Monika Agrawal

Broadband DOA estimation using "Spatial-Only" modeling of array data

Most of the existing techniques for DOA estimation of broadband sources use both spatial and temporal modeling. This may lead to increased complexity besides a large algorithmic delay. We propose a technique that employs only spatial information in the form of a single spatial array covariance matrix. Assuming the source to have an ideal bandpass power spectral density, we formulate two subspace-based search functions for the estimation of the DOAs of broadband sources. One of these employs a multidimensional search in the parameter space, whereas the other requires a MUSIC like one-dimensional (1-D) search. The multidimensional cost function is shown to be consistent, yields performance close to the Cramer-Rao (CR) bound, and is insensitive to correlation between sources. Both the proposed methods are shown to be robust to deviations from the assumption of ideal bandpass power spectral density used in their formulation.

A modified likelihood function approach to DOA estimation in the presence of unknown spatially correlated Gaussian noise using a uniform linear array

The problem of modified ML estimation of DOAs of multiple source signals incident on a uniform linear array (ULA) in the presence of unknown spatially correlated Gaussian noise is addressed here. Unlike previous work, the proposed method does not impose any structural constraints or parameterization of the signal and noise covariances. It is shown that the characterization suggested here provides a very convenient framework for obtaining an intuitively appealing estimate of the unknown noise covariance matrix via a suitable projection of the observed covariance matrix onto a subspace that is orthogonal complement of the so-called signal subspace. This leads to a formulation of an expression for a so-called modified likelihood function, which can be maximized to obtain the unknown DOAs. For the case of an arbitrary array geometry, this function has explicit dependence on the unknown noise covariance matrix. This explicit dependence can be avoided for the special case of a uniform linear array by using a simple polynomial characterization of the latter. A simple approximate version of this function is then developed that can be maximized via the-well-known IQML algorithm or its variants. An exact estimate based on the maximization of the modified likelihood function is obtained by using nonlinear optimization techniques where the approximate estimates are used for initialization. The proposed estimator is shown to outperform the MAP estimator of Reilly et al. (1992). Extensive simulations have been carried out to show the validity of the proposed algorithm and to compare it with some previous solutions.

DOA estimation of wideband sources using a harmonic source model and uniform linear array

We consider the problem of estimation of the DOAs of multiple wideband sources incident on a uniform linear array (ULA) in the presence of spatially and temporally white Gaussian noise (WGN). The approach presented builds up on the IQML algorithm suggested by Bresler and Macovski (1986) for the case of narrowband DOA estimation. It is shown that the concept of an ARMA model for the observed data vector for the narrowband case can be generalized to model an appropriately stacked, space-time data vector obtained by combining the space-time samples. The coefficients of the corresponding 2-D predictor polynomial can be used to represent the null subspace of the wideband array steering matrix, and rooting of the polynomial at each frequency, separately, gives the DOA estimates. These separate estimates at multiple frequencies are combined into a single DOA estimate in a least squares sense. This leads to the formulation of an IQML like procedure for the spatial parameter estimation of wideband sources. Like its narrowband counterpart, the proposed approach is applicable to both noncoherent and coherent sources. The performance of the proposed method is studied via extensive computer simulations and by comparison with the Cramer-Rao bounds.

Robust adaptive beamforming for wide-band, moving, and coherent jammers via uniform linear arrays

The problem of providing robustness to the conventional narrow-band uniform linear array configuration so as to handle wide-band and moving jammers is addressed. This robustness is achieved via the use of derivative constraints in jammer directions. However, since the jammer directions are not known a priori, these constraints are incorporated with a maximum likelihood characterization of the so-called jammer subspace. This formulation does not need to assume the availability of signal-free observations, as stipulated in earlier work. Computer simulation results are presented, which show that the algorithms proposed here yield significantly better performance as compared to the previous algorithms of Gershman et al. (see ibid., vol.44, p.361-6, 1996, and IEEE Trans. Signal Processing, vol.45, p.1878-85, 1997) and Hung and Turner (1983) in a variety of situations required to handle wide-band, moving, and coherent jammers.

SER analysis of PTS based techniques for PAPR reduction in OFDM systems

A major drawback of orthogonal frequency division multiplexing (OFDM) is high peak-to-average power ratio (PAPR). An OFDM signal with high PAPR requires power amplifier@?s (PAs) with large linear operating ranges but such PAs are difficult to design and costly to manufacture. Therefore, to reduce PAPR various methods have been proposed. One of the existing technique to reduce PAPR is partial transmit sequences (PTS). The major drawback of this technique is that it requires transmission of side information (SI) with each OFDM symbol, which results in low bandwidth efficiency. It is hard to recover the side information from the OFDM signal received at the receiver. The two methods, which do not require SI to decode the OFDM symbol at the receiver, are multi-point square mapping combined with PTS (M-PTS) and concentric circle mapping based PTS (CCM-PTS). In this paper, the SER performance of PTS based methods namely CCM-PTS and M-PTS over AWGN channel is mathematically analyzed. The SER performance of CCM-PTS over AWGN is analyzed using two decoding techniques, namely minimum distance decoding and circular boundary decoding, whereas M-PTS is analyzed using minimum distance decoding. The simulation results for SER performance of CCM-PTS and M-PTS, over fading channel, have been presented using computer simulations and the SER performance of CCM-PTS by both the decoding techniques is compared with M-PTS. Also, a comparison of PAPR reduction capability and computational complexity of CCM-PTS and M-PTS has been presented. CCM-PTS method almost has the same PAPR reduction capability as M-PTS, but its SER performance is better than M-PTS and uses a simpler method to decode the data symbols.

Diversity combining in FSO systems in presence of non-Gaussian noise

Free-space optics (FSO) communication has received much attention in recent years as a cost-effective, license-free, and wide-bandwidth access technique for high data rate applications. The performance of FSO communication, however, severely suffers from turbulence caused by atmospheric conditions. Multiple photodetectors can be placed at the receiver to mitigate the turbulence and exploit the advantages of spatial diversity combining. In this paper, we analyze the bit error rate (BER) performance of an FSO communication system employing binary phase-shift keying with additive non-Gaussian noise over negative exponential distributed atmospheric turbulence and spatial diversity at the receiver. The Laplace distribution is used to model the non-Gaussian impulsive noise. We consider the case when perfect channel state information is available at the receiver for implementation of coherent detection. Analytical expressions for the BER of a single channel receiver as well as that of a diversity combining receiver using selection combining, dual-diversity equal-gain combining, and maximal-ratio combining are derived. The derived analytical expressions are verified by simulation results.

Optimum beamforming for a nearfield source in signal-correlated interferences

In this paper, the problem of optimum beamforming using a uniform linear array is considered, for the purpose of avoiding target signal cancellation, which normally results when signal-correlated interferences are present in the environment. A convenient and direct characterization of the interference subspace in terms of its orthogonal complement is provided, leading to the estimation of a signal free covariance matrix directly from the observed data. This characterization enables us, not only to improve the performance of the farfield beamformers suggested by Bresler et al. [Optimum beamforming for coherent signal and interferences, IEEE Trans. Acoust. Speech Signal Process. ASSP-36(6) (1988) 833-843], but it also allows us to generalize the results of [Y. Bresler, et al. Optimum beamforming for coherent signal and interferences, IEEE Trans. Acoust. Speech Signal Process. ASSP-36(6) (1988) 833-843] to obtain the corresponding nearfield beamformers. The three beamformers proposed, work equally well even in scenarios where interferences are correlated with the signal of interest. Computer simulations are presented to validate the performance of these beamformers in the presence of correlated and uncorrelated interferences.

Common factor estimation and two applications in signal processing

The problem of finding common factors (or common roots) of a set of polynomials without rooting is of interest in many fields of research. When the polynomials are observed in noise, i.e., their coefficients are corrupted by errors, the problem becomes challenging. In this paper we suggest a method of estimating the greatest common divisor of a set of polynomials whose coefficients are perturbed by noise. The corresponding algorithm is called COFE (COmmon Factor Estimation). The COFE algorithm has several applications of which in this paper we discuss two in detail. One of these is MUSIC (MUltiple SIgnal Classification) which is reformulated as a COFE problem. The advantages of COFE MUSIC over the existing MUSIC is the case by which we estimate the parameters. The other application is system identification, where maximum likelihood estimates of the parameters of an ARARX system can be directly obtained by the suggested COFE algorithm in a simple manner.

On the hierarchical least-squares algorithm

A so-called hierarchical recursive least-squares (HRLS) algorithm was suggested in a recent letter in an attempt to reduce the computational burden and improve the convergence rate of the classical RLS algorithm. The discussion of HRLS in the original letter, however, has several unclear points; in particular no clear explanation was offered for the good simulation results reported. In this letter we provide some analysis of the HRLS to determine when this algorithm may be expected to work or fail. It turns out that the input to the channel must be a white sequence, otherwise HRLS may yield grossly biased estimates of the channel FIR coefficients.

Underwater acoustic communication in the presence of heavy-tailed impulsive noise with bi-parameter cauchy-Gaussian mixture model

Underwater acoustic (UWA) noise is dominated by impulsive sources in shallow water areas. This leads to a situation where the noise density function shows a heavier tail than that of the Gaussian density and the performance of traditional Gaussian receiver becomes sub-optimal or even worse. In this paper we investigate the scenario where UWA channel noise is non-Gaussian. Several literatures have shown that heavy-tailed impulsive noise can be very well modelled by the bi-parameter Cauchy-Gaussian mixture (CGM) distribution which is an approximation to the symmetric a-stable class. We derive the analytical expression for probability of error with CGM noise statistics for an M-QAM UWA system, which, to the best of our knowledge, has not yet been reported elsewhere. Also we have simulated a UWA system where the performance of a traditional Gaussian receiver is studied in the presence of CGM noise statistics.