Study On Noise Covariance Matrix-based Multi-antenna Signal Detection

Signal detection is one of the fundamental issues in array processing.Early theories in signal detection mostly copes with single channel data.With the development of multiantenna technologies and hardware,the data to be processed are more frequently shown in multi-dimensional forms,namely,as complex vectors or matrices.Furthermore,as a consequence of the growing turbulence in the wireless environments,the background noise is possibly spatially correlated,and usually has unknown power.This in turn requires the researchers to design specific noise-covariance-based detection algorithms.Additionally,accurate threshold formulas need to be obtained for the derived detectors,which can be completed by inverting the null CDF of the detector.Existing approximating methods,such as the moment-match method,usually fails to result in easilyinvertible CDF.Other methods such as Wilks' theorem and Box's approximation suffer from low approximation precision or constrained applicability.In this thesis,we generalise the asymptotic expansion method,which is widely use in statistical literatures,to the complex-valued scenario.The major advantages of this method,beyond its wide applicability,is that it always result in invertible null CDF,thereby being able to produce closed-form threshold formulas.Besides,it can also be used to derive the non-null distributions of the detectors to access the performance of the detectors.The main contribution of this thesis mainly includes the following points:(1)To reduce the computational load involved in thresholding for John's test,we exploit the asymptotic expansion method to derive a close-form threshold formula.The existing null CDF is difficult to invert,thereby requiring numerical search when evaluating threshold.To tackle this issue,we generalise the asymptotic expansion method to the complex case to derive its null distribution,which turn out to be weighted sum of Chisquare CDFs.Such a distribution function enjoy the advantage of easy invertibility,thereby providing closed-form threshold formulas.Besides,the approximation error could be predicted by the remnant's order.In this context,our derived null CDF has a remnant of o(n2),suggesting a fast convergence of the approximation error with the number of samples n.(2)For stationary spatially colored noise,we devised a CFAR detector based on the GLR criteria.For stationary spatially colored noise,its covariance matrix is Toeplitz.Since there are no closed-form expressions for this ML estimate,we resort to the inverse iterative algorithm,resulting in the GLRT.The proposed test enjoys CFAR property,thereby being superior over existing prewhitening-based algorithms.Besides,it outperforms existing methods in terms of detection power and robustness.(3)For partially correlated noise,we studied the null and non-null distributions of the locally most powerful invariant test for independence of complex Gaussian vectors and derived a closed-form threshold formula.The resulted null distribution also has a Chisquare CDF as the dominant term,and further incorporates a o(n-1)term,which could be seen as higher order correction to the existing result.Moreover,as the expansions of the covariance matrix are different in the high and low SNR cases,the non-null distributions are analyzed separately in these two scenarios.Both approximations reaches a precision of o(n3/2).Numerical results show that the derived distributions are very accurate and the threshold formula is more precise than existing result.(4)To exploit the block-spherical property of noise in bistatic MIMO radar,we studied the distributions of the test for sphericity of Gaussian vectors.For its null distribution and non-null distribution in the low SNR regime,the results are respectively expanded to orders o(n-2)and o(n-3/2),with closed-form threshold formula being produced.For the high SNR case,we first evaluate its mean and variance through the asymptotic expansions,and then match them with that of the Gamma distribution,resulting in a Gamma approximation.As the non-null distribution is used for performance assessment,its inverse function is not needed and only approximation accuracy counts.This method is easily-applicable,thus could be an alternative method when the asymptotic expansions are too complicated.Simulations validate the accuracy of the derived distributions and show that Ts performs better in MIMO radar than existing Wilks' detector-based algo-rithm and is free of noise-only observations.