Distribution and characteristic functions for correlated complex Wishart matrices

Smith, Peter J.; Garth, L.M.

doi:10.1016/j.jmva.2006.09.013

Cited by 34 publications

(36 citation statements)

References 20 publications

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“…This function can be calculated with the help of the positive eigenvalues of the Hermitian matrix M by [20] into (9) and applying the rule of the change of variables [17, Th. 2.1.5]…”

Section: B Joint Density Function Of Temporal Polarimetric Covariancmentioning

confidence: 99%

“…1 shows the comparison between the theoretical bivariate distribution 1 The joint distribution of two real Wishart-distributed samples can be found in [21]. The joint distribution of two complex Wishart-distributed samples with the condition of Σ 11 = Σ 22 is presented in [20]. However, the joint distribution function of the second-order statistics of two PolSAR images is not clearly defined since, generally, derived in (12) and a simulated 2-D bivariate histogram.…”

Section: B Joint Density Function Of Temporal Polarimetric Covariancmentioning

confidence: 99%

“…Thus, the final goal of this study is to highlight the advantage of using the MI compared to (20)-which is shown in Fig. 3(e)-as a change detector.…”

Section: Gain Of the Change Detection Applicationmentioning

confidence: 99%

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A New Coherent Similarity Measure for Temporal Multichannel Scene Characterization

Erten¹,

Reigber

Ferro-Famil

et al. 2012

IEEE Trans. Geosci. Remote Sensing

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Abstract-This paper proposes a new method for a measure of coherent similarity between temporal multichannel synthetic aperture radar (SAR) images and its implementation to change detection application. The method is based on mutual information (MI) from information theory. The MI measures the amount of information in common between coherent temporal multichannel SAR acquisitions. In order to develop an algorithm for all kinds of SAR images, such as interferometric SAR, polarimetric-interferometric SAR (PolInSAR), and partial PolIn-SAR, first, the joint density function of temporal multichannel images based on their second-order statistics has been derived. Then, the derived joint density function is used to calculate an analytical expression for the MI between temporal images, which is assumed to be maximal if the temporal images are identical. Although, in this paper, a new coherent similarity measure has analytically been derived for temporal polarimetric SAR images based on complex Wishart process in time, since the mathematical formulation is general, it can equally well be implemented into any kind of multivariate remote sensing data, such as multispectral optical and interferometric images after small continuation. This derived quantity has been implemented for change detection application whose aim is to characterize the temporal behavior of the acquisitions. A comparison between the proposed and the other well-known change detection methods by means of scene characterization is shown, describing the advantages due to the fact that the proposed change detector involves almost every facet of applied change detection.

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“…This function can be calculated with the help of the positive eigenvalues of the Hermitian matrix M by [20] into (9) and applying the rule of the change of variables [17, Th. 2.1.5]…”

Section: B Joint Density Function Of Temporal Polarimetric Covariancmentioning

confidence: 99%

Section: B Joint Density Function Of Temporal Polarimetric Covariancmentioning

confidence: 99%

See 1 more Smart Citation

A New Coherent Similarity Measure for Temporal Multichannel Scene Characterization

Erten¹,

Reigber

Ferro-Famil

et al. 2012

IEEE Trans. Geosci. Remote Sensing

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“…Now the marginal statistics, such as E [X] and var(X), can be computed using standard results [11], [12], [13], [14]. Thus, we can find the ACF from var(X − Y ) and vice-versa.…”

Section: Eigenvalue Metricsmentioning

confidence: 99%

Eigenvalue variation in MIMO OFDM systems

Kongara

Smith

Garth

2008

2008 Australian Communications Theory Workshop

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Abstract-In this paper we consider the variation of eigenvalues and eigenvalue sums across the frequency bins of a MIMO OFDM system. In particular, we consider the changes in the ordered eigenvalues and the eigenvalue sum or link gain between two distinct frequency bins. The size of such changes has an important effect both on system performance and design. In addition these results have applications in other areas, including temporal variation, feedback delay and channel estimation. Novel results presented include distributions and moments for changes in link gain and the maximum eigenvalue and autocorrelation functions for the link gain and maximum eigenvalue. Furthermore, some very simple approximate results for the ordered eigenvalue differences are presented and the accuracy of the analysis is verified by Monte Carlo simulations.

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“…, f m ). In the rank one standard model for M, these eigenvalues are given by: [16], the distinct unordered eigenvalues w (with corresponding distinct eigenvalues f ) have joint density…”

Section: Iid Ricean Channelmentioning

confidence: 99%

Performance analysis of multiple-input multiple-output singular value decomposition transceivers during fading and other cell interference

Smith

Garth

Shafi³

2007

IET Microw. Antennas Propag.

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A generalised method is derived to compute the error probabilities of singular value decomposition (SVD)-based receivers for a multiple-input multiple-output (MIMO) system with uncoded transmission. The method can be used for a wide class of flat fading environments, including independent and identically distributed (i.i.d.) and semi-correlated Rayleigh and i.i.d. Ricean channels. Although the method is applied to equal-power binary phase shift keying, it can easily be extended to higher-order M-ary phase shift keying (M-PSK) and M-ary quadrature amplitude modulation (M-QAM) signal constellations and adaptive 'water-filling' schemes. The error probability curves derived from closed-form formulas and simulations demonstrate very close agreement. The error performances of channel inversion, minimum mean square error and zero forcing receivers are compared with the SVD receiver for a single-user system. The impact of multiple users is considered by studying the performance of an adaptive MIMO SVD transmission scheme operating in a cellular environment. In particular, the effect of inter-cell interference on the performance of the scheme is quantified, modelling the interference as increased Gaussian noise. A number of cellular layouts are examined and the impact of the resulting singal-to-interference and noise ratio on the constellation sizes that can be supported, the BER and so on is considered. The primary metric used for our performance analysis is the error-free transmission rate, which is derived for our adaptive system. For the cellular scenarios considered, it can be found that the effect of interference is considerable and the performance of the adaptive MIMO SVD scheme is only marginally better than that provided by conventional diversity methods. IntroductionThe pioneering work of Telatar [1] and Foschini and Gans [2] has resulted in immense interest in multiple-input multiple-output (MIMO) systems. They offer the promise of large system capacities, and thus are being considered for fourth generation wireless systems. However, the majority of work in this area has focussed on single-user MIMO systems, and recent results [3] suggest that the promised rates may not be available in cellular systems. Hence, in this paper we study the performance of both fixed and adaptive MIMO singular value decomposition (SVD) transmission schemes in a cellular environment and make the following contributions: † We present a generalised method that can be used to derive the exact symbol-error probability of fixed SVD-based MIMO receivers using uncoded transmission. We demonstrate the method for independent and identically distributed (i.i.d.) and semi-correlated Rayleigh and i.i.d. Ricean channels. Our results provide new insights in understanding the error performance of MIMO systems. For example, when the number of antennas is increased from two to four at both the transmit and receive ends, although the ergodic capacity increases, the error performance degrades. Hence, we are able to quantify the tradeoff betw...

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Distribution and characteristic functions for correlated complex Wishart matrices

Cited by 34 publications

References 20 publications

A New Coherent Similarity Measure for Temporal Multichannel Scene Characterization

A New Coherent Similarity Measure for Temporal Multichannel Scene Characterization

Eigenvalue variation in MIMO OFDM systems

Performance analysis of multiple-input multiple-output singular value decomposition transceivers during fading and other cell interference

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