of the CDMA signal. In this paper the bit-error-rate (BER) performance of the mobile-to-base link of a CDMA system for a single narrowband user which occupies a significant portion of the CDMA bandwidth is evaluated. It is shown that the narrowband model used in previous studies does not apply in this case, especially for the large, effective, bandwidths which are characteristic of the interferers in the overlay system. The dependence of the BER on the filter order, the bandwidth of the interference, and its center frequency relative to the CDMA carrier frequency are defined. Additionally the increase in BER for a digital implementation of the adaptive suppression filter relative to the optimal Wiener filter is characterized with respect to the adaptive time constant and the quantization errors due to finite wordlength. It is shown that these implementation errors can be made negligible compared to the errors which are characteristic of the optimal Wiener filter. Analytic results are validated by simulation for typical system parameters. >

Comparative tracking performance of the LMS and RLS algorithms for chirped narrowband signal recovery

This paper studies the comparative tracking performance of the recursive least squares (RLS) and least mean square (LMS) algorithms for time-varying inputs, specifically for linearly chirped narrowband input signals in additive white Gaussian noise. It is shown that the structural differences in the implementation of the LMS and RLS weight updates produce regions where the LMS performance exceeds that of the RLS and other regions where the converse occurs. These regions are shown to be a function of the signal bandwidth and signal-to-noise ratio (SNR). LMS is shown to place a notch in the signal band of the mean lag filter, thus reducing the lag error and improving the tracking performance. For the chirped signal, it is shown that this produces smaller tracking error for small SNR. For high SNR, there is a region of signal bandwidth for which RLS will provide lower error than LMS, but even for these high SNR inputs, LMS always provides superior performance for very narrowband signals.

Analysis of multiframe target detection using pixel statistics

Current track-before-detect (TBD) algorithms are developed and analyzed using a path statistic for each potential object trajectory. However this path statistic does not characterize overall performance gain. We propose a pixel-based statistic. This allows the TBD approach to be characterized as an image enhancement algorithm with detection gains compared with single frame detections. It is shown that for the TBD approach to have superior detection over single frame detection the target signal-to-noise ratio (SNR) must be greater than a threshold SNR in order to overcome the uncertainty in the target path. Tradeoffs are made for a class of velocity constrained target paths in terms of the detection gain with respect to the maximum target velocity and number of frames integrated. >

Adaptive recovery of a chirped signal using the RLS algorithm

This paper studies the performance of the recursive least squares (RLS) algorithm in the presence of a general chirped signal and additive white noise. The chirped signal, which is a moving average (MA) signal deterministically shifted in frequency at rate /spl psi/, can be used to model a frequency shift in a received signal. General expressions for the optimum Wiener-Hopf coefficients, one-step recovery and estimation errors, noise and lag misadjustments, and the optimum adaptation constant (/spl beta//sub opt/) are found in terms of the parameters of the stationary MA signal. The output misadjustment is shown to be composed of a noise (/spl xi//sub 0/M/spl beta//2) and lag term (/spl kappa//(/spl beta//sup 2//spl psi//sup 2/)), and the optimum adaptation constant is proportional to the chirp rate as /spl psi//sup 2/3/. The special case of a chirped first-order autoregressive (AR1) process with correlation (/spl alpha/) is used to illustrate the effect the bandwidth (1//spl alpha/) of the chirped signal on the adaptation parameters. It is shown that unlike for the chirped tone, where the /spl beta//sub opt/ increases with the filter length (M), the adaptation constant reaches a maximum for M near the inverse of the signal correlation (1//spl alpha/). Furthermore, there is an optimum filter length for tracking the chirped signal and this length is less than (1//spl alpha/).

Tracking of linear time-variant systems

In this paper we exploit the one-to-one correspondences between the recursive least-squares (RLS) and Kalman variables to formulate extended forms of the RLS algorithm. Two particular forms are considered, one pertaining to a system identification problem and the other to the tracking of a chirped sinusoid in additive noise. For both applications, experiments are presented that demonstrate the tracking optimality of the extended RLS algorithms, compared with the standard RLS and least-mean-squares (LMS) algorithms.

Adaptive interference suppression for CDMA based PCN systems

A number of different techniques for the suppression of narrowband interference due to overlay in code division multiple access (CDMA) systems have previously been studied. The relative performances of three such techniques for a fading channel, multi-user CDMA system are described. Personal communication network systems using suppression filters based on the transversal least mean square (LMS) and the lattice and transform domain algorithms are studied. Bit error rates are found by simulations for different suppression filters. The overlay signal is assumed to be narrowband binary phase shift keying (BPSK) and the performance of these systems is studied for varying BPSK carrier frequency offsets. Since both the lattice and LMS filters converge to the Wiener filter, their relative performance is also studied during the on/off transient of the interference. It is found that the LMS and recursive least square (RLS) perform similarly under stationary interference. The RLS is less susceptible to changes in the interference due to its faster convergence.<<ETX>>

Characterization of the performance of the track-before-detect approach to moving target detection

In the pursuit of detecting ever smaller and dimmer targets, the track-before-detect methodology has been used to integrate the target energy through a time sequence of frames. However, when target tracking is required, an additional uncertainty over detection of a stationary target is introduced. This loss is characterized by the use of a detector optimum for Gaussian white noise for point targets constrained only by its maximum velocity (V). The authors characterize the gains and losses associated with the input target SNR, the number of frames integrated, and the uncertainty introduced by target movement constrained by a maximum velocity V, by comparison of the ratio of the SNR with respect to the SNR of single frame detection and known-target-path detection techniques.<<ETX>>

Target detection from image sequences using pixel-based decision criterion

In the pursuit of detecting ever smaller and dimmer object the track-before-detect methodology has been employed to integrate the target energy through a time sequence of frames. Current track-before-detect algorithms maintain a path statistic for each potential object trajectory. This set of trajectories is usually trimmed to keep the number of statistics manageable, and it becomes difficult to characterize the performance of the detector. In this paper we propose a pixel based statistic rather than a path based statistic and use it in a track-before-detect algorithm for a class of trajectories constrained only by a maximum target velocity.

Adaptive recovery of a Doppler shifted mobile communications signal using the RLS algorithm

This paper studies the ability of the exponentially weighted RLS algorithm to track a Doppler shifted BPSK communications signal. This is modeled as a chirped AR1 process in Gaussian white noise. Expressions for the optimum Wiener filter, noise misadjustment, and lag misadjustment are shown. It is shown that as in the chirped sinusoid case the error can be written in terms of the forgetting rate /spl beta/=1-/spl lambda/ of the RLS algorithm; the noise misadjustment is of the order /spl beta/ and lag misadjustment of order 1//spl beta//sup 2/. However, as the bandwidth of the signal increases the relative lag misadjustment is shown to decrease.<<ETX>>