Opportunistic links are emerging as a novel technology for state-of-the-art wireless networks, such as cognitive radio networks, energy-harvesting networks, and low-latency vehicular networks. To increase the reliability of these networks, path-permutation codes (PPCs) were advocated in [1]. These codes are based on a virtual multiple-input multiple-output (MIMO) model on the session/network layer, and have been tailored for increased reliability of opportunistic links. By exploiting multipath-multihop routes, PPCs access one relay path at a time while repeatedly transmitting the same QAM symbol. In this paper, we introduce a generalized PPC scheme which simultaneously accesses multiple relay paths and comprises multiple QAM symbols in the packet. Phase rotations are also introduced in the PPC codewords for additional performance improvement. Numerical simulation results validate our analyses and demonstrate the superior performance of this novel coding scheme, i.e., better error rate performance, higher throughput, and stronger robustness to transmission outages.

Using an algebraic approach based on the theory of Coxeter groups, we design, and describe the performance of, a class of line codes derived from permutation modulation, useful for parallel transmission of b bits over b + 1 wires, and admitting especially simple encoding and decoding algorithms. With these codes, resistance to common-mode noise is obtained by using codewords whose components sum to zero, simultaneous switching output noise is reduced by using constant-energy signals, and the effects of intersymbol interference are reduced by having decisions based on only two values at the input of the final slicers. Codebook design is based on the theory of Group Codes for the Gaussian Channel, as specialized to Coxeter matrix groups generated by reflections in orthogonal hyperplanes. A number of designs are exhibited, some of them being novel or improving on previously obtained codes.

Using an algebraic approach, we examine the design and the performance of geometrically uniform line coding schemes transmitting b bits over w = b + 1 wires and obtained from a subset of a permutation modulation signal set.

We advocate the use of interval-type bounds on cumulative distribution functions, called probability boxes, to handle several problems arising when a wireless communication system performance must be assessed in the presence of model uncertainties, poorly known or unknown dependencies of random variables, or imprecisely specified probability distributions. The amount of uncertainty is evaluated quantitatively by using sharp bounds on performance parameters.

We consider some problems arising when a wireless communication system performance must be assessed in the presence of model uncertainties due to poorly known or unknown dependences of the random variables used to model the channel. We argue that performance bounds based on probability boxes can measure the extent of uncertainty caused by inaccurate models.

Networks formed by energy-harvesting devices impose new technological challenges on data transmission due to uncertainty of the amount of energy that can be harvested. This is even more challenging with multihop networks, in which transmission outage occurs when one single device along the relay path cannot harvest enough energy. A virtual multiple-input multiple-output (MIMO) model for multihop, multipath networks has recently been developed to facilitate reliable open-loop end-to-end transmissions, making networks robust to random transmission outages without the necessity of bandwidth-consuming and complicated end-to-end feedback and control. In this paper, a framework based on a virtual MIMO model of multihop, multipath opportunistic networks formed by energy-harvesting devices is developed. We propose rotated-algebraic path-time codes (RA-PTC), by which data are encoded using Givens rotation and cyclic division algebras. Without rate loss, a form of time diversity is exploited by repeatedly transmitting the RA-PTC-coded data. Extensive theoretical analyses are carried out using amount of fading and diversity as metrics. Both the performance enhancement due to the proposed RA-PTC and the performance loss due to energy shortage are quantified. Furthermore, a simple yet effective cyclic power control is proposed to improve transmission reliability. Numerical results demonstrate that RA-PTC and cyclic power control enable efficient and reliable end-to-end transmission in multipath, multihop opportunistic networks formed by energy-harvesting devices.

Nonergodic fading is a useful model for various wireless communication channels in both indoor and outdoor environments. With this model, a codeword is divided into multiple blocks such that fading is constant within a block and independent across blocks. Building on Poltyrev's work on infinite lattice constellations for the Gaussian channel, we derive a Poltyrev outage limit for lattice constellations transmitted over a block-faded channel. We prove that the diversity order of this Poltyrev outage limit is equal to the number of degrees of freedom in the channel. An important application is in decoding low-density lattice codes. With block fading, the presence of an outage may dramatically increase the runtime of both sphere and iterative decoders. Using our newly defined Poltyrev outage limit, decoding is not performed whenever an outage is declared, which drastically reduces the overall decoding time.

We advocate the use of the exceedingly general class of spherically invariant random processes to model fading in wireless communications. These processes encompass most of the models in practical use. After summarizing their main properties: 1) we prove that they are differential-entropy maximizers; 2) we describe a mathematical technique, based on Mellin transforms, useful to evaluate the performance of digital communication over a channel affected by spherically invariant fading; 3) We show how sharp upper and lower bounds to system performance can be derived when only a limited knowledge of the fading process statistics is available; and 4) we derive the spherically invariant fading distributions yielding the best and worst performance for a given signal-to-noise ratio.

Cognitive radios (CRs) improve the spectrum efficiency in wireless communications. Nonetheless, owing to the intrinsic randomness of ad hoc cognitive radio networks (CRNs), e.g., the opportunistic links, the traditional realization of ad hoc networking that demands the end-to-end control information, is unscalable and impractical. A virtual multiple-input multiple-output (MIMO) framework has been recently developed for the realization of error-resilient end-to-end transmission without the necessity of feedback information. In this paper, we propose an end-to-end path-permutation coded (PPC) transmission in which one relay path is accessed at a time and the transmission is hopped among multiple relay paths. The hopping order is specified by a permutation array that encodes the data, meaning that the data is conveyed by the order of indices of the accessed paths. With the PPC scheme, the control overhead and data processing complexity of the end-to-end transmission become relatively low. The PPC technique can also be utilized as a multiuser technique. At the destination node, a joint sphere decoder efficiently implements the maximum a posteriori (MAP) probability decoding that simultaneously identifies the order of accessed paths and erasures. Comprehensive theoretical analyses and simulations are conducted to demonstrate the superior performance of the PPC technique in ad hoc CRNs.

Many statistical models (mainly due to physical propagation studies and field measurements) have been proposed to characterize the statistics of the NLOS flat-fading wireless communication channel. There appears to have no known statistical theory on the formation of many of these fading envelope statistics. We offer the statistical modeling of fading envelope statistics under the NLOS assumption based on the SIRP representation. In practice, these channel statistics cannot be modeled with certainty. We advocated the use of moment-bound theory to obtain bounds on the system performance metrics. In this paper, we combine the theory of moment bounds with that of SIRP, and the use of the SDP optimization method to show how sharper bounds of the error rate and ergodic channel capacity of a communication system can be computed.

A composite hypothesis testing procedure, originally introduced in [5], is examined for robustness in the binary case. A density-free uniform exponential bound for the error probability is derived which tightens the bound of [5], it is shown that this procedure is equivalent to a hard-limited likelihood-ratio test, and asymptotic and nonasymptotic robustness is discussed.

In this paper, we study the performance of the recently proposed class of path-time codes (PTCs), which exploit time and path diversity to increase the reliability of end-to-end transmission in ad hoc multihop networks. Using the central limit theorem, we prove that PTCs reshape the statistics of a relay path including multiple cascaded links. In particular, as the number K of relay paths becomes large, the cascaded channel statistic is transformed from K-product Rayleigh to Rayleigh. This is numerically demonstrated and analytically verified by using the concept of “amount of fading” (AF). Our results show that, by using PTCs, the end-to-end error-rate performance can be boosted in addition to the diversity and coding gains.

Ad hoc cognitive radio networks (CRNs) have the potential for meeting the challenge of increasing radio spectrum efficiency. However, traditional control of ad hoc networking demands end-to-end information channel feedback, whose feasibility is hard in ad hoc CRNs due to the opportunistic nature of spectrum access. In this paper, we propose a virtual multiple-input multiple-output (MIMO) approach to facilitate error-resilient end-to-end transmission with no need for feedback information. An erasure-channel model is used to describe the randomness of outage caused by opportunistic links. At source node, a discrete Fourier transform (DFT)-based path-time code (PTC) is used to exploit path diversity. The a priori erasure probability is analyzed, and a pipeline scheduling scheme with unequal waiting periods is designed to reduce such probability. At destination node, knowledge of the a priori erasure probability is exploited to overcome the decoding challenge raised by the presence of random erasures. A joint sphere decoder (JSD) with a minimum mean-squared error sorted QR decomposition (MMSE-SQRD) effectively implements maximum a posteriori (MAP) probability decoding. This decoder simultaneously performs erasure identification and data decoding. Numerical results show that the proposed virtual MIMO framework can pave the way to efficient and reliable end-to-end transmission in ad hoc CRNs.

This work investigates polar coding for block-fading channels. We show that polarization does occur at infinity for three types of channel multiplexers. Nevertheless, the polarization process is not unique, as it is shaped by the choice of the multiplexer. The fading-plane approach is used to study the outage behavior of polar coding at a fixed transmission rate. Two types of multiplexers are shown to provide full diversity at finite and infinite code length.

Channel-modeling uncertainties may affect the performance of spectrum sensing in cognitive-radio applications. Negative effects of these uncertainties may be mitigated by an appropriate choice of the sensor operation. We show how the use of a linear-quadratic detector can improve the performance of both linear and quadratic spectrum sensors. The robustness to model uncertainties of the linear-quadratic detector is studied using moment-bound theory.

We study iterative receivers for joint decoding and channel-state estimation for transmission on block-fading channels of root- LDPC-coded signals. Root-LDPC codes are known to be most performant codes for block-fading channels, as their spacial "root" structure allows to get the full-diversity property. This property ensures a good error decoding performance of root LDPC codes, especially in contrast with the performance standard LDPC codes (having the maximum diversity equal to 1). However, as any channel code, root-LDPC codes also suffer from the diversity loss when the channel state information is not known at the receiver. In this work we propose a joint channel estimation- decoding scheme for root- LDPC codes that helps to overcome this problem and still to have the full-diversity.

We examine an extreme case of modeling uncertainties in spectrum sensing, whereby the interference which, in addition to additive noise, affects a sensor has an unknown probability distribution, and only its maximum power is known. We deal with a situation in which the sensor disregards the presence of the interference, and we study its performance. Application of moment-bound theory allows the derivation of sharp (i.e., achievable) upper and lower bounds to the receiver operating characteristics of the sensor. Coherent and energy detectors are analyzed. In particular, it is proved that, even in the large signal-to-noise ratio regime, reliable sensing becomes impossible if the maximum interference power exceeds a certain threshold.

We analyze multiuser detection under the assumption that the number of users accessing the channel is unknown by the receiver. In this environment, users' activity must be estimated along with any other parameters such as data, power, and location. Our main goal is to determine the performance loss caused by the need for estimating the identities of active users, which are not known a priori. To prevent a loss of optimality, we assume that identities and data are estimated jointly, rather than in two separate steps. We examine the performance of multiuser detectors when the number of potential users is large. Statistical-physics methodologies are used to determine the macroscopic performance of the detector in terms of its multiuser efficiency. Special attention is paid to the fixed-point equation whose solution yields the multiuser efficiency of the optimal (maximum a posteriori) detector in the large signal-to-noise ratio regime. Our analysis yields closed-form approximate bounds to the minimum mean-squared error in this regime. These illustrate the set of solutions of the fixed-point equation, and their relationship with the maximum system load. Next, we study the maximum load that the detector can support for a given quality of service specified by error probability.

We design powerful low-density parity-check (LDPC) codes with iterative decoding for the block-fading channel. We first study the case of maximum-likelihood decoding, and show that the design criterion is rather straightforward. Since optimal constructions for maximum-likelihood decoding do not perform well under iterative decoding, we introduce a new family of full-diversity LDPC codes that exhibit near-outage-limit performance under iterative decoding for all block-lengths. This family competes favorably with multiplexed parallel turbo codes for nonergodic channels.

A systolic array to implement lattice-reduction-aided linear detection is proposed for a MIMO receiver. The lattice reduction algorithm and the ensuing linear detections are operated in the same array, which can be hardware-efficient. All-swap lattice reduction algorithm (ASLR) is considered for the systolic design. ASLR is a variant of the LLL algorithm, which processes all lattice basis vectors within one iteration. Lattice-reduction-aided linear detection based on ASLR and LLL algorithms have very similar bit-error-rate performance, while ASLR is more time efficient in the systolic array, especially for systems with a large number of antennas.

The 2times2 MIMO profiles included in mobile WiMAX specifications are Alamouti's space-time code (STC) for transmit diversity and spatial multiplexing (SM). The former has full diversity and the latter has full rate, but neither of them has both of these desired features. An alternative 2times2 STC, which is both full rate and full diversity, is the Golden code. It is the best known 2times2 STC, but it has a high decoding complexity. Recently, the attention was turned to the decoder complexity, this issue was included in the STC design criteria, and different STCs were proposed. In this paper, we first present a full-rate full-diversity 2times2 STC design leading to substantially lower complexity of the optimum detector compared to the Golden code with only a slight performance loss. We provide the general optimized form of this STC and show that this scheme achieves the diversity multiplexing frontier for square QAM signal constellations. Then, we present a variant of the proposed STC, which provides a further decrease in the detection complexity with a rate reduction of 25% and show that this provides an interesting trade-off between the Alamouti scheme and SM.

The problem of jointly estimating the number, the identities, and the data of active users in a time-varying multiuser environment was examined in a companion paper (IEEE Trans. Information Theory, vol. 53, no. 9, September 2007), at whose core was the use of the theory of finite random sets on countable spaces. Here we extend that theory to encompass the more general problem of estimating unknowncontinuousparameters of the active-user signals. This problem is solved here by applying the theory of random finite sets constructed on hybrid spaces. We do so deriving Bayesian recursions that describe the evolution with time of a posteriori densities of the unknown parameters and data. Unlike in the above cited paper, wherein one could evaluate the exact multiuser set posterior density, here the continuous-parameter Bayesian recursions do not admit closed-form expressions. To circumvent this difficulty, we develop numerical approximations for the receivers that are based on Sequential Monte Carlo (SMC) methods (“particle filtering”). Simulation results, referring to a code-divisin multiple-access (CDMA) system, are presented to illustrate the theory.

We focus on full-rate, fast-decodable space-time block codes (STBCs) for 2 times 2 and 4times2 multiple-input multiple-output (MIMO) transmission. We first derive conditions and design criteria for reduced-complexity maximum-likelihood (ML) decodable 2times2 STBCs, and we apply them to two families of codes that were recently discovered. Next, we derive a novel reduced-complexity 4times2 STBC, and show that it outperforms all previously known codes with certain constellations.

In multiuser detection, the set of users active at any time may be unknown to the receiver. A two-step detection procedure, in which multiuser detection is preceded by active-user identification, is suboptimum. The optimum solution consists of detecting simultaneously the set of active users and their data, problem that can be solved exactly by applying random-set theory (RST). However, implementation of optimum detectors can be limited by their complexity, which grows exponentially with the number of potential users. In this paper we illustrate how the complexity of optimum can be reduced. In particular, sphere detection (SD) techniques (possibly in an approximate version) are examined.

In this paper, we introduce a pilot-aided multipath channel estimator for multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems. Typical estimation algorithms assume the number of multipath components and delays to be known and constant, while their amplitudes may vary in time. In this work, we focus on the more realistic assumption that also the number of channel taps is unknown and time-varying. The estimation problem arising from this assumption is solved using random set theory (RST), which is a probability theory of finite sets. Due to the lack of a closed form of the optimal filter, a Rao-Blackwellized particle filter (RBPF) implementation of the channel estimator is derived. Simulation results demonstrate the estimator effectiveness.

We study the minimum mean square error (MMSE) and the multiuser efficiency eta of large dynamic multiple access communication systems in which optimal multiuser detection is performed at the receiver as the number and the identities of active users is allowed to change at each transmission time. The system dynamics are ruled by a Markov model describing the evolution of the channel occupancy and a large-system analysis is performed when the number of observations grow large. Starting on the equivalent scalar channel and the fixed-point equation tying multiuser efficiency and MMSE, we extend it to the case of a dynamic channel, and derive lower and upper bounds for the MMSE (and, thus, for eta as well) holding true in the limit of large signal-to-noise ratios and increasingly large observation time T.

A new graph-based construction of generalized low density codes (GLD-Tanner) with binary BCH constituents is described. The proposed family of GLD codes is optimal on block erasure channels and quasi-optimal on block fading channels. Optimality is considered in the outage probability sense. A classical GLD code for ergodic channels (e.g., the AWGN channel, the i.i.d. Rayleigh fading channel, and the i.i.d. binary erasure channel) is built by connecting bitnodes and subcode nodes via a unique random edge permutation. In the proposed construction of full-diversity GLD codes (referred to as root GLD), bitnodes are divided into 4 classes, subcodes are divided into 2 classes, and finally both sides of the Tanner graph are linked via 4 random edge permutations. The study focuses on non-ergodic channels with two states and can be easily extended to channels with 3 states or more.

We show how to build full-diversity product codes under both iterative encoding and decoding over non-ergodic channels, in presence of block erasure and block fading. The concept of a rootcheck or a root subcode is introduced by generalizing the same principle recently invented for low-density parity-check codes. We also describe some channel related graphical properties of the new family of product codes, a family referred to as root product codes.

We consider the neighbor-discovery problem in a fixed wireless network where each node is identified by its signature, and the signatures are chosen so as to limit collisions. Limited-complexity constraints lead to a simple algorithm based on incoherent detection of nodes. The performance of this algorithm is evaluated by computing the probability of a false alarm and of a missed detection of a single node.

We examine the problem of determining which nodes are neighbors of a given one in a wireless network. We consider an unsupervised network operating on a frequency- flat Gaussian channel, where K + 1 nodes associate their identities to nonorthogonal signatures, transmitted at random times, synchronously, and independently. A number of neighbor- discovery algorithms, based on different optimization criteria, are introduced and analyzed. Numerical results show how reduced- complexity algorithms can achieve a satisfactory performance.

The problem of jointly estimating the number, the identities, and the data of active users in a dynamic multiuser environment was examined in (E. Biglieri and M. Lops, 2006). This paper extends the results of (E. Biglieri and M. Lops, 2006) to the more general case where some unknown continuous parameters of the active-user signals must also be estimated. This problem, which cannot be solved with traditional signal processing techniques, is solved here by applying the theory of random finite sets constructed on hybrid spaces. In particular, we derive Bayes recursions that describe the evolution with time of a posteriori densities of the unknown parameters and data. Since these recursions do not admit closed-form expressions, we use numerical approximations based on Monte Carlo methods ("particle filtering"). Simulation results, referring to a CDMA system, are presented to illustrate the theory.

High-quality channel estimation and tracking is central for coherent detection in wireless communication systems. Typical tracking algorithms assume the number of multipath components and delays to be known and constant, while their ampli- tudes may vary in time. In this work we focus on the more realistic assumption that also the number of channel taps is unknown and time-varying. The more complex estimation problem arising from this assumption is solved using Random-Set Theory, which allows one to regard the multipath-channel response as a single set-valued variable. Using a particle-filter implementation, we derive an estimator that simultaneously tracks the amplitudes and the number of channel taps for orthogonal frequency division multiplexed (OFDM) systems.

Mobile WiMAX systems are based on the IEEE 802.16e specifications, which include two mandatory MIMO profiles for the downlink. One of these is Alamouti's space-time code (STC) for transmit diversity, and the other is a 2times2 spatial multiplexing MIMO scheme. In this paper, we compare the two schemes assuming that the latter employs maximum-likelihood detection. The analysis shows that at the same spectral efficiency, Alamouti's STC combined with maximum-ratio combining (MRC) at the receiver significantly outperforms the 2times2 spatial multiplexing scheme at high values of the signal-to-noise ratio (SNR). Next, selection of a MIMO option is included in link adaptation to maximize network capacity, and operating SNR regions are determined for different modulation, coding and MIMO combinations.

In random-access communication systems, the number of active users varies with time, and has considerable bearing on receiver's performance. Thus, techniques aimed at identifying not only the information transmitted, but also that number, play a central role in those systems. An example of application of these techniques can be found in multiuser detection (MUD). In typical MUD analyses, receivers are based on the assumption that the number of active users is constant and known at the receiver, and coincides with the maximum number of users entitled to access the system. This assumption is often overly pessimistic, since many users might be inactive at any given time, and detection under the assumption of a number of users larger than the real one may impair performance. The main goal of this paper is to introduce a general approach to the problem of identifying active users and estimating their parameters and data in a random-access system where users are continuously entering and leaving the system. The tool whose use we advocate is random-set theory (RST): applying this, we derive optimum receivers in an environment where the set of transmitters comprises an unknown number of elements. In addition, we can derive Bayesian-filter equations which describe the evolution with time of the a posteriori probability (APP) density of the unknown user parameters, and use this density to derive optimum detectors. In this paper, we restrict ourselves to interferer identification and data detection, while in a companion paper we shall examine the more complex problem of estimating users' parameters.

We consider the use of multiple transmit and receive antennas (MIMO) in a wideband code-division multiple-access system with space-time coding. Using large-system asymptotic analyses, we examine the performance of linear receivers whereby multiuser detection and MIMO decoding are kept separate.

We examine the performance of a reduced-complexity doubly iterative decoder for space-time turbo codes on a quasi-static fading channel. The decoder works by using preliminary soft values of the coded symbols, obtained after a limited number of turbo iterations, to reduce the spatial interference from the received signal. Then, new turbo iterations are performed to improve on the quality of the soft values, and so on. Using a number of approximations, we obtain a receiver interface that achieves a good tradeoff between performance and complexity, and allows the use of turbo space-time codes for a large number of transmit and receive antennas.

We introduce a doubly-iterative decoder for space–time turbo codes on a quasi-static fading channel. The decoder works by using preliminary soft values of the coded symbols, obtained from a limited number of turbo iterations, to reduce the spatial interference from the received signal. After this reduction, new turbo iterations are performed to improve on the quality of the soft values, and so on. Using a number of approximations, we obtain a receiver interface that achieves a good trade-off between performance and complexity, and allows the use of turbo space–time codes for a large number of transmit and receive antennas.

Under the assumption of a frequency-flat slow Rayleigh fading channel with multiple transmit and receive antennas, we examine the effects of imperfect estimation of the channel parameters on error probability when known pilot symbols are transmitted among information data. Three different receivers are considered. The first one derives an estimate of the channel (by using either a maximum-likelihood or a minimum-mean-square error criterion), next uses this estimate in the same metric that would he applied if the channel were perfectly known. The second receiver derives again an estimate of the channel, but uses the maximum-likelihood metric conditioned on the channel estimate. Our last receiver processes simultaneously the pilot and data symbols received. Simulation results are exhibited, showing that only a relatively small percentage of the transmitted frame need he allocated to pilot symbols in order to experience an acceptable degradation of error probability due to imperfect channel knowledge. Algorithms for the recursive calculation of the decision metric of the last two receivers are also developed, for application to sequential decoding of trellis space-time codes.

Abstract In this tutorial paper, we describe iterative receivers that combine a soft decoder for a general space‐time code with a spatial‐interference canceler. The performance of these receivers is analyzed by using EXIT charts, a convenient graphical description that yields quite accurate results. By properly combining the EXIT characteristics of the canceler and of the decoder, the convergence behavior of the iterative algorithms can be understood, and design guidelines derived. The idea here is to observe that both the interference canceler and the decoder can be studied by examining the evolution of the extrinsic information passed along to the connected blocks. Copyright © 2004 John Wiley & Sons, Ltd.

We compare complexities and performances of some suboptimum linear and nonlinear (BLAST) interfaces used for decoding space-time codes used over a Rayleigh fading channel. We observe how the introduction of an interleaver can be beneficial here. We introduce a new simple iterative linear interface, based on hard Viterbi decoding and offering a performance considerably improved with respect to noniterative receivers.

A family of upper bounds to error probabilities of coded systems was recently proposed by D. Divsalar (see IEEE Communication Theory Workshop, 1999; JPL TMO Prog. Rep. 42-139, 1999). These bounds are valid for transmission over the additive white Gaussian noise channel, and require only the knowledge of the weight spectrum of the code words. After illustrating these bounds, we extend them to fading channels. Contrary to the union bound, our bounds maintain their effectiveness below the signal-to-noise ratio (SNR) at which the cutoff rate of the channel equals the rate of the code. Some applications are shown. First, we derive upper bounds to the minimum SNR necessary to achieve zero error probability as the code block length increases to infinity. Next, we use our bounds to predict the performance of turbo codes and low-density parity-check codes.

We describe a simple technique for the numerical calculation, within any desired degree of accuracy, of the pairwise error probability (PEP) of space-time codes. This method is very general, and applies to the calculation of the probability P(/spl nu/ > x), where /spl nu/ and x are independent random variables whose moment-generating functions (MGF) are known. In particular, it applies to the calculation of the expectation E[Q(/spl radic//spl xi/)], where Q(/spl middot/) is the Gaussian tail function and /spl xi/ is a random variable whose moment-generating function is known.

We study the asymptotic behavior of space-time codes when a linear receiver interface is used in lieu of the maximum-likelihood interface. Specifically, we determine the behavior of pairwise error probabilities with maximum-likelihood decoding and with four types of receiver interfaces: the maximum-likelihood interface, the linear zero-forcing interface, the linear minimum-mean-square-error interface, and the matched-filter interface. An asymptotic analysis is performed by assuming that the number of receiving antennas grows to infinity while the number of transmitting antennas is finite, and that both numbers grow to infinity but their ratio remains constant. We show that with all the interfaces studied here the asymptotic performance of space-time codes is determined by the Euclidean distances between code words. Moreover, the performance of linear interfaces comes close to maximum-likelihood if the number r of receive antennas is sufficiently larger than the number t of transmit antennas. The dependence of error probabilities on Euclidean distance is valid for intermediate signal-to-noise ratios even when the number of antennas is small.

We study the asymptotic behavior of space-time codes when the number of transmit and receive antennas grows to infinity. Specifically, we determine the behavior of pairwise error probabilities with maximum-likelihood (ML) decoding and with three types of receiver interfaces: the ML interface, the linear zero-forcing (ZF) interface, and the linear minimum-mean-square-error (MMSE) interface. Two situations are studied: when the number of receiving antennas grows to infinity while the number of transmitting antennas is finite, and when both numbers grow to infinity but their ratio remains constant. We show that with ML or linear interfaces the asymptotic performance of space-time codes is determined by the Euclidean distances between codewords. Moreover, with the two linear interfaces examined here the number r of receive antennas must be much larger than the number t of transmit antennas to avoid a sizeable loss of performance; on the other hand, when r /spl Gt/ t, the performance of these linear interfaces comes close to that of ML. The dependence of error probabilities on Euclidean distance is valid for intermediate signal-to-noise ratios (SNRs) even when the number of antennas is small. Simulations validate our theoretical findings, and show how asymptotic results may be substantially valid even in a nonasymptotic regime: thus, even for few antennas, off-the-shelf codes may outperform space-time codes designed ad hoc.

We describe a simple technique for the numerical calculation, within any desired degree of accuracy, of the pairwise error probability (PEP) of space-time codes over fading channels. This method applies also to the calculation of E[Q(/spl radic//spl xi/)] for any nonnegative random variable /spl xi/ whose moment-generating function /spl Phi//sub /spl xi//(s)=E[exp(-s/spl xi/)] is known. Its application to the multiple antenna independent Rayleigh-fading channel and to the Rayleigh block fading channel is discussed, and illustrated by two simple examples.

We study the performance of a UNITS downlink, as achieved by a single-user (RAKE) and a multiuser (linear MMSE) receiver with adaptive modulation and multicode in the presence of multipath fading. We advocate an adaptive transmission scheme that varies the number of virtual users and the modulation spectral efficiency in order to optimize the system throughput. Two multipath channel models are considered, exhibiting 3 and 9 paths, respectively. Over the more favorable multipath channel, the multiuser MMSE receiver yields a significant performance enhancement with respect to the RAKE receiver.

We study the problem of maximizing the total system throughput under a bit error rate constraint for all users in the uplink of a single-cell synchronous CDMA system. Users realize variable bit rates by using a combination of multicode transmission and adaptive QAM modulation. We assume random signature sequences for all users, and perform an asymptotic analysis. We parametrize each user's resource allocation scheme by two parameters, viz., the number of signatures the user transmits with and the number of signal points in the user's QAM constellation, and optimize the total throughput over this parameter space. We examine four different settings: single-user matched filter (SUMF) and minimum-mean-square error (MMSE) receiver at the base station, with and without maximum power constraints. For a single user system, we describe the jointly optimum number of multicodes and constellation sizes for these four different system models. When multiple users are present, we show that the total throughput is maximized when only one user transmits: with no maximum power constraints this user can be chosen arbitrarily, otherwise it should be the one with the largest SNR. This solution, although optimal in the sense of maximizing the total throughput, is unfair to all but one user: thus, we examine a scheduling mechanism that assigns equal time frames to all users, thus yielding maximum fairness, and discuss the resulting total throughput loss.

We examine a multiple-access AWGN channel with synchronous DS-CDMA in which the channel amplitude and noise variance parameters are unknown a priori. We derive an iterative joint multiuser decoder and parameter estimator based on soft interference cancellation and on soft decision-driven least-squares estimation. Our derivation is obtained by applying the sum-product algorithm to the factor graph of the joint a posteriori probability measure of the information bits and of the unknown channel parameters.

Using asymptotic analysis, we study the effect of frequency-flat fading on code division multiple access (CDMA) systems with linear receivers and random spreading sequences. Specifically, we let the number of users grow without bound, while the ratio of number of users to spreading sequence length is kept fixed to a value /spl alpha/. We treat separately the cases of slow fading (nonergodic channel) and of fast fading (ergodic channel). For the former channel, we derive the outage probability, while for the latter we compute the channel capacity. In both cases, multiple classes of users with different qualities of service are dealt with. As /spl alpha//spl rarr//spl infin/, the system throughput tends to the same limit of 1.44 bit/symbol as for the nonfading channel with both single-user matched filter (SUMF) and linear minimum mean-square-error (MMSE) receivers. The outage probability exhibits a floor for all /spl alpha/ with the SUMF receivers, while with MMSE receiver the floor is present only for /spl alpha/>1. We also address the tradeoffs involved in the allocation of available bandwidth between spreading and coding.

We derive the performance limits of a radio system consisting of a transmitter with t antennas and a receiver with r antennas, a block-fading channel with additive white Gaussian noise (AWGN), delay and transmit-power constraints, and perfect channel-state information available at both the transmitter and the receiver. Because of a delay constraint, the transmission of a codeword is assumed to span a finite (and typically small) number M of independent channel realizations; therefore, the relevant performance limits are the information outage probability and the "delay-limited" (or "nonergodic") capacity. We derive the coding scheme that minimizes the information outage probability. This scheme can be interpreted as the concatenation of an optimal code for the AWGN channel without fading to an optimal beamformer. For this optimal scheme, we evaluate minimum-outage probability and delay-limited capacity. Among other results, we prove that, for the fairly general class of regular fading channels, the asymptotic delay-limited capacity slope, expressed in bits per second per hertz (b/s/Hz) per decibel of transmit signal-to-noise ratio (SNR), is proportional to min (t,r) and independent of the number of fading blocks M. Since M is a measure of the time diversity (induced by interleaving) or of the frequency diversity of the system, this result shows that, if channel-state information is available also to the transmitter, very high rates with asymptotically small error probabilities are achievable without the need of deep interleaving or high-frequency diversity. Moreover, for a large number of antennas, delay-limited capacity approaches ergodic capacity.

This paper derives general results on the partial auto-correlation function of the optimal spreading sequences for asynchronous CDMA systems with respect to the minimization of the average error probability under the standard Gaussian approximation (SGA) condition without the assumption of stationary random processes on the spreading sequences. We construct a family of optimal spreading sequences from the existing Gold codes, which have the same number of codes as a set of Gold codes. An asynchronous CDMA system using such optimal spreading sequences allows 15% more users than when purely random binary sequences or Gold codes are employed. Moreover, the acquisition time performance of the proposed optimal spreading sequences is also shown to be better than that of Gold codes.

A family of upper bounds to error probabilities of coded systems on the additive white Gaussian noise channel was recently proposed by Divsalar (see 1999 IEEE Communication Theory Workshop, Aptos, CA., 1999). Their calculation depends only on the weight spectrum of the code words. We first elaborate upon these bounds to show how they can be further tightened by using numerical integration instead of a Chernoff bound, and by reducing the number of code words to be included in the bound. Next, we extend them to fading channels.

In this paper we present the analog on-chip learning architecture of a gradient descent learning algorithm: the Weight Perturbation learning algorithm. From the circuit implementation point of view our approach is based on current mode and translinear operated circuits. The proposed architecture is very efficient in terms of speed, size, precision and power consumption; moreover it exhibits also high scalability and modularity.

We use results from the asymptotic analysis of code-division multiple access with random spreading as a tool for gaining insight and deriving design guidelines on practical system issues, inspired by the current UMTS/IMT2000 standardization process. In particular, we consider a simple synchronous single-cell system with perfect power control and linear detection, and we examine the following: (1) the optimal tradeoff between coding rate and spreading gain and (2) the comparison of different multirate schemes. Our analysis shows that, for the sake of system spectral efficiency maximization, there exists a threshold E/sub b//N/sub o/ below which the single-user matched filter (SUMF) is optimal (within the limits of our system model). As far as multirate schemes are concerned, we show that multicode and variable-spreading with SUMF detection are equivalent, while the former is uniformly better than the latter with linear minimum-mean-square error detection. Variable-spreading can perform very close to multicode if high-rate users are detected by observing the whole "low-rate" symbol interval. Finally, we compare the capacity regions of the multimodulation and multicode schemes versus the E/sub b//N/sub o/ ratio.

We study the synergy between coded modulation and antenna-diversity reception on channels affected by slow Rician fading. Specifically, we assess the impact of channel-state information (CSI) on error probability. We show that with a good coding and constant envelope modulations (for example, phase-shift keying) scheme the loss in performance when CSI is not available is moderate (around 1.5 dB). Moreover, as the diversity order grows, the channel tends to become Gaussian.

Given an abstract group /spl Gscr/, an N-dimensional orthogonal matrix representation G of /spl Gscr/, and an "initial vector" x/spl isin/R/sup N/, Slepian defined the group code generated by the representation G to be the set of vectors Gx. If G is a group of permutation matrices, the set Gx is called a "permutation code". For permutation codes a "stack algorithm" decoder exists that, in the presence of low noise, produces the maximum-likelihood estimate of the transmitted vector by using far fewer computations than the standard decoder. In this correspondence, a new concept of equivalence of codes of different dimensions is presented which is weaker than the usual definition of equivalent codes. We show that every group code is (weakly) equivalent to a permutation code and we discuss the minimal degree of this permutation code.

We study optimal constant-rate coding schemes for a block-fading channel with strict transmission delay constraint, under the assumption that both the transmitter and the receiver have perfect channel-state information. We show that the information outage probability is minimized by concatenating a standard "Gaussian" code with an optimal power controller, which allocates the transmitted power dynamically to the transmitted symbols. We solve the minimum outage probability problem under different constraints on the transmitted power and we derive the corresponding power-allocation strategies. In addition, we propose an algorithm that approaches the optimal power allocation when the fading statistics are not known. Numerical examples for different fading channels are provided, and some applications discussed. In particular, we show that minimum outage probability and delay-limited capacity are closely related quantities, and we find a closed-form expression for the delay-limited capacity of the Rayleigh block-fading channel with transmission over two independent blocks. We also discuss repetition diversity and its relation with direct-sequence or multicarrier spread-spectrum transmission. The optimal power-allocation strategy in this case corresponds to selection diversity at the transmitter. From the single-user point of view considered in this paper, there exists an optimal repetition diversity order (or spreading factor) that minimizes the information outage probability for given rate, power, and fading statistics.

We study the information outage rate of a block-fading Gaussian channel with strict delay constraint and constant rate transmission, under the assumption that both the transmitter and the receiver have perfect knowledge of the channel. We find the power allocation strategy minimizing the outage rate under a constraint on the average transmitted power. Numerical examples for the Rayleigh fading channel are provided. In particular, an explicit formula for the delay-limited capacity of the 2-block Rayleigh fading channel is derived.

We show how parallel concatenated codes (PCCs, also known as "turbo codes") can be endowed with unequal error protection (UEP). Given the two component encoders of the PCC encoder and the desired interleaver size, UEP is achieved by: (1) suitably positioning the different importance classes of information symbols into the encoder input frame; (2) puncturing the PCC redundancy symbols with a nonuniform pattern; and (3) choosing the interleaver of the PCC encoder in a class of interleavers that guarantees isolation of the importance classes. By controlling the amount of redundancy assigned to each importance class and the class positioning in the input frame, a whole family of UEP PCCs with different UEP levels can be obtained from the same component encoders and interleaver size. From a practical viewpoint, a family of UEP PCCs can be decoded by the same "turbo" iterative decoder, provided that the decoder hardware implementation allows for programmable puncturing and interleaving.

Turbo codes are a practical solution for achieving large coding gains. We present a new turbo coding scheme where the component codes are convolutional codes (CCs) over the ring of integers modulo M, with M being the alphabet size of the source encoder. The a priori knowledge of the source statistics is used during the iterative decoding procedure for improved decoder performance. As an example of application, we examine differential pulse code modulation (DPCM) encoded image transmission.

In this paper we review the most peculiar and interesting information-theoretic and communications features of fading channels. We first describe the statistical models of fading channels which are frequently used in the analysis and design of communication systems. Next, we focus on the information theory of fading channels, by emphasizing capacity as the most important performance measure. Both single-user and multiuser transmission are examined. Further, we describe how the structure of fading channels impacts code design, and finally overview equalization of fading multipath channels.

It has been recognized by Zehavi (1992) that the performance of coded modulation over a Rayleigh fading channel can be improved by bit-wise interleaving at the encoder output, and by using an appropriate soft-decision metric as an input to a Viterbi (1990) decoder. The paper presents in a comprehensive fashion the theory underlying bit-interleaved coded modulation, provides tools for evaluating its performance, and gives guidelines for its design.

Multiuser detection schemes are applied to a regional GEO satellite mobile system based on FDM/TDMA. The study focuses on the system uplink (mobile to satellite) and analyzes the performance of candidate schemes taken from the class of linear multiuser receivers. A new simple MMSE combiner is proposed, which provides performance close to optimal in terms of output MSE and lends itself to a simple adaptive implementation. Results pertaining to FDM/TDMA coded transmission with slow frequency hopping and short-depth interleaving are presented.

Zehavi (1992) showed that the performance of coded modulation over a Rayleigh fading channel can be improved by bit-wise interleaving the encoder output and by using an appropriate soft-decision metric as an input to a Viterbi decoder. The goal of this paper is to present in a comprehensive fashion the theory underlying bit-interleaved coded modulation, to provide tools for evaluating its performance, and to give guidelines for its design.

We address the problem of designing and analyzing the performance of a coded modulation scheme for the fading channel when space diversity is used. Under fairly general conditions, a channel affected by fading can be turned into an additive white Gaussian noise (AWGN) channel by increasing the number of diversity branches. Consequently, it can be expected (and is indeed verified by our analyses and simulations) that a coded modulation scheme designed to be optimal for the AWGN channel also will perform asymptotically well on a fading channel with diversity. This paper presents bounds on the bit-error probability of a system with coded modulation and diversity for space- and time-correlated Rician flat fading. Specifically, we derive a new method which allows evaluation of the pairwise error probability extremely easily, as well as accurately and computationally fast. The accuracy achieved improves considerably on the widely used, but rather loose Chernoff bound. Starting from this analysis, we study the asymptotic behavior of the fading channel with diversity as the number of diversity branches increases, and we address the effects of diversity on coded modulation performance and design criteria, including the effect on interleaver depth (which affects the total delay of the system).

For pt. I see ibid., vol.45, no.6, p.563-572, 1997. We study coded modulation with block differential detection in an arbitrarily correlated Rician fading channel with space diversity. Coded differential q-PSK is included in our analysis as a special case. A metric is chosen that is optimum for perfect interleaving, slow fading, and independent diversity branches. For slow fading, we compare the the cutoff rates of the channels resulting from different choices of block length N and diversity index M. Specifically, we show that block detection with diversity may or may not generate a better coding channel than usual differential detection, according to the code selected and the combination of values of M and N. In particular, for low-diversity orders (M=1,2) and for low-to-medium code rates, differential detection is still an optimal or near-optimal solution, while for high-diversity orders (M/spl ges/2) and medium-to-high code rates (up to uncoded modulation) block detection with N>2 can provide a significant gain. An error floor always exists when fading is fast. It decreases exponentially with the product of code diversity and space diversity, so that the latter emerges as a very effective technique for lowering the error floor of a system affected by fast fading. Performance examples based on actual coding schemes are also shown.

For pt.II see ibid., vol.45, no.6, p.55-67, 1997. In previous work, we have studied the impact of diversity on coded digital communication systems operating over fading channels. In particular, we have shown that diversity may be thought of as a way of making the channel more similar to a Gaussian one. The present paper extends this analysis to fading channels affected by co-channel interference (CCI). Three receiver models are examined, namely, with coherent detection and perfect channel-state information (CSI), with differential; and with pilot-tone detection. We study the effect of diversity on the irreducible error floor caused by CCI and fading, and the asymptotic behavior of the channel as the diversity order increases. Our results show that, when perfect CSI is available, diversity is able to turn asymptotically the channel into a CCI-free additive white Gaussian noise (AWGN) channel with the same signal-to-noise ratio (SNR). On the other hand, differential and pilot-tone detection do not remove interference in the limit. Nevertheless, also with these detection schemes, diversity achieves significant gains when the SNR is large enough. Calculation of the channel cutoff rate provides guidelines for the design of coded systems with CCI in fading environments. A wide range of examples, validated by computer simulation, illustrates our conclusions.

We compare three receivers for coded narrowband transmission affected by fading and co-channel interference. The baseline receiver is based on conventional diversity reception with maximal-ratio combining. A multiuser approach allows us to derive a maximum-likelihood multiuser receiver and its reduced-complexity suboptimal version. Finally, a decorrelating diversity receiver, which seeks a tradeoff between performance and complexity, is studied. Closed-form performance parameters are derived for all the proposed receivers in the case of coded coherent PSK and independent frequency nonselective Rayleigh fading.

To evaluate an upper bound on error probabilities of signal constellations used for transmission over the additive white Gaussian noise (AWGN) channel, enumeration of all the constellation intradistances is required. These may be infinite in number, for example, when convolutional codes are used and the constellations are lattices. Truncation of the series does not necessarily provide a bound anymore, and must be done with care. Yet the union bound is very simple, as it does not require any further knowledge about the signal constellation than the distance enumerator. In this paper, we describe some methods that can be used to evaluate error probabilities of infinite signal constellations, and that require only a finite number of terms. These methods are applicable, for example, to convolutional codes decoded with a finite-depth Viterbi algorithm and to signal constellations carved from lattices. Coded modulations based on lattices and convolutional or block codes can also be dealt with. As an example of application, we analyze a variable-rate 3-stage coded modulation encoder/decoder, which has been built and is based on a combination of convolutional codes with a single-parity-check block code.

We determine upper and lower bounds to the generalized Hamming weights of generalized concatenated codes. They are derived from the generalized Hamming weights of the outer codes and certain properties of the inner code and its partitions.

Numerical evaluation of some typical lattice parameters such as density, thickness, dimensionless second moment (quantizing constant), etc., are considered. Computational complexity grows exponentially with the dimension of the lattices and all known results rely on the very regular structure of some of these. In the paper the authors present a general algorithm which enables computation of all the common parameters for any given lattice by means of a complete description of its Voronoi cell. Using this algorithm, they have computed previously unknown values of the quantizing constants of some particularly interesting lattices. These results can be used to evaluate the performance of lattice quantizers and lattice signal constellations for the Gaussian channel. As an application they evaluate a tight upper bound for the error probability of a lattice constellation used for transmission over the additive white Gaussian noise channel.

We describe computational techniques for the evaluation of error probability of modulation schemes based on binary lattices and multilevel coding. These techniques stem from the representation of a binary lattice in the form of a trellis whose structure depends on the block codes on which the binary lattice is based. Multilevel coded-modulation schemes can also be described through a trellis; by combining with this the trellis structure of the lattice constellation we obtain a single trellis that can be used for maximum-likelihood decoding using the Viterbi algorithm and for computing the error probability. An upper bound to error probability can be obtained from the transfer function of the trellis with suitable labels, and is applicable to both maximum-likelihood and staged decoding.>

The main building block for the construction of a geometrically uniform coded modulation scheme is a subgroup of G/sup I/, where G is a group generating a low-dimensional signal constellation and I is an index set. In this paper we study the properties of these subgroups when G is cyclic. We exploit the fact that any cyclic group of q elements is isomorphic to the additive group of Z/sub q/ (the ring of integers modulo q) so that we can make use of concepts related to linearity. Our attention is focused mainly on indecomposable cyclic groups (i.e., of prime power order), since they are the elementary "building blocks" of any abelian group. In analogy with the usual construction of linear codes over fields, we define a generator matrix and a parity check matrix. Trellis construction and bounds on the minimum Euclidean distance are also investigated. Some examples of coded modulation schemes based on this theory are also exhibited, and their performance evaluated.>

In this paper, simple approximations are derived for the BER performance of coherent PSK-TCM over the Rayleigh channel with diversity, including the cases of branch and time correlation. Starting from a simple approximation of the Gaussian error function, a common methodology is described based on the derivation of the moment generating function of the sum of correlated squared-Rayleigh RVs. A simple final result is obtained requiring only the knowledge of the eigenvalues of some channel-related covariance matrices and the distance profile of the TCM scheme.

The power density spectrum of block-coded modulated signals is computed. Sufficient conditions for this spectrum to be the same as for uncoded modulation are derived. In the special case of a PSK-based-scheme, necessary conditions are derived in order to achieve spectrum shaping. The spectral lines obtained may be used for block synchronization.>

In this paper we discuss multidimensional signaling for transmission over the satellite channel, i.e., a bandlimited radio channel with nonlinearities. We derive a set of basis signals that are orthogonal and whose bandwidth occupancy is minimal, in the sense that they maximize the power inside a fixed frequency interval (/spl minus/B, B). Since we remove the assumption that the signals be confined in one symbol interval, the concept of orthogonality must be revisited. We design basis signals that satisfy the following requirements: (a) When passed through their matched filter, the sample sequence has no intersymbol interference; (b) when passed through the filter matched to another basis signal, the sample sequence has no interchannel interference, and (c) their bandwidth occupancy is minimum. The performance of four-dimensional signals designed according to this criterion is evaluated in terms of bandwidth occupancy and error probability over nonlinear satellite channels. Comparisons with two-dimensional modulation schemes (in particular QPSK) are also made.>

We consider the geometrical uniformity properties of signal space codes generated by multilevel coded modulation. First we examine multilevel schemes based on 2/sup L/-ary PSK signal sets, and we derive conditions on the binary component codes which lead to geometrically uniform signal space codes. Next we study the geometrical uniformity of multilevel schemes based on signal sets having a generating group isomorphic to a direct product. Finally, we provide an easy-to-test criterion for finding if a given signal set (or signal space code) obtained as the union of two orbits of the same generating group has the uniform distance property.>

The design of constellations that allow a high degree of parallelism in the staged decoder structure and in addition allow soft decoding of the component algebraic codes based on a systolic algorithm amenable to VLSI implementation is considered. Combination of these multidimensional constellations with trellis-coded modulation (TCM) is also considered. Set partitioning is based on the partition of a linear code into a subcode and its cosets, and the author shows that a highly parallel demodulator structure can also be applied when TCM is used.>

The authors consider a communication scheme based on continuous phase modulated (CPM) signals used in conjunction with trellis-coded modulation (TCM) for transmission over a channel affected by Gaussian noise and fading. This scheme provides a power saving due to the coding gain of TCM and a reduced bandwidth occupancy due to the features of CPM signals. Moreover, CPM provides constant-envelope signals. To keep the complexity of the receiver manageable and to be able to use interleaving/deinterleaving techniques to spread the fade bursts, suboptimal detection schemes must be used. Two such schemes, based on coherent and noncoherent detection of CPM, are considered. Their performance is evaluated by computing the computational cutoff rate of the discrete channel generated by CPM.>

The class of uniform trellis-coded modulation (TCM) techniques is defined, and simple explicit conditions for uniformity are derived. Uniformity is shown to depend on the metric properties of the two subconstellations resulting from the first step in set partitioning, as well as on the assignment of binary labels to channel symbols. The uniform distance property and uniform error property, which are both derived from uniformity but are not equivalent, are discussed. The derived concepts are extended to encompass transmission over a (not necessarily Gaussian) memoryless channel in which the metric used for detection may not be maximum likelihood. An appropriate distance measure is defined that generalizes the Euclidean distance. It is proved that uniformity of a TCM scheme can also be defined under this new distance. The results obtained are shown to hold for channels with phase offset or independent, amplitude-only fading. Examples are included to illustrate the applicability of the results.>

Analytical performance bounds are presented for trellis-coded MPSK, transmitted over a satellite-based land mobile channel. Upper bounds are evaluated using the well-known transfer function bounding technique, and lower bounds are achieved through knowledge of exact pairwise error probabilities. In order to analyze practical trellis-codes (four or more states), the uniform properties displayed by a certain class of trellis-codes are exploited, enabling the encoder transfer function to be obtained from a modified state transition diagram, having no more states than the encoder itself. Monte Carlo simulation results are presented in confirmation of all performance bounds and indicate a general weakness in the transfer function upper bounds. A new asymptotically tight upper bound is derived based on a simple modification to the standard transfer function bound, and results are presented for the four- and eight-state trellis-codes in Rician and Rayleigh fading.>

A communication scheme based on continuous-phase modulated (CPM) signals used in conjunction with trellis-coded modulation (TCM) is considered. To keep the complexity manageable, a detection scheme based on differential detection of CPM signals is used. Methods that estimate the Doppler-induced frequency shift from the receiver signal are studied. Since differential detection transforms a frequency shift into a phase shift, the phase estimation problem is examined first. Three Doppler frequency estimation schemes that are based on open-loop structures and that are designed to achieve different ranges of Doppler frequencies that can be estimated are introduced. These estimators show different degrees of complexity and (at least for high signal-to-noise ratios) significantly different estimation errors. Their performance is compared by using a simulation approach.>

Using a new representation for continuous-phase modulated (CPM) signals, it is shown how a closed-form expression for the power spectral density of full-response M-ary CPM with modulation index J/M can be obtained by straightforward computations. This result is used to provide an explanation of the fact that this power spectral density depends only on J and not on M.>

The computation of upper and lower bounds to error probability in digital transmission over nonlinear channels with a finite memory is considered. By using orthogonal Volterra series, the authors derive a canonical representation for discrete nonlinear systems, based on a linear convolutional code and a memoryless mapper. This representation shows that finite-memory, discrete nonlinear systems can be analyzed in much the same way as TCM (trellis-coded modulation) schemes. In particular, TCM over nonlinear channels can be analyzed. A technique is derived that expresses an upper bound to error probability based on the computation of the transfer of a state diagram with N branches, and whose branch labels are matrices rather than scalars. Some examples of its application are given. In particular, error bounds are derived for nonlinear TCM schemes and for TCM schemes operating on nonlinear channels.>

The authors examine the tradeoffs involved in the design of digital raised-cosine Nyquist filters for application in digital computer simulation or for incorporation in all-digital data modems. Both floating-point arithmetics (for simulation applications) and finite-precision arithmetics are considered. Tapped-delay-line (finite impulse response) with time- or frequency-domain design, direct-form infinite-impulse-response, Rao-Kailath, and Lei-Yao structures are examined. The main criteria for a comparison among the various solutions, besides their relative complexities, are the digital filter behavior in the time domain (residual intersymbol interference) and in the frequency domain (stopband attenuation).>

The effects of imperfect carrier phase recovery on uncoded and trellis-encoded PSK (phase-shift keying) are compared. A recently proposed clock-aided carrier recovery scheme is analyzed and compared to the standard frequency multiplication circuit. Results obtained through a combination of analysis and computer simulation compare uncoded 4-PSK with trellis-encoded 8-PSK carrying two bits per channel symbol. The quality of the recovered carrier phase is evaluated using the ratio of tone power to background. The system error probability is evaluated and used to determine how accurate the time clock recovery must be in a clock-aided carrier recovery circuit in order to outperform classical recovery systems. It is shown that if the clock recovery system is accurate enough, clock-aided carrier recovery used with coded 8-PSK can compensate for the increased sensitivity of the latter to phase errors.>

The filter minimizes the mean-square error between the sampled input to the decision device and the corresponding transmitted symbols. It is shown that the structure of this optimal receiving filter corresponds to a bank of matched filters, each followed by a linear transversal filter. Applications of this theory cover nonlinear channels with memory, linearly or nonlinearly modulated signals, and disturbances other than Gaussian noise (e.g. interference from other data sources).>

The performance of trellis codes is determined by their minimum Euclidean distance. Upper bounds on this minimum distance valid for phase-shift-keyed (PSK) signals that improve on previously derived bounds are derived. Although the bound is valid only for PSK signals, the bounding techniques developed here can be extended to other equal-energy configurations and hence could pave the way to obtaining more general results.>

The compensation of channel nonlinearities in digital radio communication systems is considered. A discrete system with memory, inserted between the source and the modulator, is designed with the aim of providing an equivalent channel with a distortionless linear part and no nonlinearities up to a given order. This design is based on a Volterra series model of the channel and on the theory of pth-order inverse systems. Since the compensator design is based on a mathematical model of the channel, the problem of model identification is considered. A modeling technique is described that uses computer simulation and orthogonal Volterra series. Several examples show the performance of this class of compensators.>

A class of multidimensional signals, based on generalized group alphabets, is introduced and its basic properties are derived. The combination of generalized group alphabets and coding is also examined: two coding schemes are considered-G. Ungerboeck's scheme (1982) for combination with convolutional codes, and V.V. Ginzburg's (1984) scheme for combination with block codes. It is concluded that the performance of these schemes makes them attractive for transmission over band-limited digital channels.>

Simple sufficient conditions are found for the spectrum of Ungerboeck-coded signals to be equal to the spectrum of uncoded signals. It is shown that a carefully designed Ungerboeck code does not shape the spectrum.

Two related cancellation techniques based on "tentative" decisions are proposed for removing intersymbol interference, due to channel nonlinearities, for voiceband data transmission. Cancellation of intersymbol interference avoids the need for equalizing or "inverting" analog nonlinear operations as in the decision-feedback method previously proposed by Falconer. The nonlinear cancellation approach removes nonlinear interference terms without excessive noise enhancement and allows effective implementation with ROM's to generate the needed nonlinear signal variables that are to be weighted and summed. The first technique can be incorporated as an "add-on" unit to a present-day modem; the second technique requires a different receiver architecture but offers somewhat enhanced improvement. Simulation results for 9.6 kbit/s data transmission over nonlinear channel models show that both techniques can offer substantial performance improvements for 16-point QAM systems.

TOPSIM III is a flexible, easy to use, stand-alone Fortran package for the digital simulation of communication systems in the time domain. TOPSIM III provides a simple high-level language for the description of the system. Programs can be written following the same structure used in drawing the system block diagram. The paper discusses the time domain simulation approach used in the design of the package and describes its capabilities. The contents of the subprogram libraries are presented, describing some of the building blocks that can be used in the simulation as well as the performance evaluation facilities available in the package. Some simple examples illustrate the use of TOPSIM III as a tool for analysis and design of digital communication systems.

Currently, 4-PSK is the prevalent modulation format in use for digital satellite communications. To improve bandwidth efficiency, 8PSK could be used instead, but a higher power would be needed; to improve power efficiency, error-correcting codes could be used, but at the expense of a larger bandwidth. Recently, Ungerboeck [1] has proposed a class of codes in which a constellation of2Msignals is used to transmit information at the rate oflog_{2} Mbits per symbol, and has shown that coding gains of up to several decibels can be achieved on the additive white Gaussian noise (AWGN) channel with no increase in bandwidth occupancy and a relatively small added complexity. Thus, these codes seem to be particularly attractive for application in the band-limited environment typical of satellite communication systems, provided that the performance gain that they provide on the AWGN channel is not lost over a satellite channel. The goal of this work is to assess the performance of this class of codes when used to transmit 3 information bits per symbol on a band-limited, nonlinear satellite channel. Three modulation formats are considered, namely 16-PSK, 16-QAM, and a 16-ary amplitude-phase keying scheme with two amplitude levels. It is found that 16-PSK outperforms the two other modulation formats, and that the use of these codes can provide a substantial performance improvement even on a satellite channel.

The "moment bound theory" is known to provide a useful technique to evaluate error probabilities for digital communication systems in the presence of additive noise and random interference. In this correspondence this theory is extended to the case where the moments of the interference are known only within certain intervals, and upper and lower bounds to the error probabilities are sought. A situation like this can occur in several applications. For example, the exact statistics of the interference may not be known, and only estimates of the first moments may be available. Another example arises when the signal is disturbed by intersymbol interference generated by a channel impulse response whose samples are known only in a certain interval--either because they have been measured with finite accuracy, or because we want to estimate the error probability for a class of channel impulse responses. Several numerical examples are provided which show the range of applicability of this technique.

Conventional techniques attempting to compensate for the influence of linear and nonlinear distortion in digital satellite channels include optimization of channel filtering. With conventional linear filtering it has been experienced that there is still room for considerable improvement, so that it appears reasonable to investigate some forms of nonlinear filtering in an attempt to cope with those distortions. In this paper a nonlinear equalizer structure is proposed, and its performance is analyzed. It is shown, by some examples Of application to a 4-phase PSK satellite channel, that it can prove quite effective in terms of a tradeoff between performance improvement and hardware complexity.

This paper deals with a class of nonlinear, time-invariant systems with memory - called discrete Volterra processors - based on the truncation of discrete-time Volterra series expansions of input-output relationships. These systems can be implemented by a finite-length transversal filter, a finite number of multipliers, and a summing bus, and share the interesting property of being described by a linear combination of suitable nonlinear functions of the input samples. Two examples of application are considered in some detail: (i) The design of minimum mean-square error predictors of discrete-time random processes, and (ii) The identification of discrete nonlinear systems with memory.

A random coding bound is derived for block coded transmission over channels characterized by a deterministic finite-memory part followed by the addition of white Gaussian noise. (Intersymbol interference channels are a special case.) According m this bound, a "product-measure cutoff rate" can be defined quite naturally for such a class of channels.

In many digital communication systems with additive noise and random interference disturbances, the error probability can be expressed as the statistical expectation of the complementary noise distribution function with respect to some function of the random interference variableZ. Conditions are presented for constructing a new class of upper and lower error bounds, utilizing an arbitrary number of generalized moments of the random interference. These bounds are based on four forms of the principal representation of Krein in the theory of approximation. General results are given for anL-level input system, an arbitrary noise distribution function, and an arbitrary transformationf(Z). A class of simple bounds using polynomial transformations on the centeredZfor the binary input system with additive Gaussian noise is presented. These bounds depend on the signal-to-noise ratio, the maximum interference distortions, the number of moments, and the polynomial transformation integer. In general the bounds obtained are very tight and need only modest computational efforts. Indeed, this approach yields the tightest possible bounds for a given set of moments of the random interference. Two techniques are discussed for evaluating principal representations as well as relationships to generalized quadrature rules. Numerical results are presented illustrating the tightness of these bounds.

A good deal of effort has been spent, in the past few years, to devise numerical algorithms for evaluating the performance of digital communication systems over noisy linear channels, i.e., in the presence of intersymbol interference and noise. In this concise paper we present a method for computing the error probability of multilevel baseband digital modulation systems when the channel is nonlinear with memory. The algorithm is based on a Volterra series expansion of the nonlinearity; with this model, we show that the moments of the disturbance can be computed recursively, and the same techniques in use for linear channels can be applied for evaluating the error probability. This approach can be generalized to consider noise entering the nonlinear channel. The computing algorithms are described in detail, and a complete example is worked out.

The theory of cyclic-group codes for the Gaussian channel is reviewed, and the following new results are shown: i) the initial vector problem for these codes can be formulated as a linear programming problem, and ii) the codeword generation and the

Permutation modulation codes are a class of group codes for the Gaussian channel whose codewords are obtained by permuting the components of a given initial vectorXin Euclideann-dimensional space. In this paper, the problem of choosing the components ofXin such a way that the minimum distance between any two codewords is maximized is solved. In particular, a closed-form expression is obtained for this minimum distance and is used to investigate the asymptotic behavior of some selected codes.

Two main classes of receivers for data modems using linear modulation systems over time-dispersive channels have been investigated by many authors for both theoretical and practical purposes, 1) structure-constrained linear receivers, such as zeroforcing and mean-square-error tapped-delay-line equalizers, and 2) nonlinear receivers, such as decision-feedback equalizers and maximum likelihood sequence estimators. In this paper a linear receiver that turns out to be practical and optimum in the mean-square sense is analyzed in detail, and some interesting features of this receiver are stressed; for instance, it is shown that in the absence of noise it becomes a zero-forcing equalizer, provided that stability can be achieved. A comprehensive set of results is also presented, showing that conventional tapped-delay-line equalizers perform very close to the optimum.

A generalized method is presented for the computation of peak and rms values of intersymbol interference in correlated digital PAM signals. These values can be used to compute a recently proposed upper bound on the error probability for such signals.

An expression for the error probability of multilevel coherent phase-shift-keyed (CPSK) systems in the presence of intersymbol, interchannel, and co-channel interferences and additive Gaussian noise is derived. An exact expression is given for the binary CPSK system, whereas upper and lower bounds are presented for the multilevel systems. The approach proposed in this paper overcomes the difficulties of the exhaustive methods and allows accurate and fast evaluation of the character error probability. Only the impulse responses of the overall channels are needed, and the computational labor is reduced to the numerical evaluation of one particular type of integral, whose computation is based upon nonclassical Gaussian quadrature rules. The model of the system is general enough to allow the choice of a rectangular or otherwise-shaped modulating pulse and a constant or shaped envelope of the modulating carrier. Phase incoherence between adjacent carriers is also assumed, and a random misalignment among the modulating bit streams can be taken into account, if necessary. Extensive numerical results are presented for 2- and 4-level systems. The presentation of the results stresses a possible utilization of them in system design problems.

A computer simulation technique is used to evaluate the performance of the MAP strategy for sequential block orthogonal signaling over a Gaussian channel with noiseless and delayless feedback. The system performance is given in terms of the character error probability. The obtained results are compared with those derived using other suboptimum strategies previously proposed.

A number of theorems are given, which give insight into the algebraic structure of group codes for the Gaussian channel, as defined by Slepian. The problem of the existence of group codes for a given pair of defining parameters (i.e., number of codewordsM, and dimension of the signal spacen) is partially solved.