Radars use coherence to increase the signal-processing gain. In electronic support, that same coherence can be exploited to accurately estimate carrier frequency when measured modulo the pulse repetition frequency. Such estimates can be used for passive emitter geolocation, for example. In the pioneering work of Howard & Lavoie on this topic [1], [2], results are demonstrated only where the pulse repetition interval (PRI) is an integer and where pulses are sinusoidal. In this paper, we show how the results can be generalised to a broad class of pulse shapes, without needing to know the pulse shape in advance. We also show how the signals may be efficiently processed when the PRI is non-integer.

A class of detectors for cyclostationarity is introduced. These detectors are based on the use of generalized coherence to measure correlation among two or more collections of random vectors. The generalized coherence framework allows any finite collection of pertinent samples of the cyclic auto-correlation function estimates formed from the measured signal data to be combined into the detection statistic. The performance of this approach is demonstrated and compared against other established cyclostationarity detectors in both a cognitive radio scenario and a multi-channel passive surveillance scenario.

This paper considers the problem of testing for mutual independence of multiple sets of complex Gaussian vectors. This problem has classical roots in statistics and has been of recent interest in the signal processing literature in connection with multi-channel signal detection. The maximal invariant statistic for this problem is described both as a collection of subspaces of the data space (i.e., points on a complex Grassmannian manifold) and as a corresponding set of complex matrices. The distribution of the maximal invariant is also derived under both hypotheses in the testing problem.

A geometrical perspective is introduced that enables unification and generalization of several results regarding the distributions of quantities that arise in connection with an important class of multiple-channel detectors. Standard models on sets of normalized vectors following from joint Gaussian assumptions in this context are relaxed to the geometrically appealing model of uniform distributions on the Stiefel manifold of K-frames in N-dimensional space. In addition to bolstering geometric insight, several prior results are subsumed and strengthened by results obtained under this formulation. Additionally, a generalization of a classical theorem of W. G. Cochran is enabled by this framework.

A measure of the smallest angle between two p-dimensional subspaces of a higher-dimensional vector space is introduced. This p-coherence is seen to generalize standard measures of coherence, and its relationship to canonical correlation is noted. The use of p-coherence as a test statistic for the presence of a common p-dimensional signal subspace in data collected by two arrays of K > p sensors is proposed.

Estimating the number of linearly independent signals impinging on a collection of receivers is of increasing recent interest, particularly in connection with MIMO systems for communications and sensing. This paper derives maximum a posteriori estimators for signal rank from noisy data collected at multiple receivers. Situations in which noise variance is known and unknown are both treated. These estimators are shown to significantly outperform maximum-likelihood/BIC rank estimators.

Bayesian and generalized likelihood ratio tests are derived for detection of a common unknown signal of known rank K in M > K independent channels of white gaussian noise. The cases of known and unknown noise variance are both treated. These derivations encompass the development of explicit expressions for an invariant measure on the grassmannian manifold of K-dimensional subspaces of complex N-dimensional space and parameterization of this manifold to enable the calculation of the necessary marginalization integrals. Performance of the detectors is compared by simulation.

The generalized coherence (GC) estimate is a well studied statistic for detection of a common but unknown signal on several noisy channels. In this paper, it is shown that the GC detector arises naturally from a Bayesian perspective. Specifically, it is derived as a test of the hypothesis that the signals in the channels are independent Gaussian processes against the hypothesis that the processes have some arbitrary correlation. This is achieved by introducing suitable non-informative priors for the covariance matrices across the channels under the two hypotheses. Subsequently, reduced likelihoods are obtained by marginalizing the joint distribution of the data and the covariance matrix in each case. The likelihood ratio is then shown to be a monotonic function of the GC detection statistic. This derivation extends to the case of time-correlated signals, allowing comparison with the generalized likelihood ratio test (GLRT) recently proposed by Ramírez et al.

A well known computationally efficient method for parameters estimation of linear frequency modulated (LFM) signals is to mix the received signals with a shifted version of itself. The drawback is the dominating cross terms in low signal to noise ratio scenarios. In this paper we present a novel technique for the detection/estimation of a weak LFM signal using an array of receivers which can strongly suppress these cross terms. The technique is to take the tensor product of the received signal vector with a delayed version of itself. This approach results in the extended array signal model. The Bayesian approach to the joint direction of arrival (DOA) and chirp rate detector/estimator is derived based on this extended array signal model. We demonstrate the interference suppression abilities of this approach using simulations.

The Golden code is a full-rate full-diversity space-time code which has been incorporated in the IEEE 802.16 (WiMAX) standard. The worst case complexity of a tree-based sphere decoder for a square QAM constellation is O(N3), where N is the size of the underlying QAM constellation; the worst case will dominate average decoding complexity on any channel with a significant line of sight component. In this paper, we present a simple algorithm with quadratic complexity for decoding the Golden code that can be employed by mobile terminals with either one or two receive antennas, that is resilient to near singularity of the channel matrix, and that gives essentially maximum likelihood (ML) performance. Dual use is an advantage, since there will likely be some IEEE 802.16 mobile terminals with one receive antenna and some with two antennas. The key to the quadratic algorithm is a maximization of the likelihood function with respect to one of the pair of signal points conditioned on the other. This choice is made by comparing the determinants of two covariance matrices, and the underlying geometry of the Golden code guarantees that one of these choices is good with high probability.

Space-time codes built with multiplexed Alamouti components provide multiplexing as well as diversity gain. Their orthogonal structure also leads to simpler decoding algorithms. We consider a 4 × 2 system with multiplexed Alamouti codes. An exhaustive search maximum likelihood (ML) decoding for a 4×2 system is of order M4, for a modulation scheme with constellation size M. For multiplexed orthogonal designs, an exact fast ML decoding algorithm has recently been reported whose complexity order is M2for a 4 × 2 system with QAM constellations. Nevertheless, the quadratic complexity of this fast ML algorithm may still be infeasible in practice for large constellations (e.g. M ≥ 64 QAM). In this paper, we present a method for designing low complexity sub-optimal decoders based on a combination of search based ML decoding and linear decoding. Our formulation facilitates a direct investigation of the trade-off between performance and complexity. The complexity of our hybrid decoder is flexible and it can be fixed based on the desired performance for a hardware implementation. Although extendable to more general multiplexed Alamouti systems, we focus here on a 4 × 2 space-time-polarization system comprising of two dual-polarized transmit antennas and one dual-polarized receive antenna.

This paper focuses on conditional optimization as a decoding primitive for high rate space-time codes that are obtained by multiplexing in the spatial and code domains. The approach is a crystallization of the work of Hottinen which applies to space-time codes that are assisted by quasi-orthogonality. It is independent of implementation and is more general in that it can be applied to space-time codes such as the Golden Code and perfect space-time block codes, that are not assisted by quasi-orthogonality, to derive fast decoders with essentially maximum likelihood (ML) performance. The conditions under which conditional optimization leads to reduced complexity ML decoding are captured in terms of the induced channel at the receiver. These conditions are then translated back to the transmission domain leading to codes that are constructed by multiplexing orthogonal designs. The methods are applied to several block space-time codes obtained by multiplexing Alamouti blocks where it leads to ML decoding with complexityO(N2) whereNis the size of the underlying QAM signal constellation. A new code is presented that tests commonly accepted design principles and for which decoding by conditional optimization is both fast and ML. The two design principles for perfect space-time codes are nonvanishing determinant of pairwise differences and cubic shaping, and it is cubic shaping that restricts the possible multiplexing structures. The new code shows that it is possible to give up on cubic shaping without compromising code performance or decoding complexity.

Perfect space-time block codes (STBCs) were first introduced by Oggier et al. to have full rate, full diversity and non-vanishing determinant. A maximum likelihood decoder based on the sphere decoder has been used for efficient decoding of perfect STBCs. However the worst-case complexity for the sphere decoder is an exhaustive search. In this paper we present a reduced complexity algorithm for 3 times 3 perfect STBC which gives essentially maximum likelihood (ML) performance and which can be extended to other perfect STBC. The algorithm is based on the conditional maximization of the likelihood function with respect to one of the set of signal points given another. There are a number of choices for which signal points to condition on and the underlying structure of the code guarantees that one of the choices is good with high probability. Furthermore, the approach can be integrated with the sphere decoding algorithm with worst case complexity corresponding exactly to that of our algorithm.

Multiple-input multiple-output (MIMO) functionality has been shown to dramatically increase the capacity of wireless communication systems when the environment provides rich multipath scattering. In a predominantly line-of-sight (LOS) environment, the loss of diversity reduces the potential gain considerably. This can be remedied in part by the use of dual-polarized antennas, which increases the rank of the wireless channel and introduces diversity, while minimizing the antenna's form factor. However the performance of a dualpolarized antenna is still degraded by antenna rotations that are typical of mobile terminal operation. This paper presents a solution which uses a triad antenna at the transmitter and a triad at the receiver, to provide a 8-10 dB gain over the baseline dual-polarized system. A triad is composed of three orthogonal dipoles oriented in perpendicular directions. A triad antenna can generate an arbitrary oscillating dipole moment at the transmitter and consequently an arbitrary polarized electric field at the receiver, subject only to the constraints imposed by the physics of the electromagnetic (EM) field. We show that, in LOS environments, the capacity of the channel is invariant under arbitrary rotations of the transmit and/or receive antennas about their centres. Simulation results show that the performance is stable as the propagation environment varies from rich scattering to pure LOS. A full rate 3 × 3 space-time block code (STBC) is proposed for the triad system that is designed for low complexity decoding.

Space–time codes built out of Alamouti components have been adopted in wireless standards such as UMTS, IEEE 802.11n, and IEEE 802.16, where they facilitate higher data rates through multiplexing of parallel data streams and the addition of two or more antennas at the receiver that perform interference cancellation. This correspondence provides new theoretical insight into different algorithms for interference cancellation through a Bayesian analysis that expresses performance as a function of signal-to-noise ratio (SNR) in terms of the “angles” between different space–time coded data streams.

Space-time codes built out of Alamouti components have been adopted in wireless standards such as UMTS, IEEE 802.1 In and IEEE 802.16 where they facilitate higher data rates through multiplexing of parallel data streams and the addition of two or more antennas at the receiver that perform interference cancellation. This paper provides new theoretical insight into an algorithm for interference cancellation through a Bayesian analysis that expresses performance as a function of SNR in terms of the ''angles" between different space-time coded data streams. Our approach provides insights into the coupling of channel coding to spatial and polarization degrees of freedom.