A framework is proposed for developing and evaluating algorithms for extracting multipath propagation components (MPCs) from measurements collected by channel sounders at millimeter-wave frequencies. Sounders equipped with an omni-directional transmitter and a receiver with a uniform planar array (UPA) are considered. An accurate mathematical model is developed for the spatial frequency response of the sounder that incorporates the non-ideal cross-polar beampatterns for the UPA elements. Due to the limited Field-of-View (FoV) of each element, the model is extended to accommodate multi-FoV measurements in distinct azimuth directions. A beamspace representation of the spatial frequency response is leveraged to develop three progressively complex algorithms aimed at solving the single-snapshot maximum likelihood estimation problem: greedy matching pursuit (CLEAN), space-alternative generalized expectation-maximization (SAGE), and RiMAX. The first two are based on purely specular MPCs whereas RiMAX also accommodates diffuse MPCs. Two approaches for performance evaluation are proposed, one with knowledge of ground truth parameters, and one based on reconstruction mean-squared error. The three algorithms are compared through a demanding channel model with hundreds of MPCs and through real measurements. The results demonstrate that CLEAN gives quite reasonable estimates which are improved by SAGE and RiMAX. Lessons learned and directions for future research are discussed.

We investigate the relationship between Orthogonal Time Frequency Space (OTFS) modulation and Orthogonal Short Time Fourier (OSTF) signaling. OTFS was recently proposed as a new scheme for high Doppler scenarios and builds on OSTF. We first show that the two schemes are unitarily equivalent in the digital domain. However, OSTF defines the analog-digital interface with the waveform domain. We then develop a critically sampled matrix-vector model for the two systems and consider linear minimum mean-squared error (MMSE) filtering at the receiver to suppress inter-symbol interference. Initial comparison of capacity and (uncoded) probability of error reveals a surprising observation: OTFS under-performs OSTF in capacity but over-performs in probability of error. This result can be attributed to characteristics of the channel matrices induced by the two systems. In particular, the diagonal entries of OTFS matrix exhibit nearly identical magnitude, whereas those of the OSTF matrix exhibit wild fluctuations induced by multipath randomness. It is observed that by simply replacing the unitary matrix, relating OTFS to OSTF, by an arbitrary unitary matrix results in performance nearly identical to OTFS. We then extend our analysis to orthogonal frequency division multiplexing (OFDM) and also consider a more extreme scenario of relatively large delay and Doppler spreads. Our results demonstrate the significance of using OSTF basis waveforms rather than sinusoidal ones in OFDM in highly dynamic environments, and also highlight the impact of the level of channel state information used at the receiver.

Seven decades after the foundation of classical information theory and the invention of the transistor that launched the digital communication and computing revolutions, we are entering a new era of quantum information science and engineering (QISE). Despite holding its impressive sway for nearly 60 years, the celebrated Moore’s law is beginning to hit physical limits, as the ever-shrinking transistor size is making it necessary to account for quantum effects. Concurrently, the growing demand for high-rate processing is imposing unsustainable power and heat dissipation requirements. Thus, there is an urgent need to develop quantum information processing systems that can circumvent the limitations of existing technology.

Beamspace channel estimation is essential for wideband millimeter-wave (mmWave) MIMO with lens antenna array to achieve substantial increase in data rates with considerably reduced number of radio-frequency chains. However, most of existing beamspace channel estimation schemes are designed for narrowband mmWave systems, while rather scarce wideband schemes ideally assume beamspace channel enjoys the common support in frequency-domain. In this paper, inspired by the classical successive interference cancellation for multi-user detection, we propose an efficient successive support detection (SSD) based scheme without the assumption of common support. Specifically, we first demonstrate that each path component of the wideband beamspace channel exhibits a unique frequency-varying sparse structure. Based on this, we then successively estimate all sparse path components. For each path component, its supports at different frequencies are jointly estimated to improve the estimation accuracy, and then its influence is removed to estimate the remained path components. Once all path components have been estimated, the wideband beamspace channel can be recovered at a low complexity. Simulation results verify that the proposed SSD based beamspace channel estimation scheme achieves higher accuracy than existing wideband schemes.

Millimeter-wave (mmW) wireless is as a promising technology for meeting the Gigabit rate and low latency requirements of emerging fixed and mobile 5G applications. This is enabled by the large (GHz) bandwidths and high-gain beamforming due to high-dimensional antenna arrays possible at mmW frequencies. Initial propagation measurements underscore the highly directional nature of mmW communication, dominated by line-of-sight and single-bounce multipath, making beamforming a critical operational functionality. However, existing channel measurements are limited to mechanically pointed horn antennas and single-beam phased arrays of moderate sizes. On the other hand, multi-beam operation is necessary for spatial multiplexing. In this paper, we introduce a new measurement methodology and initial results based on beamspace MIMO channel modeling and communication. The measurement results are based on a novel beamspace MIMO prototype system that uses a lens array for analog beamforming and enables, for the first time, simultaneous multi- beam channel measurements with a beamwidth of about 4 degrees equivalent to that of a two- dimensional array with 636 critically spaced elements. Initial indoor channel measurements follow Friis formula for pathloss, and illustrate the new beamspace channel measurement and modeling methodology.

We propose a new multiple input multiple output (MIMO) transceiver architecture- Differential MIMO (D-MIMO) - that enables linear interference suppression between multiple spatially multiplexed and differentially encoded data streams. The D-MIMO transceiver architecture is particularly attractive in emerging high-frequency systems, such as millimeter-wave systems, in which the requirement of a phase-coherent local oscillator at the receiver can be challenging. A direct application of conventional linear interference suppression techniques is not possible with differential communication. Thus, we first develop a general model for D-MIMO systems, with a corresponding D-MIMO channel matrix, that forms the basis of the development in this paper. A surprising result is that a quasi-coherent version of the underlying channel matrix can also be estimated from the D-MIMO matrix, making conventional linear interference suppression possible as well. This leads to two D-MIMO transceiver architectures that are developed. Numerical results illustrate the promising and nearly identical performance of the proposed transceivers and the communication breakdown that can occur without interference suppression.

Millimeter-wave (mm-wave) systems operating from 30-300GHz provide a unique opportunity for meeting the exploding capacity demands on wireless networks. In addition to orders-of-magnitude larger bandwidths, the small wavelengths at mm-wave enable high-dimensional multiple-input multiple-output (MIMO) operation. However, fully exploiting the advantages of mm-wave requires prohibitively high transceiver complexity when using conventional MIMO techniques. In this paper we propose and analyze the sum capacity of several linear, reduced-complexity multiuser MIMO (MU-MIMO) precoders that exploit the concept of beamspace MIMO (B-MIMO) communication - multiplexing data onto orthogonal spatial beams that serve as approximate channel eigenfunctions. Due to quasi-optical propagation at mm-wave, MIMO channels are expected to be low-rank and the low channel rank is manifested in the sparsity of the beamspace channel matrix. This enables near-optimal rank and complexity reduction via the concept of multi-beam selection. We present numerical capacity results that demonstrate the reduced-complexity B-MIMO precoders are able to closely approximate the performance of their full-dimensional counterparts with complexity that tracks the number of mobile stations (MSs). In mm-wave systems, where the number of MSs is expected to be much lower than the system dimension, this enables a considerable reduction in the digital signal processing complexity and in systems equipped with analog beamforming front-ends the hardware complexity is also reduced. Thus, the proposed reduced-complexity multiuser precoders provide a near-optimal route for achieving multi-Gigabit/s sum rates in mm-wave MU-MIMO networks with the lowest transceiver complexity.

Multiple-input multiple-output (MIMO) systems that exploit multi-antenna arrays and millimeter-wave systems operating in the 30-300GHz band offer synergistic opportunities for meeting the exploding data requirements of wireless networks. While combining these technologies offers the advantages of high-dimensional MIMO, it increases transceiver complexity dramatically in conventional MIMO approaches due to the large number of antennas required for optimal performance. On the other hand, the dimension of the communication subspace is typically much smaller than the system dimension in practice. By multiplexing data onto highly directional orthogonal beams, beamspace MIMO (B-MIMO) provides direct and near-optimum access to the low-dimensional communication subspace and dramatically lowers transceiver complexity when realized with analog beamforming. In this paper we present and analyze the capacity of several low-complexity B-MIMO transceivers for realizing multi-Gigabits/s speeds.

This paper investigates generation of a secret key from a reciprocal wireless channel. In particular we consider wireless channels that exhibit sparse structure in the wideband regime and study the impact of sparsity on the secret key capacity. We explore this problem in two steps. First, we study key generation from a state-dependent discrete memoryless multiple source. The state of the source captures the effect of channel sparsity. Secondly, we consider a wireless channel model that captures channel sparsity and correlation between the legitimate users' channel and the eavesdropper's channel. Such dependency can significantly reduce the secret key capacity. According to system delay requirements, two performance measures are considered: (i) ergodic secret key capacity and (ii) outage probability. We show that in the wideband regime when a white sounding sequence is adopted, a sparser channel can achieve a higher ergodic secret key rate than a richer channel can. For outage performance, we show that if the users generate secret keys at a fraction of the ergodic capacity, the outage probability will decay exponentially in signal bandwidth. Moreover, a larger exponent is achieved by a richer channel.

A fundamental task in wireless communication is channel estimation: Compute the channel parameters a signal undergoes while traveling from a transmitter to a receiver. In the case of delay-Doppler channel, i.e., a signal undergoes only delay and Doppler shifts, a widely used method to compute the delay-Doppler parameters is the matched filter algorithm. It uses a pseudo-random sequence of length N, and, in case of non-trivial relative velocity between transmitter and receiver, its computational complexity is O(N2logN). In this paper we introduce a novel approach of designing sequences that allow faster channel estimation. Using group representation techniques we construct sequences, which enable us to introduce a new algorithm, called the flag method, that significantly improves the matched filter algorithm. The flag method finds m delay-Doppler parameters in O(mNlogN) operations. We discuss applications of the flag method to GPS, and radar systems.

A fundamental task in wireless communication is channel estimation: Compute the channel parameters a signal undergoes while traveling from a transmitter to a receiver. In the case of delay-Doppler channel, a widely used method is the matched filter algorithm. It uses a pseudo-random waveform of length N, and, in case of non-trivial relative velocity between transmitter and receiver, its computational complexity is O(N2log(N)). In this paper we introduce a novel approach of designing waveforms that allow faster channel estimation. Using group representation techniques we construct waveforms, which enable us to introduce a new algorithm, called the flag method, that significantly improves the matched filter algorithm. The flag method finds the channel parameters in O(m · N log(N)) operations, for channel of sparsity of order m. We discuss applications of the flag method to GPS, and radar system as well.

We design and analyze a method to extract secret keys from the randomness inherent to wireless channels. We study a channel model for a multipath wireless channel and exploit the channel diversity in generating secret key bits. We compare the key extraction methods based both on entire channel state information (CSI) and on single channel parameter such as the received signal strength indicators (RSSI). Due to the reduction in the degree-of-freedom when going from CSI to RSSI, the rate of key extraction based on CSI is far higher than that based on RSSI. This suggests that exploiting channel diversity and making CSI information available to higher layers would greatly benefit the secret key generation. We propose a key generation system based on low-density parity-check (LDPC) codes and describe the design and performance of two systems: one based on binary LDPC codes and the other (useful at higher signal-to-noise ratios) based on four-ary LDPC codes.

We study the fundamental limits to secret key generation from an excited distributed source (EDS). In an EDS, a pair of terminals observe dependent sources of randomness excited by a pre-arranged signal. We first determine the secret key capacity for such systems with one-way public messaging. We then characterize a tradeoff between the secret key rate and exponential bounds on the probability of key agreement failure and on the secrecy of the key generated. We find that there is a fundamental tradeoff between reliability and secrecy.

Recent attention on performance analysis of single-user multiple-input-multiple-output (MIMO) systems has been on understanding the impact of the spatial correlation model on ergodic capacity. In most of these works, it is assumed that the statistical degrees of freedom (DoF) in the channel can be captured by decomposing it along a suitable eigenbasis and that the transmitter has perfect knowledge of the statistical DoF. With an increased interest in large-antenna systems in state-of-the-art technologies, these implicit channel modeling assumptions in the literature have to be revisited. In particular, multiantenna measurements have showed that large-antenna systems are sparse where only a few DoF are dominant enough to contribute towards capacity. Thus, in this work, it is assumed that the transmitter can only afford to learn the dominant statistical DoF in the channel. The focus is on understanding ergodic capacity scaling laws in sparse channels. Unlike classical results, where linear capacity scaling is implicit, sparsity of MIMO channels coupled with a knowledge of only the dominant DoF is shown to result in a new paradigm of sublinear capacity scaling that is consistent with experimental results and physical arguments. It is also shown that uniform-power signaling over all the antenna dimensions is wasteful and could result in a significant penalty over optimally adapting the antenna spacings in response to the sparsity level of the channel and transmit SNR.

The focus of this paper is on spatial precoding in correlated multiantenna channels where the number of data-streams is adapted independent of the number of transmit antennas. Towards the goal of a low-complexity implementation, a statistical semiunitary precoder is studied where the precoder matrix evolves fairly slowly with respect to the channel evolution. While prior work on statistical precoding has focussed on information-theoretic limits, most of these computations result in complicated functional dependencies of the mutual information with the channel statistics that do not explicitly reveal the impact of statistics on performance. In contrast, estimates that are directly in terms of the channel statistics are obtained here for the relative mutual information loss of a semiunitary precoder with respect to a perfect channel information benchmark. Based on these estimates, matching metrics are developed that capture the degree of matching of a channel to the precoder structure continuously and allow ordering two matrix channels in terms of their mutual information performance. While these metrics are based on bounds, numerical studies are used to show that the proposed metrics capture the performance tradeoffs accurately. The main conclusion of this work is a simple-to-state fundamental principle in the context of signaling design for single-user MIMO systems: the best channel for the statistical precoder is the channel that is matched to it.

We study secret key generation from reciprocal multipath wireless channels modeled as multiple parallel fading channels. We consider two channel characteristics that heavily impact secret key capacity: channel sparsity and correlation between main and eavesdropper's channels. We propose a joint model to capture the channel sparsity and correlated eavesdropping. For the case without eavesdroppers, we show that at each transmitter SNR γ there is an optimal sparsity 0 ≤ ρopt≤ 1, which specifies the fraction of non-zero channel coefficients, that yields the maximum secret key capacity. The reduction in secret key capacity due to eavesdropping is due to two sources. First is the overlap between the main and eavesdropper channels, i.e., the pattern of non-zero subchannels common to both. The second is the correlation between the channel coefficients of the overlapping channels. We show that when the power of the training signal is uniformly distributed over the non-zero channels, there is a cutoff SNR γcbelow which the secret key rate is zero, but non-zero (and increasing in γ) when γ > γc. We also show that in the low SNR regime, the optimal input signal is peaky (a non-uniform training signal) by which the secret key capacity is non-zero at all γ > 0.

High-rate data communication over a multipath wireless channel often requires that the channel response be known at the receiver. Training-based methods, which probe the channel in time, frequency, and space with known signals and reconstruct the channel response from the output signals, are most commonly used to accomplish this task. Traditional training-based channel estimation methods, typically comprising linear reconstruction techniques, are known to be optimal for rich multipath channels. However, physical arguments and growing experimental evidence suggest that many wireless channels encountered in practice tend to exhibit a sparse multipath structure that gets pronounced as the signal space dimension gets large (e.g., due to large bandwidth or large number of antennas). In this paper, we formalize the notion of multipath sparsity and present a new approach to estimating sparse (or effectively sparse) multipath channels that is based on some of the recent advances in the theory of compressed sensing. In particular, it is shown in the paper that the proposed approach, which is termed as compressed channel sensing (CCS), can potentially achieve a target reconstruction error using far less energy and, in many instances, latency and bandwidth than that dictated by the traditional least-squares-based training methods.

Many recent works that study the performance of multiple-input-multiple-output (MIMO) systems in practice assume a Kronecker model where the variances of the channel entries, upon decomposition on to the transmit and the receive eigenbases, admit a separable form. Measurement campaigns, however, show that the Kronecker model results in poor estimates for capacity. Motivated by these observations, a channel model that does not impose a separable structure has been recently proposed and shown to fit the capacity of measured channels better. In this paper, we show that this recently proposed modeling framework can be viewed as a natural consequence of channel decomposition on to its canonical coordinates, the transmit and/or the receive eigenbases. Using tools from random matrix theory, we then establish the theoretical basis behind the Kronecker mismatch at the low-and the high-SNR extremes: 1) sparsity of the dominant statistical degrees of freedom (DoF) in the true channel at the low- SNR extreme, and 2) nonregularity of the sparsity structure (disparities in the distribution of the DoF across the rows and the columns) at the high-SNR extreme.

We study fundamental limits on the generation of secret keys based on the randomness inherent to reciprocal wireless multipath channels. Estimates of the common channel at the two ends of a link are jointly Gaussian sources from which secret keys can be generated. The key generation problem is cast as an equivalent communication problem to characterize the secret key capacity. We analyze the low-SNR regime to quantify the minimum energy per secret key bit required for reliable key acquisition. Our results show that, in contrast to the low SNR behavior of conventional channel capacity, there is a non-zero SNR ¿* that achieves the minimum energy per key bit. A time-sharing scheme is proposed to achieve the minimum energy per key bit at any SNR below ¿*. We also investigate the reliability of secret key generation via error exponent analysis. In particular, our results yield a tight upper bound on the minimum energy required to generate a finite-length key with a specified probability of error in key acquisition.

An analytical upper bound on the ergodic capacity of Multiple-Input Multiple-Output (MIMO) systems is deduced with the aid of a simplified approach that relies on a fundamental power normalization. Given their high practical usability, we are particularly interested in dual configurations where both ends deploy two antenna elements. Contrary to the majority of related studies, where only the common case of Rayleigh fading is considered, our analysis is extended to account for Ricean fading where a deterministic Line-of-Sight (LoS) component exists in the communication link and both ends are affected by spatial correlation. In the following, it is shown that the proposed bound is applicable for any arbitrary Signal-to-Noise Ratio (SNR) and rank of the mean channel matrix. In fact, we consider both conventional and optimized MIMO configurations with equal LoS eigenvalues. Moreover, the tightness of the bound is explored where it is demonstrated that as the SNR tends to zero the bound becomes asymptotically tight; at high SNRs, the offset between empirical capacity and the bound is analytically computed which implies that an explicit asymptotic capacity expression can ultimately be obtained.

We propose a space–time block coding framework based on linear precoding. The codes for$P$transmit antennas are formed by transmitting the information vector (with$P$independent information symbols)$L$times where each time it is rotated by a distinct precoding matrix. The framework generalizes conventional spatial multiplexing techniques and facilitates tradeoff between rate and diversity. We propose a simple construction for precoding matrices whose parameters are chosen to guarantee maximal diversity using algebraic number theory. Our codes exhibit circular structure, which greatly simplifies the performance analysis and facilitates linear decoding. Theoretical analysis and numerical simulations demonstrated excellent performance of the proposed algebraic precoding framework.

Despite the popularity and importance of linear dispersion (LD) codes, precoding for LD codes has rarely been investigated. In this paper we propose a method for designing a precoder codebook for LD codes in spatially and temporally correlated channels. Our codebook consists of two parts: a unitary codebook and a diagonal codebook. We propose a systematic algorithm for a unitary codebook design because unitary codebooks are hard to generate using numerical optimization methods. For each column (starting with the first column), we generate a set of vectors in the null space of previous columns. These vectors are generated by skewing i.i.d. unit vector codebooks by means of channel statistics-dependent transformations. A diagonal codebook is generated using a vector quantization technique. We use mutual information as a design cri terion throughout this paper. Numerical results illustrate the benefits of matching a codebook to channel statistics and employing adaptive power shaping.

Many recent works that study the impact of spatial correlation on the performance of multi-input multi-output (MIMO) systems assume a separable (also known as the Kronecker) model where the variances of channel entries, upon decomposition onto the transmit and the receive eigen-bases, admit a separable form. If the true statistics of the channel coefficients are non-separable, the separability assumption leads to a flattening and spreading of the degrees of freedom (DoF) in the channel, and hence results in misleading estimates of capacity - an observation consistent with many measurement campaigns. Towards understanding this observation, we first elucidate the importance of channel power normalization, an often-ignored notion, in the capacity analysis of correlated channels. Using tools from random matrix theory, we characterize the mismatch in estimating capacity with the separable model, and thus provide a theoretical underpinning behind many measurement-based observations.

Secure wireless communications is a challenging problem due to the shared nature of the wireless medium. Most existing security protocols apply cryptographic techniques for bit scrambling at the application layer by exploiting a shared secret key between pairs of communicating nodes. However, more recent research argues that multipath propagation - a salient feature of wireless channels - provides a physical resource for secure communications. In this context, we propose a protocol that exploits the inherent randomness in multipath wireless channels for generating secret keys through channel estimation and quantization. Our approach is particularly attractive in wideband channels which exhibit a large number of statistically independent degrees of freedom (DoF), thereby enabling the generation of large, more-secure, keys. We show that the resulting keys are distinct for distinct pairwise links with a probability that increases exponentially with the key-size/channel DoF. We also characterize the probability that the two users sharing a common link generate the same key. This characterization is used to analyze the energy consumption in successful acquisition of a secret key by the two users. For a given key size, our results show that there is an optimum transmit power, and an optimum quantization strategy, that minimizes the energy consumption. The proposed approach to secret key generation through channel quantization also obviates the problem of key pre-distribution inherent to many existing cryptographic approaches.

Recent results in the wideband/low-SNR regime show that even one bit of perfect feedback is sufficient to achieve the same rate of capacity scaling as in the benchmark case of perfect CSI at the transmitter. However, the capacity achieving signals are peaky in the non-coherent scenario when CSI is estimated at the receiver. Signal peakiness is related to channel coherence and recent measurement campaigns show that, in contrast to previous assumptions, wideband channels exhibit a sparse multipath structure that naturally leads to coherence in time and frequency. With perfect receiver CSI, we show that limited feedback, even with an instantaneous power constraint, is sufficient to achieve the benchmark capacity in sparse multipath channels. Our analysis reveals the benefits of channel sparsity in the non-coherent scenario, where we employ a training-based signaling scheme. With an average power constraint, it is shown that the benchmark is achievable, provided the channel coherence scales at a sufficiently fast rate with signal space dimension. Furthermore, in contrast to peaky signaling schemes that violate instantaneous power constraints, we show that the benchmark is attainable in sparse channels even with finite instantaneous transmit power. We present rules of thumb on choosing the signaling parameters as a function of the channel parameters so that the full benefits of sparsity can be realized.

The focus of this paper is on spatial precoding in correlated multi-antenna channels where the number of independent data-streams can be adapted to trade off the data rate with the transmitter complexity. A structured precoding scheme is proposed, where the precoder structure evolves fairly slowly at a rate comparable with the statistical evolution of the channel, and in addition, enjoys low-complexity. A particular case of the proposed scheme, semiunitary precoding, is shown to be near- optimal in matched channels where the dominant eigenvalues of the transmit covariance matrix are well-conditioned and their number equals the number of independent data-streams, and the receive covariance matrix is also well-conditioned. In mismatched channels where the above conditions do not hold, it is shown that the loss in performance with semiunitary precoding when compared with a perfect channel information benchmark is substantial. This loss can be mitigated via limited feedback techniques that provide partial channel information to the transmitter. We also develop matching metrics that capture the degree of matching of a channel to the precoder structure continuously, and allow ordering two matrix channels in terms of their mutual information or error probability performance.

Technological advances in radio-frequency (RF) front-ends, such as reconfigurable antenna arrays, afford a new "hardware" dimension for dynamic spectrum access in cognitive wireless networks. In this paper, we study the impact of reconfigurable antenna arrays on maximizing the spectral efficiency of multiple input multiple output (MIMO) wireless communication links. Physical wireless channels exhibit spatial correlation and there is growing experimental evidence that sparse multipath is a key source of such correlation. We propose a model for sparse multipath channels and show that sparsity affords a new dimension over which MIMO capacity can be optimized: the distribution or configuration of the sparse statistically independent degrees of freedom (DoF) in the available spatial signal space dimensions. We provide an explicit characterization of the optimal capacity-maximizing channel configurations as a function of the operating SNR. We then develop a framework for realizing the optimal channel configuration at any SNR by systematically adapting the antenna spacings at the transmitter and the receiver. In contrast to a fixed-array MIMO system in which the multiplexing gain is lost at low SNRs, such adaptively reconfigurable MIMO systems deliver the maximum multiplexing gain at all SNRs. Surprisingly, three canonical array configurations are sufficient for near-optimum performance over the entire SNR range. Numerical results based on a realistic physical model are presented and implications of this work for cognitive radio and dynamic spectrum access are discussed.

The full diversity gain provided by a multi-antenna channel can be achieved by transmit beamforming and receive combining. This requires the knowledge of channel state information (CSI) at the transmitter which is difficult to obtain in practice. Quantized beamforming where fixed codebooks known at both the transmitter and the receiver are used to quantize the CSI has been proposed to solve this problem. Most recent works focus attention on limited feedback codebook design for the uncorrelated Rayleigh fading channel. Such designs are sub-optimal when used in correlated channels. In this paper, we propose systematic codebook design for correlated channels when channel statistical information is known at the transmitter. This design is motivated by studying the performance of pure statistical beamforming in correlated channels and is implemented by maps that can rotate and scale spherical caps on the Grassmannian manifold. Based on this study, we show that even statistical beamforming is near-optimal if the transmitter covariance matrix is ill-conditioned and receiver covariance matrix is well-conditioned. This leads to a partitioning of the transmit and receive covariance spaces based on their conditioning with variable feedback requirements to achieve an operational performance level in the different partitions. When channel statistics are difficult to obtain at the transmitter, we propose a universal codebook design (also implemented by the rotation-scaling maps) that is robust to channel statistics. Numerical studies show that even few bits of feedback, when applied with our designs, lead to near perfect CSI performance in a variety of correlated channel conditions.

Power and bandwidth are scarce resources in dense wireless sensor networks and it is widely recognized that joint optimization of the operations of sensing, processing and communication can result in significant savings in the use of network resources. In this paper, a distributed joint source-channel communication architecture is proposed for energy-efficient estimation of sensor field data at a distant destination and the corresponding relationships between power, distortion, and latency are analyzed as a function of number of sensor nodes. The approach is applicable to a broad class of sensed signal fields and is based on distributed computation of appropriately chosen projections of sensor data at the destination - phase-coherent transmissions from the sensor nodes enable exploitation of the distributed beamforming gain for energy efficiency. Random projections are used when little or no prior knowledge is available about the signal field. Distinct features of the proposed scheme include: (1) processing and communication are combined into one distributed projection operation; (2) it virtually eliminates the need for in-network processing and communication; (3) given sufficient prior knowledge about the sensed data, consistent estimation is possible with increasing sensor density even with vanishing total network power; and (4) consistent signal estimation is possible with power and latency requirements growing at most sublinearly with the number of sensor nodes even when little or no prior knowledge about the sensed data is assumed at the sensor nodes.

The essential task in nearly all applications of sensor networks is to extract relevant information about the sensed data and deliver it to a desired destination. The overall goal in the design of sensor networks is to execute this task with least consumption of network resources. In this regard, the relevant metrics of interest are 1) the latency (bandwidth) involved in network data acquisition; and 2) the energy-distortion (E-D) tradeoff: given some desired distortion level D, how much energy E does the sensor network consume in extracting and delivering relevant information up to distortion D at a (usually) distant destination. It is generally recognized that given sufficient prior knowledge about the sensed data, there exist distributed processing and communication schemes that have a very favorable E-D tradeoff in the sense that D darr 0 as n rarr infin while E grows at most sub-linearly with the number of nodes (n) in the network. However, it is not known whether such schemes exist when little or no prior knowledge about the sensed data is available. In this paper, we present a distributed matched-source channel communication scheme that naturally integrates the operations of processing and communications in a sensor network and is universal in the sense that it provides us with a consistent estimation scheme such that E grows sub-linearly with n even when little prior knowledge about the sensed data is assumed. This universality, however, comes at the price of increased latency (bandwidth) and a less favorable ED tradeoff and we quantify this price by comparing our scheme to the case when sufficient prior information about the sensed data is available

Existing approaches for information extraction in wireless sensor networks are heavily geared towards in-network processing, which generally incurs excess delay and energy consumption due to the attendant tasks of information routing and coordination between nodes. In this paper, we introduce an alternative concept of active wireless sensing in which a wireless information retriever (WIR) interrogates a select ensemble of nodes for rapid and energy-efficient retrieval of desired information. Active wireless sensing has two primary attributes: i) the sensor nodes are "dumb" in that they have limited computational ability, and ii) the WIR is computationally powerful, is equipped with an antenna array, and directly interrogates the sensor ensemble with wideband space-time waveforms. Our approach is based on an intimate connection between active wireless sensing and wideband multi-antenna wireless channels in multipath propagation environments: the sensor nodes play the role of active scatterers and generate a multipath response to WIR's interrogation signals. We illustrate the basic communication architecture in active wireless sensing and the corresponding signal processing at the WIR. Preliminary simulation results are presented to illustrate a fundamental rate versus reliability tradeoff in active wireless sensing

Compressive Sampling is an emerging theory that is based on the fact that a relatively small number of random projections of a signal can contain most of its salient information. In this paper, we introduce the concept of Compressive Wireless Sensing for sensor networks in which a fusion center retrieves signal field information from an ensemble of spatially distributed sensor nodes. Energy and bandwidth are scarce resources in sensor networks and the relevant metrics of interest in our context are 1) the latency involved in information retrieval; and 2) the associated power-distortion trade-off. It is generally recognized that given sufficient prior knowledge about the sensed data (e.g., statistical characterization, homogeneity etc.), there exist schemes that have very favorable power-distortion-latency trade-offs. We propose a distributed matched source-channel communication scheme, based in part on recent results in compressive sampling theory, for estimation of sensed data at the fusion center and analyze, as a function of number of sensor nodes, the trade-offs between power, distortion and latency. Compressive wireless sensing is a universal scheme in the sense that it requires no prior knowledge about the sensed data. This universality, however, comes at the cost of optimality (in terms of a less favorable power-distortion-latency trade-off) and we quantify this cost relative to the case when sufficient prior information about the sensed data is assumed.

Most existing information extraction schemes in sensor networks rely on in-network processing that requires information routing and coordination between sensor nodes and incurs a corresponding overhead in delay and energy consumption. In this paper, we propose a viable alternative – Active Wireless Sensing (AWS) – in which a Wireless Information Retriever (WIR)queries a select ensemble of nodes to obtain desired information in a rapid and energy-efficient manner. AWS has two primary attributes: i) the sensor nodes are "dumb" in that they have limited computational ability, and ii) the WIR is computationally powerful, is equipped with an antenna array, and directly interrogates the sensor ensemble with wideband space-time waveforms. AWS is inspired by an intimate connection with communication over multipath channels: the sensor nodes act as active scatterers and produce a multipath response to the WIR's interrogation signals. We develop the basic communication architecture in AWS and explore various signaling and reception strategies at the WIR, and encoding strategies at the sensors. The basic communication architecture is quite flexible and can cater to a variety of information retrieval tasks. In particular, we illustrate the framework in two extreme information retrieval tasks: high-rate information retrieval corresponding to distributed independent sensor measurements, and low-rate retrieval corresponding to localized correlated measurements. A low-complexity interference suppression technique is proposed for significantly increasing the capacity and reliability of high-rate information retrieval. Performance analysis reveals a fundamental rate versus reliability tradeoff in AWS and is illustrated with accompanying simulation results.

Many techniques have been proposed to improve the error performance of multiple antenna systems by having the receiver provide the transmitter with channel information, which guides the transmitter to adapt its transmission. However, existing works have focused on ideal situations of i.i.d. communication channels and instantaneous feedback channels, or have not used the limited number of feedback bits efficiently. This paper proposes a versatile precoder codebook design method that works well for general situations, i.e. spatially correlated communication channels and feedback channels with delay, using feedback bits efficiently. This method finds a good codebook by directly quantizing a codebook (not a channel realization) with error probability as a performance measure. Numerical studies demonstrate that (1) the codebook generated this way achieves bit error rates as good as or better than what other codebooks yield because our codebook has been optimized for error probability without imposing any limiting structure, and (2) our codebook with fewer feedback bits outperforms the channel quantization-based codebook with more feedback bits due to the efficient use of the feedback bits

Transmit beamforming with receive combining is a low-complexity solution that achieves the full diversity afforded by a multi-antenna channel. Building on our recent result which shows that even channel statistics are sufficient to achieve perfect feedback performance (in the limit of antenna dimensions) with beamforming and combining, we propose near-optimal codebook designs for correlated channels with a focus on few antennas at the transmitter and the receiver. In the process, we refine the answer to the question: When are channel statistics sufficient to achieve near perfect feedback performance? We show that the condition number of the transmit and receive covariance matrices hold the key to this question. We partition the transmit and receive covariance spaces into 4 regions based on well and ill-conditioning of the covariance matrices and show that the number of bits required for near perfect feedback performance is dependent on the condition numbers of these matrices

While the intense research on multi-antenna (MIMO) wireless communication channels was pioneered by results based on an i.i.d. channel model representing a rich multipath environment, there is growing experimental evidence that physical wireless channels exhibit a sparse multipath structure, even at relatively low antenna dimensions. In this paper, we propose a model for sparse multipath channels and study coherent MIMO capacity as a function of SNR for a fixed number of antennas. In a recent work, we had shown that the spatial distribution of the sparse multipath has a significant impact on capacity and had also characterized the optimal distribution (the ideal MIMO channel) that maximizes capacity at any operating SNR. In this paper, we refine these results and develop a framework for maximizing MIMO capacity at any SNR by systematically adapting the array configurations (antenna spacings) at the transmitter and receiver to the level of sparsity. Surprisingly, three canonical array configurations are sufficient for near-optimum performance over the entire SNR range. In a scattering environment with randomly distributed paths, the capacity gain due to optimal configuration is directly proportional to the number of antennas at low SNR's. Numerical results based on a realistic physical model are presented to illustrate capacity gains with reconfigurable antenna arrays

Recent works on the distribution function of the capacity of independent and identically distributed (i.i.d.) and semicorrelated narrowband channels show that the outage capacity computed using a Gaussian approximation is close to the true outage capacity even for few antennas. Motivated by physical scattering considerations, we study a multi-antenna channel model with independent entries that are not necessarily identically distributed and show the weak convergence of capacity to a Gaussian random variable. The channel model considered in this paper subsumes well-studied cases like the i.i.d. and separable correlation models and thus we generalize previous results on weak convergence of multi-antenna capacity. Using recent results from random matrix theory, we also study the rate of convergence of ergodic capacity of i.i.d. channels to its limit value. Employing a well-known conjecture from random matrix theory, we establish tight results for the rate of convergence and show a dependence of this rate on signal-to-noise ratio

Sensing, processing and communication must be jointly optimized for efficient operation of resource-limited wireless sensor networks. We propose a novel source-channel matching approach for distributed field estimation that naturally integrates these basic operations and facilitates a unified analysis of the impact of key parameters (number of nodes, power, field complexity) on estimation accuracy. At the heart of our approach is a distributed source-channel communication architecture that matches the spatial scale of field coherence with the spatial scale of node synchronization for phase-coherent communication: the sensor field is uniformly partitioned into multiple cells and the nodes in each cell coherently communicate simple statistics of their measurements to the destination via a dedicated noisy multiple access channel (MAC). Essentially, the optimal field estimate in each cell is implicitly computed at the destination via the coherent spatial averaging inherent in the MAC, resulting in optimal power-distortion scaling with the number of nodes. In general, smoother fields demand lower per-node power but require node synchronization over larger scales for optimal estimation. In particular, optimal mean-square distortion scaling can be achieved with sub-linear power scaling. Our results also reveal a remarkable power-density tradeoff inherent in our approach: increasing the sensor density reduces the total power required to achieve a desired distortion. A direct consequence is that consistent field estimation is possible, in principle, even with vanishing total power in the limit of high sensor density.

Existing works on MIMO channel capacity assume that the channel power scales quadratically with antenna dimensions. In a recent work, we introduced a framework for sub-quadratic channel power scaling to model physical MIMO channels, and studied a family of channels with different spatial distributions of channel power. In particular, we introduced the notion of a beamforming channel, realizable in practice via the use of reconfigurable antenna arrays, that yields the highest capacity and maximal spectral efficiency in the low SNR regime. In this paper, we show that the MIMO beamforming channel requires a significantly smaller coherence requirement to achieve the wideband capacity limit at finite bandwidth than has been known in the literature. Contrasting the recent claims that training-based signaling schemes are strictly sub-optimal over communication schemes that do not perform explicit training, we show that training offers significant advantages in achieving wideband capacity. The price of explicitly training the channel over a non-explicit training scheme is a bandwidth penalty, albeit at a significantly less stringent coherence requirement on the channel

Transmit beamforming and receive combining are low complexity techniques that help in achieving the full diversity afforded by the multi-antenna channel. Complete channel state information at the transmitter may be possible only under rare instances. Thus quantized beamforming with limited feedback on a reverse link has been a topic that has attracted great attention recently. But almost all of the work to date has focussed on modeling the channel with independent, identically distributed (i.i.d.) Rayleigh fading between antenna pairs. In this paper, we consider the correlated channel case, and show that Grassmannian line packing is an artificial artifact of the i.i.d. assumption. We show that there are dominant peaks in the eigen-domain when correlation is imposed and the codebook construction should be matched to the correlation in the channel, which renders the problem in this case easier than for i.i.d. channels

We study distributed strategies for classification of multiple targets in a wireless sensor network. The maximum number of targets is known a priori but the actual number of distinct targets present in any given event is assumed unknown. The target signals are modeled as zero-mean Gaussian processes with distinct temporal power spectral densities, and it is assumed that the noise-corrupted node measurements are spatially independent. The proposed classifiers have a simple distributed architecture: local hard decisions from each node are communicated over noisy links to a manager node which optimally fuses them to make the final decision. A natural strategy for local hard decisions is to use the optimal local classifier. A key problem with the optimal local classifier is that the number of hypotheses increases exponentially with the maximum number of targets. We propose two suboptimal (mixture density and Gaussian) local classifiers that are based on a natural but coarser repartitioning of the hypothesis space, resulting in linear complexity with the number of targets. We show that exponentially decreasing probability of error with the number of nodes can be guaranteed with an arbitrarily small but nonvanishing communication power per node. Numerical results based on real data demonstrate the remarkable practical advantage of decision fusion: an acceptably small probability of error can be attained by fusing a moderate number of unreliable local decisions. Furthermore, the performance of the suboptimal mixture density classifier is comparable to that of the optimal local classifier, making it an attractive choice in practice.

We propose an iterative extension of the Bell Laboratory Layered Space-Time (BLAST) algorithm and its variant, vertical BLAST (VBLAST). A characteristic feature of the BLAST-type algorithm is that symbol decisions with low reliability are fed back to decode other symbols. Both performance analysis based on Gaussian approximation of residual interference, and simulation results demonstrate that error propagation due to unreliable decision feedback can severely limit system performance. The extended algorithm exploits inherent signal diversity in BLAST to mitigate residual interference, thus overcoming the performance bottleneck due to error propagation. It yields an impressive performance gain over BLAST. In particular, the extension of BLAST with zero-forcing interference nulling admits a simple QR implementation and exhibits excellent performance with low complexity.

The capacity of the multiple-input multiple-output (MIMO) wireless channel with uniform linear arrays (ULAs) of antennas at the transmitter and receiver is investigated. It is assumed that the receiver knows the channel perfectly but that the transmitter knows only the channel statistics. The analysis is carried out using an equivalent virtual representation of the channel that is obtained via a spatial discrete Fourier transform. A key property of the virtual representation that is exploited is that the components of virtual channel matrix are approximately independent. With this approximation, the virtual representation allows for a general capacity analysis without the common simplifying assumptions of Gaussian statistics and product-form correlation (Kronecker model) for the channel matrix elements. A deterministic line-of-sight (LOS) component in the channel is also easily incorporated in much of the analysis. It is shown that in the virtual domain, the capacity-achieving input vector consists of independent zero-mean proper-complex Gaussian entries, whose variances can be computed numerically using standard convex programming algorithms based on the channel statistics. Furthermore, in the asymptotic regime of low signal-to-noise ratio (SNR), it is shown that beamforming along one virtual transmit angle is asymptotically optimal. Necessary and sufficient conditions for the optimality of beamforming, and the value of the corresponding optimal virtual angle, are also derived based on only the second moments of the virtual channel coefficients. Numerical results indicate that beamforming may be close to optimum even at moderate values of SNR for sparse scattering environments. Finally, the capacity is investigated in the asymptotic regime where the numbers of receive and transmit antennas go to infinity, with their ratio being kept constant. Using a result of Girko, an expression for the asymptotic capacity scaling with the number of antennas is obtained in terms

In this paper we propose a joint reduced-state sequence detector (JRSSD) for a multiple-input multiple-output (MIMO) system. The proposed JRSSD incorporates the set-partitioning principle to obtain a reduced-state trellis and is the space-time extension of the RSSD proposed in for a single-input single-output (SISO) equalization problem. We show that two elements are essential in achieving the desired complexity and performance tradeoff for the proposed JRSSD algorithm: 1) a proper multisymbol set-partition and 2) an efficient space-time structure that effectively decouples the spatial and temporal processing. We propose a simple multisymbol uniform set-partition (USP) that retains certain geometric symmetry in the partitioned subsets. We also develop two suboptimal algorithms, namely the decorrelating (DC) and ordered successive (OS) algorithms, to decouple the spatial multisymbol detection problem inherent in the processing of parallel transitions, into single-symbol detection problems. The symmetry in USP, together with the DC or OS algorithm, guarantees efficient processing of parallel transitions and leads to a low-complexity JRSSD. Furthermore, numerical simulations show that the performance of JRSSD is near that of the more complex delayed decision feedback sequence estimator (DDFSE).

We propose a novel decentralized detection scheme based on the method of types and type detectors. Contrary to conventional methods, the proposed decentralized type detection (DTD) scheme asymptotically achieves the performance of centralized detection, provided there exists an arbitrarily small (but non-zero) communication capacity between the sensing nodes and the decision center. The sensing nodes extract and transmit the type information of the observed data sequence, which is then recovered and used by a type detector at the decision center. The key to DTD is that the required network information flow (type information) is of asymptotically vanishing entropy rate but still sufficient for the hypothesis testing problem. The simple structure of type sensors greatly reduces system cost in terms of computational and communication capabilities for sensor nodes. In particular, the sensor nodes need not know the signal statistics under different hypothesis. Theoretical analysis and numerical simulations demonstrate the excellent performance of the proposed DTD scheme.

The degrees of freedom (DoF) in a wireless channel determine its statistics and capacity. The DoF in turn depend on the number and spatial distribution of physical propagation paths in the environment as well as the signal space dimensions (number of antennas, bandwidth). In this paper, we use a virtual representation of time- and frequency-selective MIMO channels to relate the DoF to the physical propagation paths. The virtual representation is characterized by virtual channel coefficients in angle-delay-Doppler space. It induces a partitioning of paths that reveals the contribution of each path to the DoF as well as fundamental dependencies in angle, delay and Doppler that constrain the DoF. As the signal space dimensions increase, the DoF increase whereas the statistics of the virtual channel coefficients deviate from Gaussian (Rayleigh) to "specular" in which the amplitude of the coefficients is deterministic and the channel variations are manifested solely in the phase. Implications of the angle-delay-Doppler dependencies on channel structure and capacity are discussed, which are particularly relevant to ultra-wideband systems.

Existing results on MIMO channel capacity assume a rich scattering environment in which the channel power scales quadratically with the number of antennas, resulting in linear capacity scaling with the number of antennas. However, such scaling in channel power is physically impossible indefinitely. We thus address the following fundamental question: for a given channel power scaling law, what is the best achievable capacity scaling law? For a channel power scaling, /spl rho//sub c/(N) = O(N/sup /spl gamma//), /spl gamma/ /spl isin/ (0,2], we argue that the channel capacity cannot scale faster than C(N) = O(/spl radic/(/spl rho//sub c/(N))) = O(N/sup /spl gamma//2/). Our approach is based on a family of space-time channels corresponding to different distributions of channel power in the spatial signal space dimensions. We develop the concept of an ideal MIMO channel that achieves the optimal scaling law for a given /spl rho//sub c/(N). For a given number of antennas, unlike existing results that either emphasize the low or high SNR regimes, we propose a methodology for capacity-optimal signaling at any SNR. The methodology is based on creating the ideal channel from any given physical scattering environment via adaptive-resolution array configurations.

Distributed signal processing techniques for classification of objects are studied assuming knowledge of sensor measurement statistics. The spatio-temporal signal field generated by an object is modeled as a bandlimited stationary ergodic Gaussian field. The model suggests a simple abstraction of correlation between node measurements: it partitions the network into disjoint spatial coherence regions over which the signal remains strongly correlated, whereas the signal in distinct coherence regions is approximately uncorrelated. The size of coherence regions is determined by spatial signal bandwidths. It is shown that this partitioning imposes a structure on optimal distributed classification algorithms that is naturally suited to the communication constraints of the network: local high-bandwidth exchange of feature vectors within each coherence region to improve the measurement signal-to-noise ratio (SNR), and global low-bandwidth exchange of local decisions across coherence regions to stabilize the inherent variability in the signal. Classifier performance is analyzed for both soft and hard decision fusion across coherence regions assuming noise-free, as well as noisy communication links between nodes. Under mild conditions, the probability of error of all classification schemes (soft, hard, noisy) decays exponentially to zero with the number of independent node measurements-the error exponent depends on both the measurement and communication SNRs and decreases from soft to hard to noisy fusion. Numerical results based on real data illustrate the remarkable advantage of multiple sensor measurements in distributed decision making.

This paper develops a general framework for communication over doubly dispersive fading channels via an orthogonal short-time Fourier (STF) basis. The STF basis is generated from a prototype pulse via time-frequency shifts. In general, the orthogonality between basis functions is destroyed at the receiver due to channel dispersion. The starting point of this work is a pulse scale adaptation rule first proposed by Kozek to minimize the interference between the basis functions. We show that the average signal-to-interference-and-noise (SINR) ratio associated with different basis functions is identical and is maximized by the scale adaptation rule. The results in this paper highlight the critical impact of the channel spread factor, the product of multipath and Doppler spreads, on system performance. Smaller spread factors result in lesser interference such that a scale-adapted STF basis serves as an approximate eigenbasis for the channel. A highly effective iterative interference cancellation technique is proposed for mitigating the residual interference for larger spread factors. The approximate eigendecomposition leads to an intuitively appealing block-fading interpretation of the channel in terms of time-frequency coherence subspaces: the channel is highly correlated within each coherence subspace whereas it is approximately independent across different subspaces. The block-fading model also yields an approximate expression for the coherent channel capacity in terms of parallel flat-fading channels. The deviation of the capacity of doubly dispersive channels from that of flat-fading channels is quantified by studying the moments of the channel eigenvalue distribution. In particular, the difference between the moments of doubly dispersive and flat-fading channels is proportional to channel spread factor. The results in this paper indicate that the proposed STF signaling framework is applicable for spread factors as large as 0.01.

The combination of code-division multiple-access and multicarrier (MC) modulation has been proposed to develop high data-rate wireless communication systems. Due to the longer symbol duration in comparison with single-carrier systems, MC systems are more sensitive to various imperfections, including phase noise and frequency offsets due to local oscillators and Doppler spreading due to motion that results in temporal channel variations. The performance of current systems is significantly limited by these imperfections because they disperse the transmitted power in a particular subcarrier into adjacent subcarriers, thereby causing interference between the subcarriers at the receiver. We consider a single-user communication system and use a canonical model for the received signal that efficiently captures the effects of all impairments. The model uses Fourier basis functions that are fixed for all imperfections while the expansion coefficients depend on imperfections. Using the model, we introduce a receiver structure that implements the matched filter (MF), and hence, optimal. The MF is implemented through a Rake receiver in the frequency domain. The receiver fully compensates for frequency offsets as well as phase noise, thereby eliminating the performance loss due to these factors. Furthermore, in contrast to existing designs, it delivers improved performance under fast fading by exploiting Doppler diversity. Finally, the same integrated receiver structure works for all imperfections eliminating the need for devising a separate correction technique for each.

We apply the recently introduced virtual channel representation to the problem of space-time coding for correlated multiple-input multiple-output (MIMO) channels. The virtual channel representation clearly reveals the essential degrees of freedom in correlated MIMO channels and the corresponding statistical channel structure. Coding design criteria for general correlated channels are derived from pairwise error probability analysis, which reveal the effect of channel statistics and codeword properties on code performance. We focus on the K-diagonal model for correlated channels whose nonvanishing elements correspond to K diagonals of the virtual channel matrix. The K-diagonal model can be motivated by physical scattering considerations or as a low-dimensional approximation to the channel matrix that serves as a building block for general correlated channels. Space-time D-block codes that attain D-level diversity (related to K) per receive dimension are constructed using the theory of space-time block codes. Compared with space-time block codes, identical performance but with significantly smaller delay and complexity can be achieved by matching space-time D-block codes to the K-diagonal channel structure. Our construction also facilitates a natural tradeoff between rate and diversity by decomposing the original channel into several parallel virtual K-diagonal subchannels. Simulation results demonstrate the excellent performance of the proposed techniques.

Selective broadcast schemes for point-to-multiple point transmission of identical information to several selected users are studied for a code-division multiple-access wireless system. The channel states for all selected users are assumed known at both the transmitter and the receivers. The goal is to minimize total transmit power while satisfying minimum received signal-to-noise ratio (SNR) requirements. Three designs, namely, time-only, space-time and space-only, are investigated. In the time-only design no spatial diversity is available, and we solve the optimal transmit signature code by developing iterative least distance programming (ILDP) and linear programming (LP) algorithms. In the space-time design, transmit antennas are exploited in addition to the temporal dimension, and we show the ILDP algorithm is still applicable. The LP algorithm can also be adapted with the integration of space-time block codes, which we term the space-time block coding LP (STC-LP) algorithm. In the space-only design, only the spatial dimension is available and we study the optimization of the transmit antenna weights to satisfy the users' SNR requirements. We show that the STC-LP algorithm applies in this case. We also propose an iterative spatial diagonalization algorithm to explore the unique structure of the space-only problem.

We introduce a continuous representation of multi-antenna (MIMO) fading channels that reveals the effect of array parameters and scattering characteristics on channel degrees of freedom and capacity. It is shown that the intrinsic degrees of freedom in the scattering environment provide an upper bound on the rank of the MIMO channel matrix (and hence the spatial multiplexing gain) and are determined by two key parameters: angular spreads and the scattering correlation scales seen by the transmitter and receiver. Similarly, the spatial signal spaces at the transmitter and receiver are determined by two key parameters each: the aperture size and the smallest scale of signal variation. For any given scattering environment, the continuous representation helps us determine the optimal number of antennas and the antenna spacings to maximize the spatial multiplexing gain (and hence capacity). In particular, we show that linear capacity scaling with the number of antennas is possible in ideally uncorrelated scattering environments with vanishing correlation scales. Conversely, for a non-vanishing scattering correlation scale, the capacity eventually saturates with the number of antennas.

We propose a space-time block coding framework based on precoding. The code design is aimed to the tradeoff between rate, diversity and complexity. Specifically, for P transmit antennas, our block codes are based on L distinct precoding matrices, where L/spl les/P. We further propose a simple structure for the precoding matrices that are product of distinct permutation matrices and a diagonal unitary matrix, whose diagonal elements are design parameters. In particular, when L=P, the codewords are constructed as circulant matrices. And we explicitly give the expression of the eigenvalues of the error codeword matrix, derive the bounds for the coding gain. If the design parameters are chosen according to algebraic number theory, diversity advantage L can be guaranteed for the resulting codes. Our framework is also appealing on that simple decoding strategies can be applied.

Most space-time codes are designed for multiantenna systems assuming the ideal i.i.d. channel model, but their performance degrades over correlated channels. This paper investigates space-time code design for correlated channels using the pair-wise error probability (PEP) criterion. It is shown that, unlike i.i.d channels, performance depends not just on the code error covariance matrix but also its interaction with the channel covariance matrix. Using the example of orthogonal space-time block codes, it is shown that linear preceding can facilitate this interaction to improve performance over correlated channels. Depending on the channel covariance matrix, it may be optimal to trade diversity for higher coding gain even at high signal-to-noise ratios (SNR), i.e. better performance is obtained by lower diversity codes by pumping more power along the dominant transmit signal space dimensions to improve coding gain. This results in reduced dimensional codes which have improved performance than codes without precoding.

Multi input multi output (MIMO) channels under a particular set of correlated channel assumptions, viz. the product correlation, have been shown to differ from i.i.d. channels essentially in the scaling factor of capacity increase [Chen-Nee Chuah, et al. (2002)]. Using a scattering environment based channel representation, we extend the paradigm of capacity scaling to a regime where it saturates or scales depending on how the environment grows with the number of antennas. We also show how the capacity per dB at low SNR's depends on the channel parameters. Based on some (preliminary) results on the convergence rate of the empirical spectral distribution function of an i.i.d. channel we present a rigorous understanding of the notion of 'fast convergence'.

Sensor networks provide virtual snapshots of the physical world via distributed wireless nodes that can sense in different modalities, such as acoustic and seismic. Classification of objects moving through the sensor field is an important application that requires collaborative signal processing (CSP) between nodes. Given the limited resources of nodes, a key constraint is to exchange the least amount of information between them to achieve the desired performance. Two main forms of CSP are possible. Data fusion - exchange of low dimensional feature vectors - is needed between correlated nodes, in general, for optimal performance. Decision fusion $exchange of likelihood values - is sufficient between independent nodes. Decision fusion is generally preferable due to its lower communication burden. We study the CSP of multiple node measurements, each modeled as a Gaussian signal vector (corresponding to the target class) corrupted by additive white Gaussian noise. The measurements are partitioned into groups. The signal components within each group are perfectly correlated whereas they vary independently between groups. Three classifiers are compared: the optimal maximum likelihood classifier; a data averaging classifier that treats all measurements as correlated; a decision fusion classifier that treats them all as independent. The performances of the three CSP classifiers are compared using analytical and numerical results based on real data. These indicate that the sub-optimal decision fusion classifier, that is most attractive in the context of sensor networks, is also a robust choice from a decision theoretic viewpoint.

Optimal estimation of multi-input multi-output correlated channels using pilot signals is considered, assuming knowledge of the second order channel statistics at the transmitter. Assuming a block fading channel model and minimum mean square error (MMSE) estimation at the receiver, we design the transmitted signal to optimize two criteria: MMSE and the conditional mutual information between the MIMO channel and the received signal. Our analysis is based on the recently proposed virtual channel representation for uniform linear arrays, which corresponds to beamforming in fixed virtual directions and exposes the structure and the true degrees of freedom in correlated channels. However, the analysis can be generalized to other known channel models. We show that optimal signaling is in block form corresponding to beams transmitted in successive time intervals along the transmit virtual angles, with powers determined by water filling arguments based on the optimization criteria. The block length depends on the channel correlation and decreases with SNR. Consequently, from a channel estimation viewpoint, a faster fading rate can be tolerated at low SNRs relative to higher SNRs.

A key to reliable communication is a fundamental understanding of the interaction between the signal space and the channel. In time- and frequency-selective MIMO (space-time) fading channels this interaction happens in time, frequency and space. In this paper we propose a four-dimensional Karhunen-Loeve-like virtual representation for space-time channels that captures the essence of such interaction and exposes the intrinsic degrees of freedom in the channel. The four dimensions are: time, frequency and the two spatial dimensions at the transmitter and receiver. The key signal space parameters are the signaling duration, bandwidth and the two array apertures. The corresponding channel parameters are the delay, Doppler and the two angular spreads associated with the scattering environment. The representation induces a virtual partitioning of propagation paths in time, frequency and space that reveals their contribution to channel capacity and diversity. It also exposes fundamental dependencies between time, frequency and space thereby revealing the essential degrees of freedom.

We address signal design for optimal estimation of correlated multi-input multi-output (MIMO) channels using pilot signals, assuming knowledge of the second-order channel statistics at the transmitter. Assuming a block fading channel model and minimum mean square error (MMSE) estimation at the receiver, we design the transmitted signal to optimize two criteria: MMSE and the conditional mutual information between the MIMO channel and the received signal. Our analysis is based on the proposed virtual channel representation, however, it is generalized to other known channel models like the one in D.Shiu et al. [Mar. 2000]. We show that optimal signaling is in a block form, where the block length depends on the signal to noise ratio (SNR) as well as the channel correlation matrix. The block signal corresponds to transmitting beams in successive time intervals along a fixed virtual transmit angles, whose powers are determined by (non-identical) water filling arguments based on the optimization criteria. Our analysis effectively provides characterization of the dominant subspaces of the channel as a function of the SNR and the scattering environment, which is critical to achieving capacity and space-time code design. In particular, at low SNR the block length reduces to one and all the power is transmitted on the beam corresponding to the strongest transmit angle, while at high SNR the block length has a maximum length equal to the number of active virtual transmit angles and the power is assigned equally to all active transmit angles. Consequently, from a channel estimation viewpoint, a faster fading rate can be tolerated at low SNRs relative to higher SNRs.

The capacity of MIMO systems under ideal (i.i.d.) channel conditions has been shown to increase linearly with the number of antennas. Capacity scaling in a correlated channel environment as well but the constant of scaling is shown in Chee-Nee Chuah, D.N. C. Tse, J.M. Khan, R.A. Valanzuela [2002] to be less than that of the i.i.d. scaling factor. Using a channel representation motivated by physical scattering considerations, the virtual channel representation, we show this effect does occur provided the number of effective scattering paths keeps asymptotically increasing with the increase in the number of antennas. Otherwise we show that saturation of capacity occurs. Using random banded matrix theory results, we also show that the effect of correlation is to reduce the effective received SNR according to the degree of correlation. This also yields a closed form expression for the asymptotic capacity of correlated MIMO channels.

Spatial multiplexing techniques send independent data streams on different transmit antennas to maximally exploit the capacity of multiple-input multiple-output (MIMO) fading channels. Most existing multiplexing techniques are based on an idealized MIMO channel model representing a rich scattering environment. Realistic channels corresponding to scattering clusters exhibit correlated fading and can significantly compromise the performance of such techniques. In this paper, we study the design and performance of spatial multiplexing techniques based on a virtual representation of realistic MIMO fading channels. Since the nonvanishing elements of the virtual channel matrix are uncorrelated, they capture the essential degrees of freedom in the channel and provide a simple characterization of channel statistics. In particular, the pairwise-error probability (PEP) analysis for correlated channels is greatly simplified in the virtual representation. Using the PEP analysis, various precoding schemes are introduced to improve performance in virtual channels. Unitary precoding is proposed to provide robustness to unknown channel statistics. Nonunitary precoding techniques are proposed to exploit channel structure when channel statistics are known at the transmitter. Numerical results are presented to illustrate the attractive performance of the precoding techniques.

The highly distributed infrastructure provided by sensor networks supports fundamentally new ways of designing surveillance systems. In this paper, we discuss sensor networks for target classification and tracking. Our formulation is anchored on location-aware data routing to conserve system resources, such as energy and bandwidth. Distributed classification algorithms exploit signals from multiple nodes in several modalities and rely on prior statistical information about target classes. Associating data to tracks becomes simpler in a distributed environment, at the cost of global consistency. It may be possible to filter clutter from the system by embedding higher level reasoning in the distributed system. Results and insights from a recent field test at 29 Palms Marine Training Center are provided to highlight challenges in sensor networks.

An understanding of the interaction between the channel and the signal space is key to reliable communication. Multipath fading channels exhibit inherent diversity that can be exploited via appropriate signaling and reception. We develop a virtual multiple-input multiple-output framework for characterizing single-transmitter single-receiver multipath fading channels, where the virtual multiple inputs and outputs are created by the dimensions of the signaling scheme. The essence of the framework is a representation of the system with respect to appropriately chosen basis waveforms for the signal space that expose the inherent structure of the channel. The structure makes it possible to derive closed-form expressions for ergodic and outage capacity for a variety of transceivers and to design novel transceivers. In many cases, the analysis clearly reveals the key factors that affect system performance. We provide new capacity expressions for a variety of transceivers. In particular, by analyzing particular transceivers, we provide new expressions that bound the outage capacity performance of the multipath channel. A novelty of this work lies in being able to apply codes developed for orthogonal frequency-division multiplexing systems and multiple antenna systems to existing code-division multiple-access-based systems.

The dramatic linear increase in ergodic capacity with the number of antennas promised by multiple-input multiple-output (MIMO) wireless communication systems is based on idealized channel models representing a rich scattering environment. Is such scaling sustainable in realistic scattering scenarios? Existing physical models, although realistic, are intractable for addressing this problem analytically due to their complicated nonlinear dependence on propagation path parameters, such as the angles of arrival and delays. In this paper, we leverage a recently introduced virtual representation of physical models that is essentially a Fourier series representation of wide-band MIMO channels in terms of fixed virtual angles and delays. Motivated by physical considerations, we propose a D-connected model for correlated channels defined by a virtual spatial channel matrix consisting of D nonvanishing diagonals with independent and identically distributed (i.i.d.) Gaussian entries. The parameter D provides a meaningful and tractable measure of the richness of scattering. We derive general bounds for the coherent ergodic capacity and investigate capacity scaling with the number of antennas and bandwidth. In the large antenna regime, we show that linear capacity scaling is possible if D scales linearly with the number of antennas. This, in turn, is possible if the number of resolvable paths grows quadratically with the number of antennas. The capacity saturates for linear growth in the number of paths (fixed D). The ergodic capacity does not depend on frequency selectivity of the channel in the wide-band case. Increasing bandwidth tightens the bounds and hastens the convergence of scaling behavior. For large bandwidth, the capacity scales linearly with the signal-to-noise ratio (SNR) as well. We also provide an explicit characterization of the wide-band slope recently proposed by Verdu. Numerical results are presented to illustrate the key theoretical results.

Selective broadcast schemes for point-to-multiple point transmission of identical information are studied for a CDMA wireless system. The channel states for all selected users are assumed known at both the transmitter and the receivers. The goal is to find signaling schemes that satisfy the received SNR requirement at all desired users while minimizing total transmit power. We solve for the optimal transmit signature code and receive filters by developing Iterative Least Distance Programming (ILDP) and Linear Programming (LP) algorithms. We show that the optimal selective broadcast scheme is more power efficient than simple broadcast schemes and is robust against modest channel estimate delays.

We analyze space-time block codes for transmit diversity utilization from a signal processing viewpoint. The study shows that space-time block codes are not able to efficiently exploit all available signal space dimensions. In particular, the rate limitation of space-time block codes incurs a large capacity penalty. We propose a novel signal processing technique, layered transmit diversity, which achieves full rate transmission. The technique combines interference cancellation processing in the Bell Laboratory Layered Space-Time (BLAST) architecture and space-time block coding to jointly process real and imaginary parts of received signals. it is shown that layered transmit diversity can approach channel capacity.

The key to reliable communication is a fundamental understanding of the interaction between the signal space and the channel. In time- and frequency-selective multi-antenna (space-time) fading channels this interaction happens in time, frequency and space. In this paper we propose a four-dimensional Karhunen-Loeve-like Fourier series representation for space-time channels that captures the essence of such interaction and exposes the intrinsic degrees of freedom in the channel. The four dimensions are: time, frequency and the two spatial dimensions at the transmitter and receiver. The key signal space parameters are the signaling duration, bandwidth and the two array apertures. The corresponding channel parameters are the delay, Doppler and the two angular spreads associated with the scattering environment. The representation induces a virtual partitioning of propagation paths in time, frequency and space that reveals their contribution to channel capacity and diversity. It also exposes fundamental dependencies between time, frequency and space thereby revealing the essential independent degrees of freedom in the channel.

We propose a low complexity receiver structure for a multiple transmit antenna, multiple receive antenna (MIMO) system in the EDGE environment. In such a MIMO system, independent data streams are transmitted through different transmit antennas. In the proposed low complexity receiver structure, these data streams are separated and detected individually. The signal separation at the receiver is performed by the space-time interference cancellation filters. Each filter has a target data stream and intends to maximize the signal to interference and noise ratio (SINR) of that target data stream. Each filter is followed by a prefilter and a decision feedback sequence estimator (DFSE) which includes a feedback filter and a MAP sequence estimator. The maximum SINR (MSINR) interference cancellation comes in two flavors: blind and explicit methods. The blind MSINR method was first proposed in Liang et al. (1997) as a two-stage co-channel interference (CCI) suppression method with multiple receive antennas. We show that the blind MSINR method can be directly applied in the MIMO context and also derive another variation of the MSINR method, which we term the explicit MSINR method. While both methods achieve decent performance at low complexity, the explicit method utilizes the knowledge of all the training sequences and performs better than the blind method.

Optimal multi-antenna wide-band signaling schemes are derived for multipath channels assuming perfect channel state information at the transmitter. The scheme that minimizes the bit-error probability in the single-user case is a rank-one space-time beamformer which focuses the signal transmission in the direction of the most dominant channel mode. Several suboptimal variations are discussed for multiuser applications. The optimal signaling scheme given channel statistics at the transmitter is also derived. The optimal scheme in this case is a full-rank space-time beamformer that transmits on all channel modes. Analysis and simulation results are used to compare the schemes proposed in this paper. Finally, we discuss the optimal signaling scheme when a delayed version of the channel state is available at the transmitter. It is shown that in this case the optimal scheme is a rank-1 beamformer when the channel variations are sufficiently slow and is a full rank beamformer in a sufficiently fast fading channel.

We propose a decentralized space-time multiuser detection scheme based on the notion of canonical space-time coordinates (CSTCs) for representing the received signal. The CSTC representation provides a natural framework for decentralized multi-access interference (MAI) suppression in lower dimensional subspaces that results in complexity reduction relative to existing chip rate filtering schemes. The framework is based on a partitioning of the signal space into active and inactive CSTCs. The active CSTCs contain the signal of the desired user, facilitate maximal diversity exploitation and minimal complexity interference suppression. The inactive CSTCs only contain MAI and can be included progressively to attain a desired level of MAI suppression at the cost of increased complexity. We develop CSTC-based linear coherent multiuser detectors using the linearly constrained minimum variance (LCMV) criterion. We characterize the set of inactive coordinates and analyze the performance of the LCMV receiver as a function of the number of inactive CSTCs. Channel estimation and detector sensitivity to channel estimation errors are discussed. We demonstrate that the low-complexity adaptive receivers designed via the CSTC framework are more robust to channel estimation errors than existing chip-domain filtering schemes.

We introduce a new signaling scheme for time- and frequency-selective channels that is a generalization of multi-carrier code division multiple access (MC-CDMA) signaling used in slowly time-varying channels. The Fourier basis functions used in conventional MC-CDMA systems encounter temporal distortion in rapidly time-varying channels resulting in degraded performance. The proposed scheme transmits the data over a set of orthonormal time-frequency basis functions whose time-frequency support is matched to the coherence time and bandwidth of the channel. The time-frequency signaling scheme approximately diagonalizes the time-varying multipath channel and each basis function encounters flat Rayleigh fading. We derive an optimal choice of basis parameters that yield the most accurate diagonalization for given multipath and Doppler spreads of the channel. The proposed system fully exploits the diversity afforded by the channel and delivers improved performance in rapidly time-varying channels in contrast to degraded performance of existing systems under such conditions.

An orthogonal decomposition of a general wideband space-time multipath channel is derived assuming antenna arrays at both the transmitter and receiver. This decomposition provides a framework for efficiently managing the available space-time channel dimensions using channel state information at the transmitter and receiver. Signaling and receiver designs for high-throughput applications are derived using this decomposition. For a fixed-throughput system, we investigate a power allocation scheme that minimizes the effective bit-error rate. In addition, a strategy to maximize the average throughput is discussed.

Accurate and tractable channel modeling is critical to realizing the full potential of antenna arrays in wireless communications. We propose a framework for modeling multi-antenna multipath channels based on the notion of virtual spatial angles. The virtual angles are fixed a priori and are determined by the number of antennas at the transmitter and receiver and the spacing between the antennas. The model essentially corresponds to a coordinate transformation via fixed spatial basis functions at the transmitter and receiver. The resulting linear virtual channel representation encompasses all existing models and provides a natural link between the physical propagation environment and the channel statistics induced by it. For any given scattering environment, the model facilitates realistic estimates of channel capacity and clearly reveals the two key parameters affecting capacity: the number of parallel channels and the level of diversity.

Reliable coherent communication over multipath wireless channels requires accurate estimation of time-varying channel parameters. For coherent estimation, a key channel characteristic is the coherence time that approximately corresponds to the interval over which the channel parameters remain strongly correlated. We address linear MMSE estimation of code division multiple access (CDMA) multipath channels based on a pilot transmission. We derive a simple characterization of the estimator in terms of a bank of filters. We show that the estimator performance is primarily governed by an effective SNR that is proportional to the coherence time. We also propose two suboptimal estimators that are easy to implement and demonstrate that they deliver near-optimal performance if properly designed.

A spread-spectrum spatio-temporal signaling scheme based on electric field polarization is proposed. The information symbol is transmitted via two perpendicular transverse electric field components, each with a unique signature sequence. At the receiver, all three electric field components are measured. It is demonstrated that polarization signaling provides another degree of freedom for increasing spatial diversity to improve the performance of the wireless link.

The time scale over which a channel is observed determines whether a deterministic or statistical characterization is appropriate. We show that the channel estimation algorithm of Tsatsanis and Xu (see Proc. 31st Conf. Inform. Sci. Systems (CISS) John Hopkins Univ., Baltitmore, MD, p.724-29, 1997) and the acquisition algorithm of Sayeed and Aazhang (see Proc. 91st Conf. Inform. Sci. Systems (CISS) Princeton, NJ, 1998) share a common MMSE formulation. They differ only in the assumption of the channel characterization. From this observation we develop a new blind MMSE interference resistant algorithm for both timing acquisition and channel estimation that is applicable to both deterministic and statistical channel models. Simulations illustrate the effectiveness of the new method.

The mobile wireless channel affords inherent diversity to combat the effects of fading. Existing code-division multiple-access systems, by virtue of spread-spectrum signaling and RAKE reception, exploit only part of the channel diversity via multipath combination. Moreover, their performance degrades under fast fading commonly encountered in mobile scenarios. In this paper, we develop new signaling and reception techniques that maximally exploit channel diversity via joint multipath-Doppler processing. Our approach is based on a canonical representation of the wireless channel, which leads to a time-frequency generalization of the RAKE receiver for diversity processing. Our signaling scheme facilitates joint multipath-Doppler diversity by spreading the symbol waveform beyond the intersymbol duration to make the channel time-selective. A variety of detection schemes are developed to account for the intersymbol interference (ISI) due to overlapping symbols. However, our results indicate that the effects of ISI are virtually negligible due to the excellent correlation properties of the pseudorandom codes. Performance analysis also shows that relatively small Doppler spreads can yield significant diversity gains. The inherently higher level of diversity achieved by time-selective signaling brings the fading channel closer to an additive white Gaussian noise channel, thereby facilitating the use of powerful existing coding techniques for Gaussian channels.

Multiple-access interference (MAI) and time-varying multipath effects are the two most significant factors limiting the performance of code-division multiple-access (CDMA) systems. While multipath effects are exploited in existing CDMA systems to combat fading, they are often considered a nuisance to MAI suppression. We propose an integrated framework based on canonical multipath-Doppler coordinates that exploits channel dispersion effects for MAI suppression. The canonical coordinates are defined by a fixed basis derived from a fundamental characterization of the propagation effects. The basis corresponds to uniformly spaced multipath delays and Doppler shifts of the signaling waveform that capture the essential degrees of freedom in the received signal and eliminate the need for estimating arbitrary delays and Doppler shifts. The framework builds on the notion of active coordinates that carry the desired signal energy, facilitate maximal exploitation of channel diversity, and provide minimum-complexity MAI suppression. Progressively powerful multiuser detectors are obtained by incorporating additional inactive coordinates carrying only MAI. Signal space partitioning in terms of active/inactive coordinates provides a direct handle on controlling receiver complexity to achieve a desired level of performance. System performance is analyzed for two characteristic time scales relative to the coherence time of the channel. Adaptive receiver structures are identified that are naturally amenable to blind implementations requiring knowledge of only the spreading code of the desired user.

A canonical space-time characterization of mobile wireless channels is introduced in terms of a fixed basis that is independent of the true channel parameters The basis captures the essential degrees of freedom in the received signal using discrete multipath delays, Doppler shifts, and directions of arrival (DOA). The canonical representation provides a robust representation of the propagation dynamics and eliminates the need for estimating delay, Doppler and DOA parameters of different multipaths, Furthermore, it furnishes a natural framework for designing low-complexity space-time receivers. Single-user receivers based on the canonical channel representation are developed and analyzed, It is demonstrated that the resulting canonical space-time receivers deliver near-optimal performance at substantially reduced complexity compared to existing designs.

We propose a canonical space-time receiver structure for wireless communications based on front-end processing with respect to a fixed basis that is independent of the true channel parameters. The basis is dictated by a canonical characterization of channel propagation dynamics in terms of discrete multipath delays, Doppler shifts, and directions of arrival that capture the essential degrees of freedom in the received signal. In addition to dramatically reducing the number of channel parameters to be estimated, performance analysis demonstrates that canonical space-time receivers can deliver optimal performance at substantially reduced complexity compared to existing designs.

A design framework for space-time multiuser detectors is introduced based on the notion of canonical space-time coordinates (CSTC). The CSTC system employs a fixed set of basis signals which eliminates the need for estimating direction of arrivals (DOAs) and delays of the channel, thereby allowing significant reduction in receiver complexity. The proposed framework is based on a hybrid structure for multiuser detection which combines the power of centralized processing and the flexibility of decentralized reception. In the first stage, a subset of users whose spreading codes are assumed known are suppressed in a centralized fashion. The remaining interference is suppressed via the second stage in an adaptive decentralized mode. The hybrid scheme offers a flexible design framework by offering lower complexity compared to fully centralized receivers and improved adaptive performance compared to fully decentralized schemes.

We introduce a new approach for achieving diversity in spread-spectrum communications over fast-fading multipath channels. The RAKE receiver used in existing systems suffers from significant performance degradation due to the rapid channel variations encountered under fast fading. We show that the Doppler spread induced by temporal channel variations in fact provides another means for diversity that can be further exploited to combat fading. We develop the concept of Doppler diversity and propose a framework that exploits joint multipath-Doppler diversity in an optimal fashion. Performance analysis shows that even the relatively small Doppler spreads encountered in practice can be leveraged into significant diversity gains via our approach. The framework is applicable in several mobile wireless multiple access systems and can provide substantial performance improvement over existing systems.

We present a new framework for code-division multiple access (CDMA) communication over fast fading mobile wireless channels. The performance of the RAKE receiver, which is at the heart of existing CDMA systems, degrades substantially under fast fading encountered in many mobile scenarios. Due to the time-varying nature of the fast fading channel, we employ joint time-frequency processing, which is a powerful approach to time-varying signal processing. Whereas the RAKE receiver exploits multipath diversity to combat fading, our framework is based on joint multipath-Doppler diversity facilitated by a fundamental time-frequency decomposition of the channel into independent flat fading channels. Diversity processing is achieved by a time-frequency generalization of the RAKE receiver which can be leveraged into several important aspects of system design. Performance analysis shows that CDMA systems based on the time-frequency RAKE receiver, due to their inherently higher level of diversity, can potentially deliver significant performance gains over existing systems.

We propose a new framework for multiuser detection in fast-fading channels that are encountered in many mobile communication scenarios. Existing multiuser RAKE receivers, developed to combat multipath fading and multiuser interference in slow fading, suffer substantial degradation in performance under fast fading due to errors in channel state estimation. The detectors proposed in this paper employ a novel receiver structure based on time-frequency (TF) processing that is dictated by a canonical representation of the wide-sense stationary uncorrelated scatterer (WSSUS) channel model. The workhorse of the framework is a TF generalization of the RAKE receiver that exploits joint multipath-Doppler diversity. Analytical and simulated results based on realistic fast-fading assumptions demonstrate that the proposed multiuser detectors promise substantially improved performance compared to existing systems due to the inherently higher level of diversity afforded by multipath-Doppler processing.

In many practical detection and classification problems, the signals of interest exhibit some uncertain nuisance parameters, such as the unknown delay and Doppler in radar. For optimal performance the form of such parameters must be known and exploited as is done in the generalized likelihood ratio test (GLRT). In practice, the statistics required for designing the GLRT processors are not available a priori and must be estimated from limited training data. Such design is virtually impossible in general due to two major difficulties: identifying the appropriate nuisance parameters and estimating the corresponding GLRT statistics. We address this problem by using results that relate joint signal representations (JSRs), such as time-frequency and time-scale representations, to quadratic GLRT processors for a wide variety of nuisance parameters. We propose a general data-driven framework that: (1) identifies the appropriate nuisance parameters from an arbitrarily chosen finite set, and (2) estimates the second-order statistics that characterize the corresponding JSR-based GLRT processors.

Reliable detection of engine knock is an important issue in the design and maintenance of high performance internal combustion engines. Cost considerations dictate the use of vibration signals, measured at the engine block, for knock detection. Conventional techniques use the energy in a bandpass filtered version of the vibration signal as a measure. However, the low signal-to-noise ratio (SNR) in the vibration measurements significantly degrades the performance of such bandpass energy detectors. We explore the design and application of more general quadratic detection procedures, including time-frequency methods, to this challenging problem. We use statistics estimated from labeled training data to design the detectors. Application of our techniques to real data shows that such detectors, by virtue of their flexible structure, improve the effective SNR, thereby substantially improving the detection performance relative to conventional methods.

Generalized joint signal representations (JSRs) extend the scope of joint time-frequency representations (TFRs) to a richer class of nonstationary signals, but their use, just as in the case of TFRs, has been primarily limited to qualitative, exploratory data analysis. To exploit their potential more fully, JSR-based statistical signal processing techniques need to be developed that can be successfully applied in real-world problems. We present an optimal detection framework based on arbitrary generalized quadratic JSRs, thereby making it applicable in a wide variety of detection scenarios involving nonstationary stochastic signals, noise and interference. For any given class of generalized JSRs, we characterize the corresponding class of detection scenarios for which such JSRs constitute canonical detectors, and derive the corresponding JSR-based detectors. Our formulation also yields a very useful subspace-based interpretation in terms of corresponding linear JSRs that we exploit to design optimal detectors based on only partial signal information.

Generalized joint signal representations extend the scope of joint time-frequency representations to a richer class of nonstationary signals. Cohen's marginal-based generalized approach is canonical from a distributional viewpoint, whereas, in some other applications, for example, in a signal detection framework, a covariance-based formulation is needed and/or more attractive. We present a canonical covariance-based recipe for generating generalized joint signal representations. The method is highlighted by its simple characterization and interpretation, and naturally extends the concept of the corresponding linear representations.

Time-frequency based methods, particularly quadratic (Cohen's-class) representations, are often considered for detection in applications ranging from sonar to machine monitoring. We propose a method of obtaining near-optimal quadratic detectors directly from training data using Fisher's optimal linear discriminant to design a quadratic detector. This detector is optimal in terms of Fisher's scatter criterion as applied to the quadratic outer product of the data vector, and in early simulations appears to closely approximate the true optimal quadratic detector. By relating this quadratic detector to an equivalent operation on the Wigner distribution of a signal, we derive near-optimal time-frequency detectors. A simple example demonstrates the excellent performance of the method.

Joint time-frequency representations have proven very useful for analyzing signals in terms of time-frequency content. In an attempt to tailor joint representations to a richer class of signals, two approaches (Cohen's (1991) and Baraniuk's (see Proc. ICASSP 1993, p.III-320, 1993)) to obtaining joint representations of arbitrary variables have been proposed. Baraniuk's generalization appears broader than Cohen's, since the latter can be recovered from the former as a special case. One of the main results of this paper is that, despite being apparently quite different, the two approaches to generalized joint representations are exactly equivalent. We explicitly characterize the mapping which relates the representations of the two methods, and also determine the corresponding relationship between the operators of the two methods. A practical implication of the results is that one can avoid the group transforms in Baraniuk's approach, which may not be computationally efficient, by replacing them with Fourier transforms in Cohen's method.

Current theories of a time-varying spectrum of a nonstationary process all involve, either by definition or by implementation, an assumption that the signal statistics vary slowly over time. This restrictive quasi-stationarity assumption limits the use of existing estimation techniques to a small class of nonstationary processes. We overcome this limitation by deriving a statistically optimal kernel, within Cohen's (1989) class of time-frequency representations, for estimating the Wigner-Ville spectrum of a nonstationary process. Both time-frequency invariant and time-frequency varying kernels are derived. It is shown that, in the presence of any noise, optimal performance requires a nontrivial kernel, and that optimal estimation may require smoothing filters very different from those based on a quasi-stationarity assumption. An example illustrates that the optimal estimators can potentially yield tremendous improvements in performance over existing methods.>