There exists a gap in terms of the signals provided by pacemakers (i.e., intracardiac electrogram (EGM)) and the signals doctors use (i.e., 12-lead electrocardiogram (ECG)) to diagnose abnormal rhythms. Therefore, the former, even if remotely transmitted, are not sufficient for doctors to provide a precise diagnosis, let alone make a timely intervention. To close this gap and make a heuristic step towards real-time critical intervention in instant response to irregular and infrequent ventricular rhythms, we propose a new framework dubbed RT-RCG to automatically search for (1) efficient Deep Neural Network (DNN) structures and then (2) corresponding accelerators, to enable R eal- T ime and high-quality R econstruction of E C G signals from E G M signals. Specifically, RT-RCG proposes a new DNN search space tailored for ECG reconstruction from EGM signals and incorporates a differentiable acceleration search (DAS) engine to efficiently navigate over the large and discrete accelerator design space to generate optimized accelerators. Extensive experiments and ablation studies under various settings consistently validate the effectiveness of our RT-RCG. To the best of our knowledge, RT-RCG is the first to leverage neural architecture search (NAS) to simultaneously tackle both reconstruction efficacy and efficiency.

Multi-user MIMO (MU-MIMO) is a technique that improves spectral efficiency by allowing concurrent communication between one access point (AP) and multiple clients. In practice, the expected gain is not always achieved and is sometimes even negative. We experimentally demonstrate that the downlink MU-MIMO performance in a practical network not only depends on the client's channel but is also influenced by factors that are not captured by conventional models, such as client motion and device type. We propose a data-driven algorithm with a low computational complexity that determines whether a client should operate in MU mode and the MU-MIMO group for clients in MU mode. Such a mode and group selection algorithm is based on a sequence of channel state information (CSI), SNR, and client device type. The algorithm can automatically adapt to the motion and characteristics of individual clients. Experimental results using implementation on a commodity 802.11ac AP show that the proposed data-driven mode and group selection algorithm can improve network throughput by up to 35% over existing algorithms based on conventional models. We also show that the proposed data-driven algorithm has limited sensitivity to environmental changes and can be deployed into new environments without retraining.

Multi-User Multiple-Input and Multiple-Output (MU-MIMO) is a technique that allows concurrent transmissions between one access point (AP) and multiple clients to improve spectral efficiency. In practice, however, the MU-MIMO is sensitive to client mobility and is sometimes even harmful to the performance in networks with moving clients. In this paper, we identify that it is essential to optimize the MU-MIMO performance with moving clients by jointly selecting the sounding period, the number of spatial streams, and client grouping with the consideration of the client density of the network. We develop a data-driven model that estimates client throughput with the consideration of these parameters, as well as an algorithm that jointly determines the parameters for each client with low computational complexity. Using a commodity 802.11ax network, we experimentally demonstrate the significant impact of the key factors on MU-MIMO performance. Based on experimental data, we develop an emulation model to evaluate network performance with different client densities and mobility. Emulation results show that our proposed algorithm outperforms conventional schemes by over 20% in MU-MIMO networks with moving clients.

Low-intensity focused ultrasound (LIFU) has been shown to modulate neural activity. Recent experiments suggest potential applications of LIFU stimulation for treating neuropsychiatric disorders like depression and Alzheimer's. The modulation effect is usually positively correlated with the ultrasound intensity, and there exists a minimum intensity threshold for the neuromodulation to be effective. Therefore, precise configuring of the ultrasound transducer is required to sonicate the target brain region at the desired intensity with appropriate spatial resolution. In this study, we investigate the optimization of targeting through fine temporal and spatial power delivery control of a phased array of ultrasound elements. A novel metric of the ultrasound neuromodulation resolution is proposed, and an optimization problem is formulated and solved to minimize side effects in the form of off-target region sonications. Simulation results show that our method is able to significantly improve the focusing resolution compared to the benchmark and reduce the volume experiencing possible off-target neuromodulation.

We propose a novel approach to filter bank learning for time-series by considering spectral decompositions of signals defined as a Group Transform. This framework allows us to generalize classical time-frequency transformations such as the Wavelet Transform, and to efficiently learn the representation of signals. While the creation of the wavelet transform filter-bank relies on affine transformations of a mother filter, our approach allows for non-linear transformations. The transformations induced by such maps enable us to span a larger class of signal representations, from wavelet to chirplet-like filters. We propose a parameterization of such a non-linear map such that its sampling can be optimized for a specific task and signal. The Learnable Group Transform can be cast into a Deep Neural Network. The experiments on diverse time-series datasets demonstrate the expressivity of this framework, which competes with state-of-the-art performances.

We provide the first frame agnostic thresholding scheme based on risk minimization, which can be applied to arbitrary frames and provide its theoretical guarantees. We investigate the proposed scheme, study its empirical risk, and demonstrates how it falls back to the standard Donoho thresholding scheme for orthogonal basis. We then validate our technique and apply it to the overcomplete wavelet transforms of the Deep Scattering Network. We are thus obtaining an invariant and thresholded representation of the signals providing significant performance gains compared to the non-thresholded version.

In fifth generation (5G) cellular systems with massive MIMO, coherent hybrid beamforming with phased arrays can be used to achieve high beamforming gain with low system complexity. Typically, hybrid beamforming systems require beam training between the base station (BS) and mobile users to optimize the beamforming coefficients, which causes extra overhead. For avoiding this overhead, long-term beamforming methods are considered to design beams that do not frequently change to serve a specific region over a long period. A framework is hence necessary to acquire the user distribution and apply it for beam design. However, in the absence of beam training, standard localization schemes usually require external assistance or incur extra measurement cost. We propose a framework called Beamforming with Iterative Traffic Sensing (BITS), which alternately infers the active user distribution based on celllevel sum network spectral efficiency and optimizes the beams accordingly. The sum network spectral efficiency can be readily measured during data transmission periods with no extra communication overhead. Simulation results show quick and significant performance improvement when we infer the user distribution with sparsity using Key Performance Indicators (KPIs) that are available to the BS and iteratively improve the beamforming.

We study the geometry of deep (neural) networks (DNs) with piecewise affine and convex nonlinearities. The layers of such DNs have been shown to be max-affine spline operators (MASOs) that partition their input space and apply a region-dependent affine mapping to their input to produce their output. We demonstrate that each MASO layer's input space partitioning corresponds to a power diagram (an extension of the classical Voronoi tiling) with a number of regions that grows exponentially with respect to the number of units (neurons). We further show that a composition of MASO layers (e.g., the entire DN) produces a progressively subdivided power diagram and provide its analytical form. The subdivision process constrains the affine maps on the potentially exponentially many power diagram regions with respect to the number of neurons to greatly reduce their complexity. For classification problems, we obtain a formula for a MASO DN's decision boundary in the input space plus a measure of its curvature that depends on the DN's nonlinearities, weights, and architecture. Numerous numerical experiments support and extend our theoretical results.

Due to abundant frequency resources, millimeter wave (mm-wave) spectrum has drawn much attention as a solution to bandwidth scarcity. However, many characteristics of mm-wave transmissions, such as blockage and reduced coverage, make conventional network architectures very inefficient for use in mm-wave networks. A recently proposed multi-tier mm-wave network architecture allows for relaying around blockages and enlarges the coverage of each base station at an acceptable deployment cost. Nevertheless, this architecture introduces major challenges to the scheduling of each tier. The necessity of both enabling flexible user association and fully exploiting the wireless backhaul requires a cross-tier consideration of the multi-tier mm-wave network. We comprehensively analyze the scheduling problem of a downlink multi-tier mm-wave network by jointly regulating the transmissions in all tiers. The cross-tier optimization problem is NP-hard, but a sub-optimal scheme which iteratively optimizes the schedule in different tiers of the network is proposed with polynomial computational complexity. Simulation results show that our algorithm significantly outperforms the benchmarks in both spectral efficiency and fairness with various user distributions.

Service provision over wireless networks is a key performance criterion, yet an onerous task due to the stochastic nature of channels, transmission overhead, and service delay requirements. This paper considers services differentiated by preference without benefit or penalty for early or delayed completion, instead a benefit exists for maintaining the average delay of completed services below a predefined limit. The average delay is constrained at each network instance via joint optimization of probing order and transmission decisions, resulting in a nonlinear expanding-then-collapsing optimization constraint. A permutation in the transmission order does not impact the sum delay but can impact the average delay. Therefore, finding the optimal order is paramount for proper service provision. A particular greedy ordering is shown to reduce the set of feasible solutions without losing global optimality. Practical solutions are proposed via stochastic programming formulation and an optimal stopping strategy that does not use a priori knowledge. The stopping strategy results in a set of thresholds, which can be practically computed a priori and implemented in a decentralized manner. Simulations show that our proposed Dantzig inspired stopping strategy achieves near optimal sum service value with higher throughput than a stochastic programming formulation.

In this paper, we consider rate maximization of a single full-duplex (FD) massive MIMO base station (BS) with multiple downlink (DL) and uplink (UL) users. The BS applies transmit precoders on the DL transmission. These precoders are designed to reduce the multiuser interference among DL transmissions and to reduce the self-interference (SI) level from the DL transmissions at the BS UL receiving antennas. The self-interference is reduced by zero- nulling the DL transmissions at some of the UL receiving antennas. We derive lower bounds on the achievable DL and UL capacities. Based on the derived bounds, we optimize over the ratio of the transmit to receive antennas at the base station to maximize the achievable capacities. We also optimize over the portion of UL receive antennas that are zero-nulled by the DL transmit precoders to limit the effect of SI on the UL transmissions. Two different formulations of the rate region maximization problem are presented. The first formulation, which maximizes the UL rate for a given DL rate, is proved to be a convex optimization problem; for this formulation, an exact solution for the optimization problem is derived. The second formulation, which maximizes the DL rate for a given UL rate, is proved to be non-convex; therefore, the dual problem is formulated and solved. Numerical results validate the derived DL and UL bounds as well as the proposed rate maximization solutions.

Recent work has proposed the integer-forcing (IF) linear receiver architecture as a promising alternative to the joint maximum likelihood (ML) receiver. It has been proven that the IF linear receiver can operate very close to the (optimal) performance of the joint ML receiver, but with essentially the same implementation complexity as a zero-forcing (ZF) linear receiver. In this paper, we take the first steps towards a complete software-defined radio (SDR) implementation of the IF linear receiver. Using the Wireless Open-Access Radio Platform (WARP) and IEEE 802.11 protocols, we develop an OFDM-based experimental framework to evaluate the performance of IF linear receivers in realistic indoor settings, and compare it to the performance of ZF and joint ML receivers. Our framework includes a channel estimation protocol and algorithm for selecting the best integer matrix for approximating the channel matrix. We have performed indoor experiments for a 2 × 2 MIMO network, which demonstrate that the symbol error rate (SER) of the IF linear receiver indeed outperforms the ZF linear receiver and can operate close to the joint ML receiver. We also argue, via simulations, that IF continues to outperform conventional linear receivers, even in the presence of significant channel estimation errors.

Migrating to higher frequencies using millimeter wave (mmWave) signaling will expand the networks capacity to satiate the current demand for higher throughput. However, the overhead cost required for a centralized scheduler to function in an mmWave network quickly becomes intractable as user and access point (AP) density increase. Alternatively, a decentralized approach where users in mmWave networks opportunistically transmit may greatly benefit from a higher AP density. Taking advantage of the AP diversity projected for mmWave networks a user may sequentially probe APs before selecting a destination AP for transmission. An opportunistic user in an mmWave network must balance the benefit of AP diversity against the overhead cost. We present an mmWave opportunistic network model encompassing the probability of an AP becoming unavailable and the cost of initial access. Our optimal opportunistic strategy is a set of thresholds, which are computable a priori. Bounds on average overhead, delay and throughput of our strategy are also presented. Via numerical analysis, we show that at finite and relatively small probings our proposed strategy outperforms practical alternatives.

We derive the optimal signaling for a multiple input multiple output (MIMO) full-duplex (FD) two-way channel under imperfect transmit front-end chains. We characterize two-way rates of the channel by using a game-theoretical approach, where we focus on the Pareto boundary of the achievable rate region and the Nash equilibrium (NE). For a MIMO FD channel, the Pareto boundary achieves the global optimality. However, deriving the Pareto boundary amounts to solving a family of centralized non-convex problems. By introducing auxiliary variables, we decouple and convert the Pareto boundary into a family of convex problems, which enables us to obtain the Pareto boundary with low computational complexity. In a MISO FD two-way channel, we further present a closed-form expression for the Pareto-optimal signaling. In our numerical examples, we quantify gains in the achievable rates of the Pareto-optimal signaling over the zero-forcing beamforming and NE. For a distributed MIMO FD channel, we establish the existence of NE and present a condition for the uniqueness of NE. We then propose an iterative water-filling algorithm, which is capable of reaching the NE. Through simulations, the threshold of the self-interference level is found below which the FD NE outperforms the half-duplex TDMA.

Integer-forcing (IF) precoding, also known as downlink IF, is a promising new approach to communication over multiple-input multiple-output (MIMO) broadcast channels. Inspired by the integer-forcing linear receiver for multiple-access channels, it generalizes linear precoding by inducing an effective channel matrix that is approximately integer, rather than approximately identity. Combined with lattice encoding and a pre-inversion of the channel matrix at the transmitter, the scheme has the potential to outperform any linear precoding scheme, despite enjoying similar low complexity. In this paper, a specific IF precoding scheme, called diagonally scaled exact IF (DIF), is proposed and shown to achieve maximum spatial multiplexing gain. For the special case of two receivers, in the high SNR regime, an optimal choice of parameters is derived analytically, leading to an almost closed-form expression for the achievable sum rate. In particular, it is shown that the gap to the sum capacity is upper bounded by 0.27 bits for any channel realization. For general SNR, a regularized version of DIF (RDIF) is proposed. Numerical results for two receivers under Rayleigh fading show that RDIF can achieve performance superior to optimal linear precoding and very close to the sum capacity.

This paper proposes a low-complexity scheme to construct Voronoi constellations for the shaping of high-dimensional lattice codes. The Voronoi region of a low-dimensional lattice is used as a prototype for the shaping region for a high-dimensional lattice codebook. The proposed scheme retains the shaping and coding gains of the respective lattices. Further, the proposed scheme provides a general approach for shaping popular high-dimensional lattices, including LDA lattices, for which no practical shaping algorithm exists to our knowledge. Finally, the proposed scheme preserves the algebraic properties of nested lattice codes, making it suitable for compute-and-forward applications. Using E8and BW16as prototype shaping lattices, we numerically show that the proposed scheme results in 0:65 dB and 0:86 dB shaping gains.

Future millimeter wave (mmWave) frequency networks leveraging great swaths of unlicensed bandwidth, dense access point deployments, and beamforming may satiate the current demand for higher throughput. In a dense network, a centralized scheduling approach becomes infeasible. Therefore a user may opportunistically transmit to one of the multiple access points (AP) in its vicinity. Leveraging the AP diversity, a user may probe several APs before selecting a destination for the transmission. However, it is possible that the destination AP becomes unavailable or is in blockage when the user decides to transmit due to the density of the network. We present a novel mm Wave opportunistic network model which encompasses the probability of an AP becoming unavailable. Our optimal opportunistic transmission strategy maximizes the throughput of an opportunistic user. Results show that when users are unwilling to bear large delays, our strategy outperforms alternative methods. Additionally, our strategy performs equally to alternatives when users can shoulder the burden of delay.

We propose two low-complexity lattice code constructions that have competitive coding and shaping gains. The first construction, named systematic Voronoi shaping, maps short blocks of integers to the dithered Voronoi integers, which are dithered integers that are uniformly distributed over the Voronoi region of a low-dimensional shaping lattice. Then, these dithered Voronoi integers are encoded using a high-dimensional lattice retaining the same shaping and coding gains of lowand high-dimensional lattices. A drawback to this construction is that there is no isomorphism between the underlying message and the lattice code, preventing its use in applications such as compute-and-forward. Therefore, we propose a second construction, called mixed nested lattice codes, in which a high-dimensional coding lattice is nested inside a concatenation of low-dimensional shaping lattices. This construction not only retains the same shaping/coding gains as first construction but also provides the desired algebraic structure. We numerically study these methods, for point-to-point channels as well as compute-and-forward using low-density lattice codes as coding lattices and E8 and Barnes-Wall as shaping lattices. Numerical results indicate a shaping gain of up to 0.86 dB, compared with the state-ofthe-art of 0.4 dB; furthermore, the proposed method has lower complexity than the state-of-the-art approaches.

We propose a class of signaling schemes that leverage transmitter cooperation in wireless networks employing compute-and-forward or physical-layer network coding. We devise a lattice-coding approach to superposition block Markov encoding from which we construct a cooperative lattice coding strategy. Transmitters broadcast lattice codewords, decode each other's messages, and then cooperatively transmit resolution information which aids relays in decoding finite-field linear combinations of the incoming messages. We show that cooperation provides a substantial improvement in achievable computation rate and outage probability over noncooperative strategies. Using this strategy, we derive a new achievability scheme for the multiway relay channel, the rates of which are near capacity in many regimes and enjoy a diversity advantage over noncooperation.

Wireless networks are evolving to meet the needs of transforming wireless services. The demands of wireless service users should guide the evolution of networks to be service centric, meaning towards greater and more efficient service provisioning capabilities. Users commonly abandon delayed services and many services are rendered useless due to delay. Such delays can be caused by collisions or the stochastic nature of wireless networks. Through scheduling, a wireless network can overcome these obstacles. To meet the need for timely services, we present a service centric scheduling framework aimed at maximizing service payoffs under strict deadlines. We consider three scenarios for the amount of network information available for scheduling: full, local, and statistical. An optimization framework under full network information is presented along with a method for deriving the optimal solution. With local information scenario, which is a more practical consideration than full information, we present a greedy strategy and an approach via optimal stopping theory to derive an optimal threshold to minimize the time to transmission. A fixed scheme and an opportunistic scheme are presented under the assumption that statistical network information is available alongside local information. Our opportunistic scheme maximizes the average service payoff. A complexity reducing technique which potentially decreases the required computations to make the optimal opportunistic decision is also presented. We evaluate the performance of the various schemes via simulations.

Directed information, an information theoretic quantity, is developed in this paper to infer the causal connectivity from electrocorticography (ECoG) recordings of an epileptic patient. The causal connectivity can be used to infer the optimal electrodes for electrical stimulation based treatments of epilepsy. A parametric estimator for directed information between two ECoG signals is also proposed. The estimator estimates entropy and causally conditioned entropy and their difference is the estimate of DI. The estimator is then applied to ECoG data recorded from the electrodes in the epileptogenic zone (EZ) in two patients with focal epilepsy to learn the changes in causal connectivity during seizures.

We model the self-interference in a multiple input single output (MISO) full-duplex two-way channel and evaluate the achievable rate region. We formulate the boundary of the achievable rate region termed as the Pareto boundary by a family of coupled, non-convex optimization problems. Our main contribution is decoupling and reformulating the original non-convex optimization problems to a family of convex semidefinite programming problems. For a MISO full-duplex two-way channel, we prove that beamforming is an optimal transmission strategy which can achieve any point on the Pareto boundary. Furthermore, we present a closed-form expression for the optimal beamforming weights. In our numerical examples we quantify gains in the achievable rates of the proposed beamforming over the zero-forcing beamforming.

We propose a reactive route discovery protocol for energy efficient transmission in a wireless multihop network with multiple input multiple output (MIMO) channels. We focus on networks consisting of MIMO nodes that use time division scheduling where the source needs to transmit a certain amount of data to the destination in a fixed amount of time. We show how the intermediate nodes find the route distributively. This protocol takes into account the quality of the MIMO channels and allocates power to them so that the end-to-end transmission energy is minimized. The resulting protocol is easy to implement and provides the most energy efficient route and the power allocation for the data transmission. We perform simulations on Rayleigh-fading channels to show the significant energy benefits of the proposed route discovery protocol against a dynamic source routing (DSR)-based routing protocol with optimal power allocation.

We propose a class of practical efficient lattice codes for real-valued full-duplex one- and two-way relay channels. First, we investigate the problem from a theoretical perspective, proposing lattice-coding instantiations of superposition block Markov encoding. Our encoding/decoding strategies recover the well-known decode-and-foward rates for the one-way relay channel and a previously-proven rate region for the two-way relay channel. Then, we construct practical, low-complexity implementations of these schemes using low-density lattice codes. Simulations show that our schemes achieve performance as close as 2.5 dB away from theoretical limits. Finally, we show that, due to features inherent to full-duplex relaying and practical codes, the gap to theoretical limits depends on the channel gains and transmit power of the relay relative to the source(s). We characterize this gap analytically, providing insight into the design of practical full-duplex relay systems.

Deep brain stimulation is a treatment for Parkinson's disease that uses electrical stimulation to modulate neural activity in order to reduce motor symptoms associated with the disease. The design of the electrical stimulation signal used is strongly linked to the efficacy of such a treatment. We present computational models of the brain structures impacted by Parkinson's disease which are modulated by electrical current injections from chronically implanted electrodes as a part of deep brain stimulation. This work demonstrates that a high frequency signal with small random deviations in pulse timing can simultaneously induce regularized activity associated with improved motor symptoms and permit greater variation in neural responses, which are necessary to encode neural information.

A lattice code construction that employs two separate lattices, a high dimension lattice for coding gain and a low-dimension lattice for shaping gain, is described. Systematic lattice encoding is a method to encode an integer sequence to a lattice point that is nearby that integer sequence. We describe the “Voronoi integers” ℤm/Λs, the set of integers inside the fundamental Voronoi region of a shaping lattice Λs, and a concrete scheme to label these integers. By first shaping the information using the Voronoi integers in low dimension, and then performing systematic lattice encoding using a high-dimension lattice, good shaping and coding gains can be simultaneously obtained. We concentrate on the case of using the E8lattice for shaping and low-density lattice codes (LDLC) with dimension ~ 10,000 for coding. While optimal shaping provides a well-known 1.53 dB gain, previously reported shaping gains with LDLC lattices are on the order of 0.4 dB. The proposed method preserves the shaping gain of the E8lattice, that is, as much as 0.65 dB. This shaping operation can be implemented with lower complexity than previous LDLC approaches.

Relay radios are used to improve the quality of point-to-point wireless links with respect to achievable rates and symbol error rates (SER). Under these metrics, the estimate-and-forward (EF) protocol has the best performance in a wide variety of cases. The EF protocol is defined as the relaying protocol in which the relay forwards an estimate of its received information. Although optimal estimates have been identified in the literature, an implementable detector at the receiver still remains to be found. In this paper, we solve this open problem by using a piecewise linear approximation of the minimum mean square error (MMSE) estimate (pLAM) of the received symbol at the relay. In the three-node cooperative wireless relay network, this new piecewise linear approximation leads to an analytical form of the detector at the destination. Furthermore, we show that the symbol error rates of this new framework closely approximate the true performance of EF when using a MMSE estimate of the received symbol at the relay. Finally, we provide several examples where we apply this new pLAM approach to multiple modulation schemes such as BPSK and 16-QAM, in both one- and two-way relay networks.

We study a wireless full-duplex network with imperfect interference cancellation and we solve the routing and power allocation problem for a single source to destination pair. Our interference model includes residual self-interference due to operating in full-duplex. We present a procedure to solve for the optimal power allocation of a given route with individual maximum power constraints for each node. The solution to the problem given a route involves finding polynomial roots of equations associated to the achieved rate at each hop. We then propose a modification to Dijkstra's algorithm with a priority metric that cannot be decoupled, but is efficiently solved by our procedure for a given route. The algorithm finds the joint route and power allocation that achieve the maximum throughput among all possible routes and power allocations. Through simulations we show that, even with imperfect interference cancellation, operating in full-duplex achieves a higher throughput than half-duplex or direct transmission for moderate maximum transmission power.

We study practical, efficient codes for the Gaussian relay channel. It has been demonstrated that low-density lattice codes (LDLCs) can provide near-capacity performance for point-to-point Gaussian channels. We present an LDLC formulation that provides performance near the decode-and-forward inner bound of the relay channel capacity. We employ a superposition block Markov strategy tailored to LDLCs and design an appropriate iterative decoder. We characterize the error performance via simulations, showing that our scheme achieves performance only 2dB away from the decode-and-forward bound.

We present a transmission energy efficient power allocation method for different end-to-end rates in a Multiple Input Multiple Output (MIMO) multihop network. This method is intended for a network consisting of MIMO nodes that use simple time division scheduling. We formulate the power allocation problem for the various degrees of freedom of MIMO hops as an energy minimization problem and present our iterative solution. Our method calculates the power allocations to the known routes for a requested data transmission time and takes the quality of the channels into account. We perform simulations to show the energy efficiency of these routes.

The joint routing and power allocation problem in a wireless full-duplex network with imperfect interference cancellation and a single source destination pair is solved. Our simplified interference model focuses on the effects of full-duplex by including residual self-interference and one hop interference while other interfering signals are assumed to be negligible. First, the optimal power allocation for a fixed route is identified. Then a modification of Dijkstra's algorithm is used to find the joint route and power allocation to maximize throughput. Due to interference, the algorithm proposed has a non decomposable objective function; however, it is efficiently solved for every candidate route. Our solution in a full interference model, that does not ignore any interference, is at most a constant bound away from the optimal solution in the full interference model. Through simulations we evaluate several scenarios and show the behavior of the solution in both interference models.

In an attempt to utilize spectrum resources more efficiently, protocols sharing licensed spectrum with unlicensed users are receiving increased attention. From the perspective of cellular networks, spectrum underutilization makes spatial reuse a feasible complement to existing standards. Interference management is a major component in designing these schemes as it is critical that licensed users maintain their expected quality of service. We develop a distributed dynamic spectrum protocol in which ad-hoc device-to-device users opportunistically access the spectrum actively in use by cellular users. First, channel gain estimates are used to set feasible transmit powers for device-to-device users that keeps the interference they cause within the allowed interference temperature. Then network information is distributed by route discovery packets in a random access manner to help establish either a single-hop or multi-hop route between two device-to-device users. We show that network information in the discovery packet can decrease the failure rate of the route discovery and reduce the number of necessary transmissions to find a route. Using the found route, we show that two device-to-device users can communicate with a low probability of outage while only minimally affecting the cellular network, and can achieve significant power savings when communicating directly with each other instead of utilizing the cellular base station.

We introduce an approach to gossip algorithms that exploits three aspects of the wireless medium: superposition, broadcast, and power control. Instead of sending pairwise messages between neighbors on a fixed network topology, we construct gossip algorithms in which nodes can simultaneously recover multiple neighbors' messages and in which nodes can adjust the set of their neighbors by adjusting transmit power. We present two averaging algorithms, each based on a hierarchical clustering of the network. In the first algorithm, clusters of nodes transmit their estimates locally and randomly select a representative node for communications at the next level. In the second, each cluster mutually averages and then cooperatively transmits at the next level. For path-loss environments, these schemes achieve order-optimal or near order-optimal performance.

We present a wide-area, multiflow ad-hoc network model leveraging information-theoretic rate control, emphasizing interfering rather than colliding transmissions. We seek to allocate resources in this network by optimizing scheduling, routing and power control to solve the max-min throughput problem for all flows involved. In general, our time-slotted, fully-interfering model leads to an NP-hard problem. Further, the rate-control element of the mixed-integer program results in a non-convex problem in the continuous domain. The complexity of the joint problem makes an optimal solution prohibitively difficult to find, leading us to propose a two-pronged approach to determine a near-optimal resource allocation. First, we propose a novel decomposition technique, breaking the joint problem into a sequence of more tractable subproblems. Second, we present a data structure serving multiple purposes: it compactly represents network conditions as they evolve with time, and also serves as the basis for our cubic-time dynamic programming algorithms used to solve and catalog the subproblems. The result is a schedule, route, and power allocation for all data frames involved. We demonstrate the performance of our techniques on the max-min throughput problem, while also showing that they are sufficiently general to apply to a wide variety of optimality criteria in which decisions over transmission schedules and packet routing must be made.

In this paper, we present the bit error probability (BEP) of a relay network employing UWB links between its nodes. Since UWB systems can resolve many paths and are thus rich in multipath diversity, the use of the Rake diversity combining is very effective. However, because of the complexity, it is impractical in the scenarios with portable terminals or in the networks with multiple relays. Time-reversal technique, in which the transmitting nodes can do the pre-diversity filtering of UWB signal before transmission, is known as an approach to achieve the performance equivalent to the Rake combining without increasing the receiver complexity. The performance of such a network with simple correlators for each link at the receiver side is analyzed considering some realistic channel estimation errors. The results show that there is a great potential in combining time reversal and UWB techniques with respect to both reducing the receiver complexity and improving the system performance. The system robustness to imperfect channel estimation is also shown in the numerical analysis and compared to traditional UWB system with All-rake receiver. The analytical expressions are also validated by computer simulations which confirm the accuracy of the approximations used in obtaining these results.

It has been conjectured that lattice codes are good for (almost) everything. As an additional bit of evidence for this claim, we offer a few results showing the utility of lattice codes for the AWGN relay channel. We show that the decode-and-forward rates of the relay channel can be achieved using lattice encoding and decoding. We present an encoding/decoding technique that uses a doubly-nested lattice code. Encoding is accomplished using a combination of superposition encoding and block Markov encoding, while decoding is accomplished using a strategy reminiscent of Cover and El Gamal's list decoding. Our technique can be extended to a wide variety of relay topologies, including the half-duplex relay channel and the cooperative multiple-access channel.

We study user cooperation in the context of physical-layer network coding. We examine a system in which users cooperatively transmit their messages to receivers whose task is to recover a finite-field linear combination of the users' messages. We present a cooperative scheme, based on a lattice-coding approach to block Markov encoding, that improves the computation rate over that of existing non-cooperative techniques. We apply our results to a simple relay network, showing that when inter-user gains are relatively strong, cooperative computation significantly improves network throughput.

Motivated by recent work applying lattice codes to physical-layer network coding, we study a system in which the receiver computes a finite-field linear combination of users' messages. Previous lattice techniques require that the linear combination be closely matched to the channel coefficients in order to achieve a non-trivial computation rate. To overcome this issue, we present a cooperative computation scheme based on a lattice-coding approach to block Markov encoding. In addition to improving the computation rate, the cooperative approach significantly increases the set of linear combinations that can be recovered at the receiver, increasing the flexibility of wireless network-coded systems.

We propose a quantizer design method for practical half-duplex estimate-and-forward (EF) relaying. First, we identify the regime in which EF relaying yields substantial gains where the SNR is low and the relay-destination link is strong. Then we discover design simplifications that reduce complexity with little loss in the above regime. For relay quantizer design, we first consider mean-squared distortion minimization. To illustrate the unsuitability of the approach, we present an example with AWGN links and a BPSK source where the quantizer with worst mean squared distortion in a given set maximizes achievable rate. A distortion-minimizing quantizer attempts to preserve the received signal at the relay. The quantizer should instead preserve source information. In information theoretical terms, the quantizer should maximize the mutual information between the source transmission and the quantizer output conditioned on the side information at the destination subject to a rate constraint. The above conclusion, derived from information theoretical principles, is then translated to a quantizer design method for the low SNR regime. Using LDPC codes of blocklength 100000, BPSK modulation, and quantizers designed using the proposed criterion, we observe performance less than a decibel away from the achievable rate at a BER of 10-4.

When designing distributed wireless networks utilizing shared bandwidth, a critical issue is allocating spatial and temporal resources to streaming information flows. We focus on large networks of half-duplex terminals sharing common bandwidth, and study methods for allocating resources on a fine-grained temporal basis, with specific emphasis on managing the interactions between streams of packets from the different flows. This is an NP-Hard interference management problem at the core, which we address with a novel data structure and polynomial-time algorithm. We show that our low-complexity interference management techniques deliver substantial performance improvements, as measured in either throughput or flow reliability.

User cooperation improves performance in wireless systems, but it requires other users to expend energy acting as relays. When energy is scarce, users have incentive to refuse to cooperate in order to conserve resources. Therefore, we investigate cooperative communications from an energy- efficiency perspective. We present a cellular framework in which two mobile users, who desire to communicate with a common base station, may cooperate via decode-and-forward relaying. We maximize users' bits-per-energy efficiency by defining the achievable bits-per-energy region and finding the power allocations that achieve its Pareto boundary. To find an efficient approach that gives selfish users incentive to cooperate, we apply game theory, finding the power allocations that achieve the Nash bargaining solution. Numerical results indicate that the Nash bargain provides a fair and efficient compromise and that both users obtain noticeably improved bits-per-energy efficiency via cooperation.

In this paper, the extension of cooperative communication to the context of TH-UWB is investigated. In particular, the average bit error probability (BEP) is provided for cooperative TH-UWB systems with decode-and-forward relaying protocol. In the considered relay network, UWB links among the nodes are modeled according to IEEE 802.15.4a standards. Our methodology is based on computing the characteristic function (CF) of the decision variable at the destination terminal. We use Gaussian quadrature numerical method to approximate the CF of interference component appeared in decision variable term. This technique permits to predict the system performance in different IEEE 802.15.4a defined channels with high accuracy and reasonable complexity. Numerical results show that significant improvement in the BEP of impulse radio UWB system is obtained by adding a relay node. The analytical expressions are also validated by computer simulations which confirm the accuracy of the approximations used in obtaining the BEP.

We analyze amplify-and-forward (AF) distributed space-time block coded (DSTBC) cooperative relaying systems over the random set relay channel (RSRC). A two-stage operation is considered where all terminals operate in half-duplex mode and where the source first transmits to a pool of N relays, each of which decides independently whether to relay the source's information to the destination or not, by comparing its own instantaneous received signal-to-noise ratio (SNR) to a threshold zeta. The K les N transmitting relays do so with constant transmit power per relay, and cooperate through linearly dispersed full-rate-full-diversity DSTBCs. The system concept is interesting in which no coordination amongst relays is required, and only backward channel state information (CSI) is assumed. We derive the mutual information (MI) achieved by such a scheme with Rayleigh fading at each channel branch and assuming perfect interleaving (ergodic channel). Then, we study the effect of the selected threshold onto achievableMI in the case where the source and each relay transmits with the same power. It is found that the maximal MI is not achieved under full-time-all-relay cooperation (K = N), despite the fact that the total receive power at the receiver increases with K. The maximum MI in this case can also be fitted to a simple function of N. Next, we investigate the effect of different power balances between the two transmission stages while fixing the total average transmit power. It is shown that the optimum power allocation depends on the threshold, such that the MI is maximized not with equal power allocation (and K = N), but rather with a power balance of around 2-to-3 and K < N, again, despite the fact that the total receive power at the receiver increases with K. Finally, we compare the maximum MI against the MI achieved with QPSK and QAM modulations, which reveals that the envelope behavior of the latter follows the same trend observed with the former.

We derive bounds on the expected capacity and outage capacity of a three-node relay network for UWB communications. We also provide a simple tight approximation for the derived upper bound on the capacity and then using this bound we obtain the outage probability of the network. Numerical results show that a significant improvement in the system capacity and outage probability is obtained by adding a relay node. Moreover, our theoretical results reveal that the diversity gain of a relay channel substantially increases by using UWB links instead of NB links. We also derive these bounds when we have a constraint on the total transmitted power of the source and the relay nodes.

We consider multiple-antenna communication systems in Rayleigh fading channel, where the transmitter does not know the channel coefficients and the receiver has only an estimate of them. We further assume that the transmitter and receiver know the statistics of the estimation error. We refer to this system as partially coherent system, for which we derive the expressions for the optimal detector and study the constellation design problem. Since the Chernoff bound on pairwise error probability of the partially coherent systems appears to be intractable, we use Stein's Lemma to propose a design criterion based on Kullback-Leibler (KL) distance between conditional distributions. Using the KL-based design criterion, we construct constellations for multiple-antenna systems which can be demodulated in the presence of channel estimation errors. The proposed constellations are multi-level, with multi-dimensional spherical constellations at each level. We show that these new constellations provide significant performance improvement over the conventional single-antenna PSK and QAM constellations, and multiple-antenna techniques such as Bell Lab's Space-Time (BLAST) architecture and orthogonal transmit diversity (OTD) schemes, when the estimation variance is comparable to the reciprocal of the signal-to-noise ratio.

In this paper, we present an information theoretic study of a decentralized multiple access channel (MAC), where users are allowed to autonomously change their data rates, transmission powers, and channel codes, independently from other users in the system. We introduce a policy-based access mechanism, where each user is allocated a set of code-books, with various data rates and powers. Successful reception of all users is guaranteed, provided that each of the users adheres to its assigned access policy, when selecting its date rate and power. We completely characterize the capacity region for such policy-based access in the low power regime, for both single and multi-antenna (MIMO) systems, and we show that nonorthogonal policies outperform orthogonal ones. We also show that known MIMO capacity scaling laws, which apply in single user systems, carry over into framework of decentralized MAC.

In this correspondence, we study design of transceiver antenna arrays and its impact on spectral efficiency of low-power systems. Our primary motivation is construction of practical and portable multi-antenna configurations with a very small and a-priori fixed volume for placing antennas. Using spectral efficiency as a target metric for array optimization, we show that any array configuration, transmit or receive, can be characterized via a parameter that we interpret as "effective degrees of freedom." For any array configuration, effective degrees of freedom describes an equivalent uncorrelated array, which results in the same low-power behavior of spectral efficiency. Joint optimization of transmit and receive antenna configurations decouples into maximizing effective degrees of freedom for transmitter and receiver separately. To achieve this goal, we introduce and study a theoretical benchmark of "limiting degrees of freedom," which is the least upper bound on effective degrees of freedom, evaluated over all configurations with finite number of antennas. Limiting degrees of freedom therefore describes the best possible performance for any transceiver array which confines its elements inside a given space. We compute a closed-form expression for limiting degrees of freedom of a circular geometry. Finally, we present numerical procedure and examples for designing linear and square arrays with nonuniform spacing, which typically exhibit significant spectral efficiency gains over uniform arrays.

We propose Low Density Parity Check (LDPC) code designs for the half-duplex relay channel. Our designs are based on the information theoretic random coding scheme for decode-and-forward relaying. The source transmission is decoded with the help of side information in the form of additional parity bits from the relay. We derive the exact relationships that the component LDPC code profiles in the relay coding scheme must satisfy. These relationships act as constraints for the density evolution algorithm which is used to search for good relay code profiles. To speed up optimization, we outline a Gaussian approximation of density evolution for the relay channel. The asymptotic noise thresholds of the discovered relay code profiles are a fraction of a decibel away from the achievable lower bound for decode-and-forward relaying. With random component LDPC codes, the overall relay coding scheme performs within 1.2 dB of the theoretical limit.

In this letter, we use power and rate adaptation to maximize the throughput in cooperative relay networks when limited feedback links to the transmitter nodes exist. We observe that, for a finite rate of feedback, the throughput maximizing outage probability can be relatively high. This suggests using higher rate codes and allowing some outages in an effort to increase the overall network throughput. Our analysis also reveals that the relaying transmission paradigm offers significant throughput gains over direct transmission for any rate of the feedback link. Our work not only demonstrates the power of cooperative coding, but also suggests the importance of network protocols incorporating feedback to allow for throughput maximization

We propose a practical coding scheme for half-duplex estimate-and-forward relaying. The proposed construction is guided by the information theoretic coding scheme for the estimate-and-forward relay protocol. Our construction incorporates several design features to reduce receiver complexity without compromising performance. Observing that the relaying gain is significant only at low SNRs, we use binary LDPC codes in the source broadcast phase of relaying. Estimation is performed by entropy constrained scalar quantization of the received signal at the relay. Finally, a procedure similar to maximal ratio combining is used to aggregate direct and relayed signals at the destination. An important practical advantage of our scheme is that it does not require source-relay symbol synchronization. The codes outperform direct and two-hop channel capacities, as well as decode-and-forward relaying when the relay-destination link is strong

Transmitter side information enables techniques such as beamforming, power control, and rate control in fading channels. It is commonly accepted in the literature that the addition of transmitter information (CSIT) to receiver information (CSIR) provides better performance than receiver information alone. In this work, we examine the performance of a symmetric, single-input, multiple-output (SIMO) channel in which CSIT is acquired through the use of training symbols, and we have a genie-aided receiver. We give a closed form expression for outage probability at high SNR while accounting for the resources consumed by training. We also analyze the diversity-multiplexing tradeoff and find that, though the diversity falls far below that of systems with perfect CSIT, it is still sufficiently superior to that achieved by CSIR-only systems to justify the cost of training. We show that, at zero multiplexing, transmitter training doubles the diversity order of a CSIR-only system and offers nonzero diversity at all achievable multiplexing gains

In this paper, we consider practical methods to approach the theoretical performance limits in the fading relay channel under different assumptions of transmitter channel knowledge. Specifically, we consider two degrees of transmitter channel knowledge: 1) perfect feedback is available and power control is employed and 2) no channel state knowledge is available at the transmitters and only spatial power allocation is possible. First, when perfect feedback is available, the optimal power control policy determines the ultimate limits of performance for constant rate transmission in the slow fading environment. However, in practice, perfect channel knowledge is not possible at the transmitters due to the finite capacity of the feedback links. We find practical methods to approach this performance limit through the use of power control with finite rate feedback. The finite-rate feedback results are shown for the low-complexity, full-diversity amplify-and-forward (AF) protocol. Interestingly, we see that only a few feedback bits are needed to achieve most of the gains of the optimal perfect feedback power control algorithm. Second, we consider the performance limit when the transmitters have no channel state knowledge and derive the optimal spatial power allocation between the source and relay for a given sum power constraint for the AF protocol. For most practical cases of interest, equal power allocation between the source and relay is shown to be nearly optimal. Our work suggests that there is minimal power savings from using spatial power allocation at the transmitters. To obtain large performance improvements over constant power transmission, it is imperative to have feedback for each realization of the channel state to allow for temporal power control.

We present a procedure for communication power optimization in a network of randomly distributed sensors with an observer (data collector) moving on a fixed path. The key challenge in using a mobile observer is that it remains within communication range of any sensor for a brief duration, and inability to transfer data in this duration leads to data loss. We establish that the process of data collection can be modeled by a queue with deadlines, where arrivals correspond to the observer entering the range of a sensor and a missed deadline means data loss. The queuing model is then used to identify the combination of system parameters that ensures adequate data collection with minimum power. The results obtained from the queuing analogy take a simple form in the asymptotic regime of dense sensor networks. Additionally, for sensor networks that cannot tolerate data loss, we derive a tight bound on minimum sensor separation that ensures that no data will be lost on account of mobility. We present two examples to illustrate our results, from which it is seen that power reduction by two orders of magnitude or more is typical relative to a static sensor network. The scenarios chosen for power comparisons also provide guidelines on the choice of path, if such a choice is available.

This paper presents a low-complexity multiuser decoding technique that can be implemented in real time for a convolutionally coded direct sequence code division multiple access (DS-CDMA) system. The main contribution, denoted here as the iterative prior update (IPU), consists of iterative interference cancellation and prior updates on sequences of coded bits combined with M-algorithm and list decoding. We illustrate performance gains over other low-complexity sequence detection and decoding strategies and argue that the algorithm converges within a few iterations and requires only a small size buffer for keeping track of the priors along iterations. The fact that the we can use existing available architectures for Viterbi decoding with slight modifications and can meet the real-time processing constraints makes the IPU algorithm an attractive alternative for cellular systems.

In this paper, we present a framework for the design of minimal power schedulers that satisfy average packet delay bounds for multiple users in a Gaussian wireless broadcast channel. We completely characterize the achievable region in the multidimensional delay-power space, and present schedulers that achieve the boundary regions. The optimal schedulers minimize the transmission power by jointly allocating rate and power to the different users based on various buffer and channel conditions. Finally, we also present low complexity scheduler designs that have near optimal performance.

We introduce a generalized definition for "low-pass" filters that covers time-varying and nonlinear systems under the same umbrella. We show that the qualitative concept of signal smoothing can be made precise through the concept of contractions in probabilistic metric spaces. For illustration, we consider classical linear time-invariant low-pass filters, nonlinear median filters, and time-varying guaranteed maximum delay schedulers employed in communication systems.

The packet outage probability for fading channels can be significantly reduced by exploiting queuing delay and transmitter channel information is demonstrated in this paper. Queuing delay gain is conceptually similar to delay diversity, but at a packet time-scale instead of symbol time-scale. First, a lower bound on outage probability assuming full channel state information at the transmitter (CSIT) is computed and then simple outage minimizing transmission policies which adapt the rate and power of the transmitted signal based jointly on buffer occupancy and channel conditions is constructed . We demonstrate that the rate of decrease of outage with increasing transmitter channel information is higher for larger delays. We also address the closely coupled problem of designing a practical feedback channel which supplies the CSIT.

The main goal of this paper is to show that multi-hop single-user communication achieves the per node transport capacity of Θ(ln N N) in homogeneous sensor networks, making it order-optimal. Our contributions in this paper are three-fold. First, we construct a route-discovery and scheduling scheme based on spatial TDMA for sensor networks. Second, we show that our schedule achieves a per node transport capacity of Θ(lnN N), the same as that achievable by beamforming. Third, we compare multi-hop communication and beamforming based methods in terms of the network power consumption required to attain a fixed throughput. Based on our power calculations, we conclude that if the channel attenuation is above a certain threshold (which we calculate), then multi-hop communication performs better, whereas below the threshold, beamforming is preferable.

In this paper a new achievable rate region for the user cooperation channel is derived which exceeds the best-known result for this channel. Since the user cooperation channel includes many other known channels as a special case, the new rate region provides improved achievable rates for these cases. The most notable example is that of the Gaussian relay channel, for which we present a new closed form inner bound higher than the only known result for many channel conditions.

We consider multiaccess problem in low power systems, where we allow each user to select its own data rate and transmit power locally and independently from other users. Here, every user has a set of low power codebooks, labeled a "policy," which accommodates a range of small spectral efficiencies, while treating instantaneous data rates of other users as an unknown compound parameter. Even with such coarse user coordination, multiuser detection enables a system, which is superior to any classic orthogonal division system. First we fully characterise the set of achievable policies, after which we demonstrate that in multiantenna systems, policies are be viewed as awarding protected receiver spatial dimensions to each user.

In this work, we show that in the wireless relay network, a tremendous savings in energy can be achieved by having side information at the transmitters and by employing power control. We present efficient protocols and the corresponding optimal power control policies that approach the universal lower bound on the outage probability of the block fading relay channel. Each of the proposed protocols have their own utility for specific channel conditions. However, a hybrid protocol between two known coding schemes is the best scheme for all channel conditions and is sufficient to approach the lower bound on outage probability. Unlike the single link channel, we show that exploiting the knowledge of the channel at the transmitters can significantly lower the outage even if the transmit powers at the source and relay have to be kept constant. In this case, it is also demonstrated that the lower bound on outage is closely followed by the outage probability of the hybrid protocol. Our results reveal that exploiting the right network protocol in conjunction with power control result in orders of magnitude savings in power over direct transmission for a target performance level.

We derive the ergodic capacity of discrete-time fading channel with additive Gaussian noise subject to both peak and average power constraint. The average power can be interpreted as the cost that we incur to achieve a certain rate. On the other hand, the motivation of this analysis comes from the fuel that there is also a peak power limitation in practical communication system. It is been shown that the optimal power adaption is no longer water-filling or constant power adaption which is the case where there is no limitation on the peak power. The numerical results show that the importance of peak power constraint becomes negligible for relatively low available average power, while it is limiting the capacity to be finite even as the available average power goes to infinity.

In this paper, we study minimal power transmission of bursty sources over wireless channels with constraints on mean queuing delay. The power minimizing schedulers adapt power and rate of transmission based on the queue and channel state. We show that packet scheduling based on queue state can be used to trade queuing delay with transmission power, even on additive white Gaussian noise (AWGN) channels. Our extensive simulations show that small increases in average delay can lead to substantial savings in transmission power, thereby providing another avenue for mobile devices to save on battery power. We propose a low-complexity scheduler that has near-optimal performance. We also construct a variable-rate quadrature amplitude modulation (QAM)-based transmission scheme to show the benefits of the proposed formulation in a practical communication system. Power optimal schedulers with absolute packet delay constraints are also studied and their performance is evaluated via simulations.

In this paper, we derive the capacity of the Gaussian degraded 'cheap' relay channel, consisting of nodes using 'cheap' radios operating in TDD mode when transmitting and sending in the same frequency band. The TDD model captures a practical limitation of most of the RF radios used in commercial wireless systems. The proof of achievability relies on a combination of superposition encoding and list decoding, while the converse is derived using the min-cut max-flow theorem for networks with 'cheap' nodes (previously derived by the authors). Even with 'cheap' radios, our capacity analysis shows that cooperative coding is beneficial and has a capacity advantage over direct transmission.

We analyze a low power, wideband CDMA system with multiple antennas. The joint "slope region" - of transmission rates at minimum energy per bit s derived as a function of proportion between vanishing rates for multiple users. Vertices of the slope region may be achieved by a matched filter linear interface, followed by successive interference cancellation. We introduce and evaluate the "robust slope region", the largest region which is inside every other slope region and is therefore independent of the relative proportion between transmission rates. Furthermore, we find the "robust slope", the maximum slope which can always be guaranteed to all users.

Progressive image transmission is difficult in the presence of a noisy channel, mainly due to the propagation of errors during the decoding of a progressive bitstream. Excellent results for this problem are made possible through combined source-channel coding, a method that matches the channel code to the source operational rate distortion as well as channel conditions. This paper focuses on the key component of combined source-channel coding: rate allocation. We develop a parametric methodology for rate allocation in progressive source-channel coding. The key to this technique is an empirical model of decoded bit-error rate as a function of the channel code rate. We investigate several scenarios. In the case of the memoryless channel, we present closed-form expressions. For the fading channel and channels with feedback, where closed-form results are elusive, our analysis leads to low-complexity algorithms. The results presented are applicable to any progressive source code, and any family of channel codes.

Mobile users' data rate and quality of service are limited by the fact that, within the duration of any given call, they experience severe variations in signal attenuation, thereby necessitating the use of some type of diversity. In this two-part paper, we propose a new form of spatial diversity, in which diversity gains are achieved via the cooperation of mobile users. Part I describes the user cooperation strategy, while Part II (see ibid., p.1939-48) focuses on implementation issues and performance analysis. Results show that, even though the interuser channel is noisy, cooperation leads not only to an increase in capacity for both users but also to a more robust system, where users' achievable rates are less susceptible to channel variations.

For pt.I see ibid., p.1927-38. This is the second of a two-part paper on a new form of spatial diversity, where diversity gains are achieved through the cooperation of mobile users. Part I described the user cooperation concept and proposed a cooperation strategy for a conventional code-division multiple-access (CDMA) system. Part II investigates the cooperation concept further and considers practical issues related to its implementation. In particular, we investigate the optimal and suboptimal receiver design, and present performance analysis for the conventional CDMA implementation proposed in Part I. We also consider a high-rate CDMA implementation and a cooperation strategy when assumptions about the channel state information at the transmitters are relaxed. We illustrate that, under all scenarios studied, cooperation is beneficial in terms of increasing system throughput and cell coverage, as well as decreasing sensitivity to channel variations.

We consider the problem of digital communication in a Rayleigh flat-fading environment using a multiple-antenna system, when the channel state information is available neither at the transmitter nor at the receiver. It is known that at high signal-to-noise ratio (SNR), or when the coherence interval is much larger than the number of transmit antennas, a constellation of unitary matrices can achieve the capacity of the noncoherent system. However, at low SNR, high spectral efficiencies, or for small values of coherence interval, the unitary constellations lose their optimality and fail to provide an acceptable performance. In this work, inspired by the Stein's lemma, we propose to use the Kullback-Leibler (KL) distance between conditional distributions to design space-time constellations for noncoherent communication. In fast fading, i.e., when the coherence interval is equal to one symbol period and the unitary construction provides only one signal point, the new design criterion results in pulse amplitude modulation (PAM)-type constellations with unequal spacing between constellation points. We also show that in this case, the new design criterion is equivalent to design criteria based on the exact pairwise error probability and the Chernoff information. When the coherence interval is larger than the number of transmit antennas, the resulting constellations overlap with the unitary constellations at high SNR, but at low SNR they have a multilevel structure and show significant performance improvement over unitary constellations of the same size. The performance improvement becomes especially more significant when an appropriately designed outer code or multiple receive antennas are used. This property, together with the facts that the proposed constellations eliminate the need for training sequences and are most suitable for low SNR, makes them a good candidate for uplink communication in wireless systems.

We study a multiple-antenna system where the transmitter is equipped with quantized information about instantaneous channel realizations. Assuming that the transmitter uses the quantized information for beamforming, we derive a universal lower bound on the outage probability for any finite set of beamformers. The universal lower bound provides a concise characterization of the gain with each additional bit of feedback information regarding the channel. Using the bound, it is shown that finite information systems approach the perfect information case as (t-1)2/sup -B/t-1/, where B is the number of feedback bits and t is the number of transmit antennas. The geometrical bounding technique, used in the proof of the lower bound, also leads to a design criterion for good beamformers, whose outage performance approaches the lower bound. The design criterion minimizes the maximum inner product between any two beamforming vectors in the beamformer codebook, and is equivalent to the problem of designing unitary space-time codes under certain conditions. Finally, we show that good beamformers are good packings of two-dimensional subspaces in a 2t-dimensional real Grassmannian manifold with chordal distance as the metric.

We propose a new scheme for multiple antenna transmission in the context of spread-spectrum signaling. The new scheme consists of using shifted Gold sequences to modulate independent information on the multiple antennas. We show that this strategy of using multiphase spreading (MPS) on different antennas greatly improves the throughput over currently known spread-spectrum multiple-antenna methods. We also find the optimal power allocation strategy among multiple transmit antennas for a fixed rate of channel state information, which might be provided via a feedback link, at the transmitter. We demonstrate the differences in optimal power distribution for maximizing capacity and minimizing probability of outage. When the transmission from the two antennas uses orthogonal spreading, we find that optimizing the power does not give much gain over the equal power transmission. However, when the transmissions are not orthogonal as in the case of MPS, then allocating power to maximize throughput gives considerable gain over equal power transmission. We also consider the effect of imperfections in the feedback channel on the optimal power allocation and show that our power allocation scheme is robust to feedback errors.

We consider the problem of streaming packetized media over the Internet from a server through a base station to a wireless client, in a rate-distortion optimized way. For error control, we employ an incremental redundancy scheme, in which the server can incrementally transmit parity packets in response to negative acknowledgements fed back from the client. Computing the optimal transmission policy for the server involves estimation of the probability that a single packet will be communicated in error as a function of the expected redundancy (or cost) used to communicate the packet. In this paper, we show how to compute this error-cost function, and thereby optimize the server's transmission policy, in this scenario.

This paper addresses the problem of broadcasting video over wireless channels. In such a scenario, different end users perceive the video signal through channels with different quality. We propose a source-channel coding system, that partitions the video data in such a way that maintains a baseline quality of service even for the user with the worst channel. The system consists of a layered source representation that is robust to error propagation effects, combined with a multilevel channel coding scheme that provides an unequal error protection to the different layers of the encoded video. Experimental results show that our system is robust and guarantees a baseline quality of service to all users over a wide range of channel conditions.

We assume a CDMA downlink multiuser scenario, where the base station is equipped with multiple transmit antennas, and each user has multiple receive antennas. For this setup we propose a new, computationally effective MIMO multiuser detector for frequency selective channels. We exploit the fact that the interference mainly comes from the spatial domain, while the residual interference is due to temporal dispersion and multiuser interference. This motivates us to suppress the residual interference in a linear fashion, while combating the spatial interference iteratively. This approach is an efficient performance-complexity tradeoff between fully iterative and linear detectors.

Channel estimation techniques for code-division multiple access (CDMA) systems need to combat multiple access interference (MAI) effectively. Most existing estimation techniques are designed for CDMA systems with short repetitive spreading codes. However, current and next-generation wireless systems use long spreading codes whose periods are much larger than the symbol duration. We derive the maximum-likelihood channel estimate for long-code CDMA systems over multipath channels using training sequences and approximate it using an iterative algorithm to reduce the computational complexity in each symbol duration. The iterative channel estimate is also shown to be asymptotically unbiased. The effectiveness of the iterative channel estimator is demonstrated in terms of squared error in estimation as well as the bit error rate performance of a multistage detector based on the channel estimates. The effect of error in decision feedback from the multistage detector (used in the absence of training sequences) is also shown to be negligible for reasonable feedback error rates using simulations. The proposed iterative channel estimation technique is also extended to track slowly varying multipath fading channels using decision feedback. Thus, an MAI-resistant multiuser channel estimation and tracking scheme with reasonable computational complexity is derived for long-code CDMA systems over multipath fading channels.

Multiple antenna transmission and reception have been shown to significantly increase the achievable data rates of wireless systems. However, most of the existing analysis assumes perfect or no channel information at the receiver and transmitter. The performance gap between these extreme channel assumptions is large and most practical systems lie in between. Therefore, it is important to analyze multiple antenna systems in the presence of partial channel information. We upper bound the outage probability performance of multiple antenna systems with preamble-based channel estimation and quantized feedback. We design causal feedback and power control schemes to minimize this upper bound on outage probability. We consider the following practical issues in our analysis and design: (1) the channel information is imperfect both at the receiver and at the transmitter and (2) part of the total available resources for the system need to be used for estimation and feedback. Our results demonstrate that for block fading channels, sending a periodic preamble and causally receiving channel state information via a feedback channel can lead to substantial gains in the outage performance over any nonfeedback scheme. Most of the gains achieved by perfect feedback can be achieved by very few bits of feedback. Furthermore, it is demonstrated that these outage probability gains can be translated into improvements in frame error rate performance of systems using space-time codes. Thus, implementing a power control, even at the cost of reduced spectral resources for the forward channel is beneficial for block fading channels.

This paper presents algorithms and architecture designs that can meet real-time requirements of multiuser channel estimation and detection in future code-division multiple-access-based wireless base-station receivers. Sophisticated algorithms proposed to implement multiuser channel estimation and detection make their real-time implementation difficult on current digital signal processor-based receivers. A maximum-likelihood based multiuser channel estimation scheme requiring matrix inversions is redesigned from an implementation perspective for a reduced complexity, iterative scheme with a simple fixed-point very large scale integration (VLSI) architecture. A reduced-complexity, bit-streaming multiuser detection algorithm that avoids the need for multishot detection is also developed for a simple, pipelined VLSI architecture. Thus, we develop real-time solutions for multiuser channel estimation and detection for third-generation wireless systems by: (1) designing the algorithms from a fixed-point implementation perspective, without significant loss in error rate performance; (2) task partitioning; and (3) designing bit-streaming fixed-point VLSI architectures that explore pipelining, parallelism, and bit-level computations to achieve real-time with minimum area overhead.

We study delay and rate constrained transmission of bursty traffic over wireless channels. We characterize the minimum power requirements via bounds for both single user and multiuser downlink problems, using a class of randomized first-come first-served policies. We show that a larger tolerable delay leads to power reduction, even for single-user Gaussian channels; a source coding interpretation is offered for the result. Further, we show that traffic with maximum-delay constraints requires more power than the same traffic with average-delay constraints.

We consider uplink scheduling for bursty traffic. We characterize the achievable rate region for Gaussian multiple access in terms of minimum required powers, with a constraint on average transmission delay for all users. We show that delay and rate constrained, power minimizing schemes perform scheduling accompanied with power control. Further, for the class of randomized stationary schedulers, it is shown that the achievable region is a convex polytope. We highlight that power requirements of a user can be reduced by either allowing additional delay (time scheduling gain) or increasing the power of another user (multiuser power exchange). Results are presented for two user additive white Gaussian noise channel and can be extended to finite state fading channels.

This paper focuses on the design of a multiuser receiver structure for the reverse link of a code-division multiple-access communication system, in the presence of multipath effects and using an antenna array at the base station receiver. The algorithm presented solves the complex multidimensional problem of channel estimation in this complex scenario using a maximum-likelihood approach. This channel estimation technique requires the transmission of a training sequence or feedback of detected data. Once a composite channel-impulse response of each user is estimated, it is directly used in the detection process instead of first extracting the individual channel parameters, such as path delays and attenuation factors. The paper presents a framework that facilitates a computationally efficient solution to the combined problem of channel estimation and detection in a scenario involving multiple users, multiple paths, and multiple sensors at the receiver.

A real-time VLSI architecture is designed for multiuser channel estimation, one of the core baseband processing operations in wireless base-station receivers. Future wireless base-station receivers will need to use sophisticated algorithms to support extremely high data rates and multimedia. Current DSP architectures are unable to fully exploit the parallelism and bit level arithmetic present in these algorithms. These features can be revealed and efficiently implemented by task partitioning the algorithms for a VLSI solution. We modify the channel estimation algorithm for a reduced complexity fixed-point hardware implementation. We show the complexity and hardware required for three different area-time tradeoffs: an area-constrained, a time-constrained and an area-time efficient architecture. The area-constrained architecture achieves low data rates with minimum hardware, which may be used in pico-cell base-stations. The time-constrained solution exploits the entire available parallelism and determines the maximum theoretical data rates. The area-time efficient architecture meets real-time requirements with minimum area overhead. The orders-of-magnitude difference between area and time constrained solutions reveals significant inherent parallelism in the algorithm. All proposed VLSI solutions exhibit better time performance than a previous DSP implementation.

We describe a new suboptimal decoding technique for linear codes based on the calculation of maximum weight basis of the code. The idea is based on estimating the maximum number locations in a codeword which have the least probability of estimation error without violating the codeword structure. In this paper we discuss the details of the algorithm for a convolutional code. The error correcting capability of the convolutional code increases with the constraint length of the code. Unfortunately the decoding complexity of Viterbi (1967) algorithm grows exponentially with the constraint length. We also augment the maximal weight basis algorithm by incorporating the ideas of list decoding technique. The complexity of the algorithm grows only quadratically with the constraint length and the performance of the algorithm is comparable to the optimal Viterbi decoding method.

We propose a new technique for the estimation of chaotic signals in the presence of additive noise. The new method uses statistical measures to restrict the space over which the signals are received. The proposed technique is applicable to a large variety of chaotic signals and has good performance indicated by the low estimation error bias and variance. The complexity of the algorithm is shown to be low.

In this paper we developed a framework for resource allocation in multi-class traffic CDMA system using adaptive power control and antenna array multiuser receiver. We devised a new scheme in which both transmit power and receiver filter adapt to the time-varying channel state. An antenna array multiuser receiver that jointly processes received signal vectors from multiple antennas and maximizes the signal-to-interference ratio for each user is proposed. It is combined with adaptive power control based on target SIR for each user. Our scheme can support multi-class traffic with different SIR requirements and guarantee their quality of service in multipath fading environment. A theoretical bound is derived to characterize capacity of CDMA system using adaptive power control and antenna array multiuser receiver in multipath fading environment. Simulations show that actual system capacity in multipath finding environment is close to the theoretical bound at large power constraint. Capacity at various power constraints can be characterized by a notion of bandwidth utility. It is also demonstrated that the antenna array multiuser receiver is quite effective in increasing capacity of users with higher SIR requirement and lower power constraint.

Space time codes have been proposed in the literature as an efficient means for improving the data rates over fading channels with multiple transmit antennas. In particular, the rank and the determinant of code difference matrices have been shown to be important in the design of space time codes for fading channels. In the present work, we investigate the problem of maximizing the coding gain of space-time codes, given by the minimum of the determinants of all the code difference matrices. We rely on equality of the singular values of the code difference matrices as a necessary and sufficient condition for obtaining the optimal coding gain. Finally, we discuss the construction of trellis codes and present simulation results.

Channel estimation techniques for code-division multiple access (CDMA) systems need to combat multiple access interference (MAI) effectively. Most existing estimation techniques are designed for CDMA systems with short repetitive spreading codes. However, current and next generation wireless systems use long spreading codes whose period is much larger than the symbol duration. In this paper, we derive the maximum likelihood channel estimate for long code CDMA systems over multipath channels using training sequences and approximate it using an iterative algorithm to reduce the computational complexity in each processing window. The asymptotic convergence of the mean of the iterative estimate to the actual channel is also shown. The effectiveness of the iterative channel estimator is demonstrated in terms of squared error in estimation as well as the bit error rate performance of a multistage detector based on the channel estimates. Finally, the proposed iterative channel estimation technique is extended to track slowly varying multipath fading channels using decision feedback. Thus, an MAI resistant multiuser channel estimate with reasonable computational complexity is derived for long code CDMA systems over multipath fading channels.

It is well-known that multilevel coding (MLC) and multistage decoding (MSD) suffice to approach capacity if the rates at different levels are chosen appropriately. In most of the practical cases, however, the rate design rule for MSD does not leave any room for coding at higher levels of the MLC scheme, which is very important in fading environments. The rate design rule for multilevel coding using iterative multistage decoding is investigated, and it is shown that using iterative MSD with updated a priori probabilities of the constellation points, a broader subregion of the capacity region of the MLC scheme can be achieved.

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.

It is well known that Shannon's separation result does not hold under finite computation or finite delay constraints, thus joint source-channel coding is of great interest for practical reasons. For progressive source-channel coding systems, efficient codes have been proposed for feed forward channels [1] and the important problem of rate allocation between the source and channel codes has been solved [2]. For memoryless channels with feedback, the rate allocation problem was studied in [3]. In this paper, we consider the case of the fading channels with feedback. Feedback routes are provided in many existing standard wireless channels, making rate allocation with feedback a problem of considerable practical importance. We address the question of rate allocation between the source and channel codes in the forward channel, in the presence of feedback information and under a distortion cost function. We show that the presence of feedback shifts the optimal rate allocation point, resultin...

In this paper we study resource allocation and capacity of CDMA system using multiuser receiver to support multiple classes of traffic with different data rates and bit error rate requirements. We developed a new resource allocation scheme using adaptive power control and multirate multiuser receiver to guarantee users' quality of service requirements in multipath fading environment. A multiuser receiver that maximizes the signal-to-interference ratio (SIR) for each symbol is proposed for multirate CDMA system. It is combined with adaptive power control based on target SIR to provide different quality of service for multiple-data-rate traffic. A theoretical bound is derived to characterize capacity of multi-class traffic CDMA system using the multiuser receiver. Simulations show that actual system capacity in multipath fading environment is close to the theoretical bound at large power constraint. It is also demonstrated that the multiuser receiver is quite effective in increasing capacity of users with higher data rate and lower target bit error rate.

We focus on the design of multiuser receiver structures for code division multiple access (CDMA) communication systems, in the presence of multipath effects and multiple sensors at the base station receiver. We present a flexible and extensible framework that allows the use of an estimated effective spreading code from the channel estimation phase, in the multiuser detection process. The effective spreading code captures all the channel parameters such as path delays, attenuation factors, and directions of arrival. Hence estimation of this one composite vector removes the necessity of estimating each individual parameter, thus reducing computational complexity. The results also show that this approach leads to better performance for multiuser detection, especially when the channel consists of a number of low energy paths in addition to a few discrete strong paths.

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.

Conventional correlation based single-user techniques for direct sequence code division multiple access (DS-CDMA) wireless communication systems are susceptible to performance degradation due to interference from other users. Previous research has focused on development of several multiuser techniques where information about multiple users is used to improve performance for each individual user. Due to performance benefits of these methods, they are attractive candidates for implementation in future cellular systems. In this paper we present an error analysis of fixed point implementation of some of these techniques.

Transmission of compressed image data over noisy channels is an important problem and has been investigated in a variety of scenarios. In this paper, we propose a progressive time-varying source-channel coding system for transmitting images over wireless channels. The core result of this paper is a systematic method of instantaneous rate allocation between the progressive source coder and channel coder. We develop closed form expressions for end-to-end distortion, as well as rate allocation, in memoryless channels. We extend the memoryless results to an algorithm for fading channels. Experimental results demonstrate the performance of this method.

The problem addressed in this paper is the estimation of the channel parameters in a code division multiple access (CDMA) communication system, in the presence of multipath effects and multiple sensors at the base station receiver. The algorithm presented solves the problem by estimating a composite channel impulse response of each user, which can be directly used in the detection process to appropriately modify the spreading code of the user. In addition, the algorithm combines the benefit of spatial processing in the form of an antenna array at the receiver to gain an increase in performance of the system.

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.

Code-division multiple access (CDMA) has emerged as an access protocol well-suited for voice and data transmission. One significant limitation of the conventional CDMA system is the near-far problem where strong signals interfere with the detection of a weak signal. Multiuser detectors assume knowledge of all of the modulation waveforms and channel parameters, and exploit this information to eliminate multiple-access interference (MAI) and to achieve near-far resistance. A major problem in practical application of multiuser detection is the estimation of the signal and channel parameters in a near-far limited system. We consider maximum-likelihood estimation of users delay, amplitude, and phase in a CDMA communication system. We present an approach for decomposing this multiuser estimation problem into a series of single-user problems. In this method the interfering users are treated as colored non-Gaussian noise. The observation vectors are preprocessed to be able to apply a Gaussian model for the MAI. The maximum-likelihood estimate (MLE) of each user's parameters based on the processed observation vectors becomes tractable. The estimator includes a whitening filter derived from the sample covariance matrix which is used to suppress the MAI, thus yielding a near-far resistant estimator.

Several linear multiuser detectors for code-division multiple access (CDMA) systems can be characterized as an inverse of some form of correlation matrices. If the correlations change, the detectors must be redesigned. An ideal computation of the decorrelating or the linear minimum mean-squared-error (LMMSE) detector requires order K/sup 3/ flops, where K is the number of users. To alleviate the computational complexity, iterative decorrelating and LMMSE detectors are proposed. The iterative detectors use steepest descent (SD), conjugate gradient (CG), and preconditioned conjugate gradient (PCG) algorithms, and require order K/sup 2/ flops per iteration. Their main advantages are the reduced number of flops and their suitability to highly parallel implementations. The correlation coefficient computation can also be embedded into the CG algorithm, which is an advantage with time-varying signature waveforms. The performance of the iterative algorithms is studied via computer simulations.

A technique is presented for jointly optimizing the signaling in the two directions of transmission on a twisted-pair communications channel. It is then applied to twisted-pair channel models with monotonic channel response and crosstalk transfer functions. While the signaling strategy presented in this paper can achieve only a lower bound on the true channel capacity, it is a significant improvement over existing signaling schemes. In particular, in contrast with existing schemes, the maximum information rate for the joint signaling strategy increases without bound as the signal-to-noise ratio (SNR) approaches infinity. It is also shown through numerical results that the proposed signaling strategy generalizes naturally to more practical nonmonotonic twisted-pair channel models incorporating bridge taps and other nonidealities. Finally, the form of the optimal signaling strategy suggests a relatively straightforward implementation using multicarrier modulation.

This paper addresses the problem of tracking the covariance matrix eigenstructure, based on SVD (singular value decomposition) updating, of a time-varying data matrix formed from the received vectors. This problem occurs frequently in signal processing applications such as adaptive beamforming, direction finding, spectral estimation, etc. As this problem needs to be solved in real time, it is natural to look for a parallel algorithm so that computation time can be reduced by distributing the work among a number of processing units. This paper proposes a parallel scheme for SVD updating that can be implemented on a fixed sized array of off-the-shelf processors, to get speedups close to the number of processors used.

CDMA is becoming an increasingly popular multiplexing scheme in wireless communication and this has necessitated the development of efficient detection techniques. The exponential complexity of the optimal detector on one end and inferior performance of conventional single-user detector at the other have led to the development of suboptimal multiuser detectors with lower complexity. Most of these detection techniques involve solution of a linear system. In their naive implementation this requires O(n/sup 3/) operations in the size of the matrix. This cost can be reduced if we move towards modern iterative techniques for solution of the system. However, maximum benefit can be achieved if we fully exploit the structure of the system. We propose several methods of reducing the computational complexity utilizing the above ideas. We have also come up with algorithms which computationally can achieve the lower bound in complexity.

In this paper, we evaluate several implementation issues in the application of subspace based methods to tracking channel parameters in code division multiple access (CDMA) communication systems, in the presence of multipath fading. We focus on the behavior of singular value decomposition (SVD) based schemes while tracking the time variations in the signal subspace, due to fading. We also evaluate the application of several techniques to reduce the complexity of the computationally expensive SVD procedure, to the channel estimation problem.

For optimizing the performance of optical code-division multiple-access (CDMA) systems, there is a need for determining the sensitivity of the bit-error rate (BER) of the system to various system parameters. Asymptotic approximations and bounds, used for system bit-error probabilities, seldom capture the sensitivities of the system performance. We develop single-run gradient estimation methods for such optical CDMA systems using a discrete-event dynamic systems (DEDS) approach. Specifically, computer-aided techniques such as infinitesimal perturbation analysis (IPA) and likelihood ratio (LR) methods are used for analyzing the sensitivity of the average BER to a wide class of system parameters. It is shown that the above formulation is equally applicable to time-encoded and frequency-encoded systems. Further, the estimates derived are unbiased, and also optimality of the variance of these estimates is shown via the theory of common random variates and importance sampling techniques.

For pt.I see ibid., vol.15, no.4, p.731-41 (1997). We develop infinitesimal perturbation analysis (IPA)-based stochastic gradient algorithms for deriving optimum detectors with the average probability of bit error being the objective function that is minimized. Specifically, we develop both a class of linear as well as nonlinear (threshold) detectors. In the linear scheme, the receiver despreads the received optical signal with a sequence that minimizes the average bit-error rate. In the case of the threshold detector, the detection threshold for the photoelectron count is optimized to achieved minimum average bit-error rate. These algorithms use maximum likelihood estimates of the multiple access interference based on observations of the photoelectron counts during each bit interval, and alleviate the disadvantage of previously proposed schemes that require explicit knowledge of the interference statistics. Computer-aided implementations of the detectors derived are shown to outperform the correlation detector. Sequential implementations of the adaptive detectors that require no preamble are also developed, and make them very viable detectors for systems subject to temporal variations.

Decorrelating, linear, minimum mean-squared error (LMMSE), and noise-whitening multiuser detectors for code-division multiple-access systems (CDMA) are ideally infinite memory-length (referred to as IIR) detectors. To obtain practical detectors, which have low implementation complexity and are suitable for CDMA systems with time-variant system parameters (e.g., the number of users, the delays of users, and the signature waveforms), linear finite-memory-length (referred to as FIR) multiuser detectors are studied in this paper. They are obtained by truncating the IIR detectors or by finding optimal FIR detectors. The signature waveforms are not restricted to be time-invariant (periodic over symbol interval). Thus, linear multiuser detection is generalized to systems with spreading sequences longer than the symbol interval. Conditions for the stability of the truncated detectors are discussed. Stable truncated detectors are shown to be near-far resistant if the received powers are upper bounded, and if the memory length is large enough (but finite). Numerical examples demonstrate that moderate memory lengths are sufficient to obtain the performance of the IIR detectors even with a severe near-far problem.

In this paper, we consider a direct-sequence code-division multiple-access (DS-CDMA) system in the framework of a discrete-event dynamic system (DEDS) in order to optimize the system performance. Based on this formulation, we develop infinitesimal perturbation analysis (IPA) for estimating the sensitivity of the average probability of bit error to factors ranging from near-far effects to imperfections in power control. The above estimates are shown to be unbiased, and this technique is then further incorporated into a stochastic gradient algorithm for achieving adaptive multiuser interference rejection for such systems, which is also subject to frequency nonselective slow fading. We use an IPA-based stochastic training algorithm for developing an adaptive linear detector with the average probability of error being the minimization criterion. We also develop a practical implementation of such an adaptive detector where we use a joint estimation-detection algorithm for minimizing the average probability of bit error. A sequential implementation that does not require a stochastic training sequence or a preamble is also developed.

A code-division multiple-access (CDMA) communication system is studied where a trellis-based scheme is used for data encoding and modulation. The signature sequences (spreading codes), which are assigned to the direct-sequence spread-spectrum (DS/SS) modulator according to the encoding rule, are taken from a biorthogonal set. We derive the optimum detector by maximizing the likelihood ratio. In addition to the optimum multiuser detector with very high computational complexity, we present a multistage detector and a scheme based on a reduced tree search algorithm. The error probability is evaluated by deriving upper and lower bounds as well as by Monte Carlo simulations. We show that the optimum receiver is near-far resistant. The results from the numerical examples indicate that the suboptimum detectors are also capable of alleviating the near-far problem.

We consider the estimation of channel parameters for code-division multiple access (CDMA) communication systems operating over channels with either single or multiple propagation paths. The multiuser channel estimation problem is decomposed into a series of single user problems through a subspace-based approach. By exploiting the eigenstructure of the received signal's sample correlation matrix, the observation space can be partitioned into a signal subspace and a noise subspace without prior knowledge of the unknown parameters. The channel estimate is formed by projecting a given user's spreading waveform into the estimated noise subspace and then either minimizing the likelihood or minimizing the Euclidean norm of this projection. Both of these approaches yield algorithms which are near-far resistant and do not require a preamble.

Code division multiple access (CDMA) is a powerful multiplexing scheme, particularly suited to the optical domain with its broad spectrum. Unfortunately, analysis of optical CDMA (OCDMA) systems has been almost exclusively restricted to systems employing a correlation detector, which suffer high degradation when received user powers are dissimilar. This study examines the performance of an optimum single-user detector and two multiuser detectors for OCDMA in the presence of additive light intensity noise and Poisson detection. The optimized single-user detector is the maximum likelihood detector given the interference from other users is a random process with known distribution. One multiuser detector is based on a local search algorithm for maximizing the likelihood function. The second multiuser detector is a generalization of the optical multistage detector to accept soft-decision from the previous stage. Approximations to the error probabilities of the OCDMA system based on either random signature sequences or deterministic codes are derived for each detector using a large deviations theory approach. The asymptotic multiuser efficiency is found to be related to the large deviations rate function. The analysis shows that the correlation detector performance decreases rapidly as the number of users increases, while the optimized single-user detector and the two multiuser detectors proposed perform considerably better and show less sensitivity to unequal received user powers.>

A multiuser communication system is considered where K users share a channel with multipath propagation by using code division for multiple access. Data modulation is carried out by binary phase shift keying and direct sequence spread spectrum signaling. The micro-cellular communication media is modeled as a frequency selective fading channel with multipath propagation. The multipath diversity of the received signals from the K users is exploited by a bank of K RAKE correlators. Algorithms based on the maximum likelihood rule have been developed for estimating the complex channel coefficients as well as for detection of the desired data packets from the sufficient statistics provided by the RAKE correlators. The performance of the resulting multiuser detector is evaluated analytically and via Monte Carlo simulations. The results indicate that the estimator of the channel coefficients has a variance close to the Cramer-Rao lower bound, and that the proposed multiuser detector is capable of eliminating the near-far effect as well as processing the signals propagated through multiple paths.>

Analytical solutions of the performance of optical communication systems are difficult to obtain and often, Monte Carlo simulations are used to achieve realistic estimates of the performance of such systems. However, for high performance systems, this technique requires a large number of simulation trials for the estimates to be in a reasonable interval of confidence, with the number of trials increasing linearly with the performance of the system. We apply an importance sampling technique to estimate the performance of direct detection optical systems, where the "gain" of importance sampling over Monte Carlo simulations is shown to increase linearly with the system performance. Further, we use this technique to study the performance of optical communication systems employing avalanche photodetectors as well as fibre-optic code division multiple access systems (FO-CDMA). We also show that the quick simulation technique developed can be used for a wide variety of coding schemes, and for the first time, we present a comparative analysis of the performance of FO-CDMA systems employing optical orthogonal codes and prime sequences. In all cases, it is shown that importance sampling simulations require less than 50-100 trials for estimating error probabilities of 10-10 and below.

Considers a multiuser detection scheme for optical direct sequence code division multiple access (OCDMA) systems, referred to as the multistage detector. Previous works in this area have proposed two detectors: the correlation detector that is simple, but has poor performance for large number of users, and the optimal (minimum probability of error) detector that has exponential complexity in the number of users. Efficient multiuser detection algorithms consider the interfering user codes at the expense of electronic speed processing, unlike the optical processing achievable with the correlation detector. The multiple access system using the proposed multistage detector is shown to be of high performance and low complexity, compared to the conventional correlation detector and the optimal detector. The model studied includes multiple access interference as well as the Poisson characteristics of the optical direct detection process. An approximation to the probability of error is derived for the multistage detector, and it is compared to the actual error probability of the correlation detector, to a lower bound to the error probability of the optimal detector, and to simulation results for the multistage detector. The probability of error is calculated using a characteristic function method. Results are presented for a random code case that show a significant improvement in the performance of the OCDMA system using this detector over the correlation detector.>

Two simple structures employing multilayer perceptrons are proposed for demodulation of spread-spectrum signals in both synchronous and asynchronous Gaussian channels. The optimum receiver is used to benchmark the performance of the proposed receiver; in particular, it is proved to be instrumental in identifying the decision regions for the neural networks. The neutral networks are trained for the demodulation of signals via backpropagation-type algorithms. A modified backpropagation-type algorithm is introduced for single-user and multiuser detection with near-optimum performance that could have applications in other classification and pattern recognition problems. A comparative performance analysis of the three receivers, optimum, conventional, and the one employing neural networks, is carried out via Monte Carlo simulations. An importance sampling technique is employed to reduce the number of simulations necessary to evaluate the performance of these receivers in a multiuser environment. In examples given, the receiver significantly outperforms the conventional receiver.>

The problem of simulating error rates in direct sequence spread-spectrum code division multiple-access (CDMA) systems is examined. Due to the computational complexity required to simulate these systems, an importance sampling technique is developed based upon previous work by the authors. A conditional weighting function is derived such that the linear shift class of biasing densities can be employed. Results are given for a variety of detector structures and background noise distributions. It is shown that this biasing scheme can dramatically reduce the run time of realistic multiple-access simulations.>

A method based on recursive computation of the expected number of attempts and successes during the collision resolution phase of an access control algorithm is introduced for the design of near-optimum control strategies for multiple access collision channels with ternary and binary feedback. With this approach it is possible to circumvent the extremely difficult and still unsolved problem of finding the access control algorithm which achieves the highest throughput by settling for a near-optimum solution. The key to the design of the algorithms is to approximate the originally infinite-dimensional optimization problem by a one-dimensional optimization problem. In the ternary feedback case, the proposed algorithm achieves a throughput virtually identical to the highest throughput reported. Several forms of binary feedback are considered, and algorithms are introduced that achieve the highest throughput reported.>

Communication networks using code division multiple access (CDMA) include applications where several packets of information are transmitted synchronously and simultaneously over a common channel. Consideration is given to the problem of simultaneously demodulating every packet from such a transmission. A nonlinear detection scheme based on a linear complexity multistage multiple-access interference rejection algorithm is studied. A class of linear detectors is considered as constituting the first stage for the multistage detector. A bit-error probability comparison of the linear and multistage detectors is undertaken. It is shown that the multistage detectors are capable of achieving considerable improvements over the linear detectors, particularly in near-far situations, i.e., in the demodulation of weak signals in the presence of strong interfering signals. This problem has been of primary concern for currently operational CDMA systems.>

The problem of estimating estimating expectations of functions of random vectors via simulation is investigated. Monte Carlo simulations, also known as simple averaging, have been used as a direct means of estimation. A technique known as importance sampling can be used to modify the simulation via weighted averaging in the hope that the estimate will converge more rapidly to the expected value than standard Monte Carlo simulations. A constrained optimal solution to the problem of minimizing the variance of the importance sampling estimator is derived. This is accomplished by finding the distribution which is closest to the unconstrained optimal solution in the Ali-Silvey sense (S. Ali et al., 1966). The solution from the constraint class is shown to be the least favorable density function in terms of Bayes risk against the optimal density function. Examples of constraint classes, which include epsilon -mixture, show that the constrained optimal solution can be made arbitrarily close to the optimal solution. Applications to estimating probability of error in communication systems are presented.>

The noncoherent demodulation of differentially phase-shift keyed signals transmitted simultaneously via a synchronous code-division multiple-access (CDMA) channel is studied under the assumption of white Gaussian background noise. A class of noncoherent linear detectors is defined with the objective of obtaining the optimal one. The performance criterion considered is near-far resistance that denotes worst-case multiuser asymptotic efficiency over near-far environments. It is shown that the optimal linear detector is a noncoherent decorrelating detector. The commonality between the properties of the decorrelating detectors for coherent and noncoherent channels is established. In particular, it is shown that no other differential phase-shift keying (DPSK), multiuser detector achieves a higher near-far resistance than does the noncoherent decorrelator.>

A multiuser detection strategy for coherent demodulation in an asynchronous code-division multiple-access system is proposed and analyzed. The resulting detectors process the sufficient statistics by means of a multistage algorithm based on a scheme for annihilating successive multiple-access interference. An efficient real-time implementation of the multistage algorithm with a fixed decoding delay is obtained and shown to require a computational complexity per symbol which is linear in the number of users K. Hence, the multistage detector contrasts with the optimum demodulator, which is based on a dynamic programming algorithm, has a variable decoding delay, and has a software complexity per symbol that is exponential in K. An exact expression is obtained and used to compute the probability of error is obtained for the two-stage detector, showing that the two-stage receiver is particularly well suited for near-far situations, approaching performance of single-user communications as the interfering signals become stronger. The near-far problem is therefore alleviated. Significant performance gains over the conventional receiver are obtained even for relatively high-bandwidth-efficiency situations.>

An analysis of the performance of nonlinear correlation reception of direct-sequence signals in single- and multiuser channels is presented. The communications channel is modeled as containing non-Gaussian background noise and, in some cases, multiple-access interference as well. The error-probability behavior is studied asymptotically as the lengths of the spreading codes increase without bound, and conditions on the spreading sequences are obtained that assure asymptotic achievement of single-user performance in a multiuser system. A long-spreading sequence approximation to the average error probability is also derived, and this result is applied to the analysis of smooth-limiting correlation receivers in impulsive channels. Simulation results are also provided to verify the analysis. Average bit-error probabilities are computed by Monte Carlo simulations for linear, hard-limiting, and smooth-limiting correlation receivers in both single- and two-user impulsive channels. The simulation results are compared to the error rates by asymptotic approximations for the smooth limiter and also to those from previous studies on linear and hard-limiting correlators.>

Detection systems are designed to operate with optimal or nearly optimal probability of a wrong decision. Analytical solutions of the performance of these systems have been very difficult to obtain. Monte Carlo simulations are often the most tractable method of estimating performance. However, in systems with small probability of error, this technique requires very large amounts of computer time. A technique known as importance sampling substantially reduces the number of simulation trials needed, for a given accuracy, over the standard Monte Carlo method. The theory and application of the importance sampling method in Monte Carlo simulation is considered in a signal detection context. A general method of applying this technique to the optimal detection problem is given. Results show that in cases examined, the gain is approximately proportional to the inverse of the error probability. Applications of the proposed method are not limited to optimum detection systems; analysis, leading to a measure of the gain in using this biasing scheme, shows that in all optimal systems considered, less than 100 trials is needed to achieve estimates with 45% confidence, even for extremely small error probabilities.>

For pt.I see ibid., vol.COM-35, no.11, p.1179-88 (1987). In part I it was demonstrated that impulsive channel noise can be a serious detriment to the performance of direct-sequence spread-spectrum multiple-access (DS/SSMA) communications when conventional linear correlation reception is used. Here, a hard-limiting correlator as an alternative for reception of multiple-access transmission in impulsive channels is considered. For K asynchronous binary PSK DS/SSMA users sharing a linear channel corrupted by impulsive noise that is modeled at the output of the front-end filter of the receiver, techniques are developed for analyzing bit error probabilities of this hard-limiting receiver by exact computation for short spreading sequences, by approximation for longer spreading sequences, and by asymptotic limits for infinitely long spreading sequences. Performance is compared to that of the linear correlator under a variety of conditions, showing that hard-limiting correlation reception can offer substantial improvement over conventional systems in impulsive channels. However, the linear receiver is more effective against multiple-access noise only, and so a tradeoff emerges between rejection of impulsive noise and rejection of multiple-access interference.>

The performance of digital linear correlation receivers is studied in a multiuser environment. There are assumed to be two types of sources interfering with data transmission: multiple-access interference, and additive channel noise which is attributed to impulsive noise sources in the environment. The contribution of multiple-access interference is examined by consideringKasynchronous users transmitting simultaneously over a linear channel using the binary PSK direct-sequence spreadspectrum multiple-access (DS/SSMA) technique. Alternatively, the effects of the non-Gaussian impulsive channel in such a system are studied by modeling the samples of noise after front-end filtering. Errorprobability performance under these conditions is compared to that for additive white Gaussian noise (AWGN) channels. Due to computational complexity, exact analysis is limited here to systems utilizing short spreading sequences. Computationally simple methods are proposed for approximating the average error probability when the length of the signature sequences is large. Furthermore, some asymptotic results are obtained for the case of infinitely long sequences. In all cases, performance variation is examined as the shape of the noise density varies with SNR held constant. The results of this analysis indicate that the presence of impulsive noise can cause significant performance degradation over that predicted from an AWGN model, even when the total noise power does not increase.

The application of companding approximation theory to the quantization of data for detection of coherent signals in a noisy environment is considered. This application is twofold, allowing for greater simplicity in both analysis and design of quantizers for detection systems. Most computational methods for designing optimum (most efficient) quantizers for signal detection systems are iterative and are extremely sensitive to initial conditions. Companding approximation theory is used here to obtain suitable initial conditions for this problem. Furthermore, the companding approximation idea is applied to design suboptimum quantizers which are nearly as efficient as optimum quantizers when the number of levels is large. In this design, iteration is not needed to derive the parameters of the quantizer, and the design procedure is very simple. In this paper, we explore this approach numerically and demonstrate its effectiveness for designing and analyzing quantizers in detection systems.