Showing papers in "IEEE Transactions on Communications in 1994"

A technique for orthogonal frequency division multiplexing frequency offset correction

Abstract: This paper discusses the effects of frequency offset on the performance of orthogonal frequency division multiplexing (OFDM) digital communications. The main problem with frequency offset is that it introduces interference among the multiplicity of carriers in the OFDM signal. It is shown, and confirmed by simulation, that to maintain signal-to-interference ratios of 20 dB or greater for the OFDM carriers, offset is limited to 4% or less of the intercarrier spacing. Next, the paper describes a technique to estimate frequency offset using a repeated data symbol. A maximum likelihood estimation (MLE) algorithm is derived and its performance computed and compared with simulation results. Since the intercarrier interference energy and signal energy both contribute coherently to the estimate, the algorithm generates extremely accurate estimates even when the offset is far too great to demodulate the data values. Also, the estimation error depends only on total symbol energy so it is insensitive to channel spreading and frequency selective fading. A strategy is described for initial acquisition in the event of uncertainty in the initial offset that exceeds 1/2 the carrier spacing, the limit of the MLE algorithm. >

MMSE interference suppression for direct-sequence spread-spectrum CDMA

Abstract: We consider interference suppression for direct-sequence spread-spectrum code-division multiple-access (CDMA) systems using the minimum mean squared error (MMSE) performance criterion. The conventional matched filter receiver suffers from the near-far problem, and requires strict power control (typically involving feedback from receiver to transmitter) for acceptable performance. Multiuser detection schemes previously proposed mitigate the near-far problem, but are complex and require explicit knowledge or estimates of the interference parameters. In this paper, we present and analyze several new MMSE interference suppression schemes, which have the advantage of being near-far resistant (to varying degrees, depending on their complexity), and can be implemented adaptively when interference parameters are unknown and/or time-varying, Numerical results are provided that show that these schemes offer significant performance gains relative to the matched filter receiver. We conclude that MMSE detectors can alleviate the need for stringent power control. In CDMA systems, and may be a practical alternative to the matched filter receiver. >

The impact of antenna diversity on the capacity of wireless communication systems

Abstract: For a broad class of interference-dominated wireless systems including mobile, personal communications, and wireless PBX/LAN networks, the authors show that a significant increase in system capacity can be achieved by the use of spatial diversity (multiple antennas), and optimum combining. This is explained by the following observation: for independent flat-Rayleigh fading wireless systems with N mutually interfering users, they demonstrate that with K+N antennas, N-1 interferers can be nulled out and K+1 path diversity improvement can be achieved by each of the N users. Monte Carlo evaluations show that these results also hold with frequency-selective fading when optimum equalization is used at the receiver. Thus an N-fold increase in user capacity can be achieved, allowing for modular growth and improved performance by increasing the number of antennas. The interferers can also be users in other cells, users in other radio systems, or even other types of radiating devices, and thus interference cancellation also allows radio systems to operate in high interference environments. As an example of the potential system gain, the authors show that with 2 or 3 antennas the capacity of the mobile radio system IS-54 can be doubled, and with 5 antennas a 7-fold capacity increase (frequency reuse in every cell) can be achieved. >

The modified Cramer-Rao bound and its application to synchronization problems

Abstract: We introduce the modified Cramer-Rao bound (CRB) which, like the true CRB, is a lower bound to the error variance of any parameter estimator. The modified CRB proves useful when, in addition to the parameter to be estimated, the observed data also depend on other unwanted parameters. The relationship between the modified and true CRB is established and applications are discussed regarding the estimation of carrier-frequency offset, carrier phase, and timing epoch in linearly modulated signals. Modified CRBs for phase and timing estimation have been already discussed in previous works where it is shown that several practical carrier-phase and clock recovery circuits do attain such bounds. Frequency discrimination, instead, is not so well-represented in the literature and a significant contribution of this paper is the calculation of the modified CRB for frequency estimation. This bound is compared with the performance of some frequency detectors and it is concluded that further work is needed in search of more efficient frequency discrimination methods. >

A chaotic direct-sequence spread-spectrum communication system

Abstract: The use of chaotic sequences as spectral spreading sequences in direct-sequence spread-spectrum (DS/SS) communication systems is proposed. The error probabilities of such systems are investigated and shown to be, for all practical purposes, identical to the conventional DS/SS systems which use binary signature sequences. Among the advantages of the use of chaotic sequences in DS/SS are the availability of a great number of them, the ease of their generation, as well as their inherent improvement in the security of transmission. >

List Viterbi decoding algorithms with applications

Abstract: A list Viterbi decoding algorithm (LVA) produces a rank ordered list of the L globally best candidates after a trellis search. The authors present two such algorithms, (i) a parallel LVA that simultaneously produces the L best candidates and (ii) a serial LVA that iteratively produces the k/sup th/ best candidate based on knowledge of the previously found k-1 best paths. The application of LVA to a concatenated communication system consisting of an inner convolutional code and an outer error detecting code is considered in detail. Analysis as well as simulation results show that significant improvement in error performance is obtained when the inner decoder, which is conventionally based on the Viterbi algorithm (VA), is replaced by the LVA. An improvement of up to 3 dB is obtained for the additive white Gaussian noise (AWGN) channel due to an increase in the minimum Euclidean distance. Ever larger gains are obtained for the Rayleigh fading channel due to an increase in the time diversity. It is also shown that a 10% improvement in throughput is obtained along with significantly reduced probability of a decoding failure for a hybrid FEC/ARQ scheme with the inner code being a rate compatible punctured convolutional (RCPC) code. >

Other-cell interference in cellular power-controlled CDMA

Abstract: An improved series of bounds is presented for the other-cell interference in cellular power-controlled CDMA. The bounds are based on allowing control by one of a limited set of base stations. In particular, it is shown that the choice of cellular base station with least interference among the set of N/sub c/>1 nearest base stations yields much lower total mean interference from the mobile subscribers than the choice of only the single nearest base station. >

On joint transmitter and receiver optimization for multiple-input-multiple-output (MIMO) transmission systems

Abstract: The problem of joint transmitter and receiver optimization for MIMO systems under the mean-squared error (MSE) criterion is revisited. We address the general problem of N (number of users) /spl ne/M (number of channel inputs) /spl ne/P (number of channel outputs) when the system is Nyquist bandlimited and obtain analytical solutions for the optimal transmit-receive pair. Next, we demonstrate how the above result is directly applicable to the problem where the system has excess bandwidth, thereby generalizing the results of Salz (1985). In conclusion, several numerical examples are included to demonstrate the performance gains obtainable with jointly optimized MIMO systems vis-a-vis systems based only on receiver optimization. >

Distributed power control in cellular radio systems

Abstract: The capacity of cellular mobile radio systems can be increased by controlling the transmitter powers so as to balance the carrier to interference ratios at the receivers. A distributed algorithm for implementing such power control was proposed earlier for satellite systems by Meyerhoff (1974). The authors tighten the mathematical arguments and apply this scheme to cellular systems. The mobile units adjust their transmitter powers at discrete time instants. Specifically at each time instant the mobile multiplies its current power by a factor equal to a constant over its current carrier to interference ratio (CIR). So power is increased or decreased based on the value of the current CIR. After a number of such power adjustments all the mobiles converge to a common CIR. They also present numerical results which show that the above scheme has the potential to converge faster than the scheme proposed by J. Zander (see IEEE Transactions on Vehicular Technology, vol.41, no.3, August 1992) for high CIR values. >

Joint parameter estimation and symbol detection for linear or nonlinear unknown channels

Abstract: We present an iterative method for joint channel parameter estimation and symbol selection via the Baum-Welch algorithm, or equivalently the Expectation-Maximization (EM) algorithm. Channel parameters, including noise variance, are estimated using a maximum likelihood criterion. The Markovian properties of the channel state sequence enable us to calculate the required likelihood using a forward-backward algorithm. The calculated likelihood functions can easily give optimum decisions on information symbols which minimize the symbol error probability. The proposed receiver can be used for both linear and nonlinear channels. It improves the system throughput by making saving in the transmission of known symbols, usually employed for channel identification. Simulation results which show fast convergence are presented. >

Joint data and channel estimation using blind trellis search techniques

Abstract: A novel method of maximum likelihood sequence estimation is proposed for data that are transmitted over unknown linear channels. This procedure does not require a startup sequence for estimating the channel impulse response. Rather, the data and the channel are simultaneously estimated. It is implemented without any loss of optimality by a trellis search algorithm which searches for the best data sequence from among a number of hypothesized trellises which are constructed from the observed sequence. The number of states in each trellis and the number of trellises grow exponentially with the channel memory. A suboptimal trellis search algorithm is proposed whose complexity at best is slightly higher than that of the adaptive Viterbi algorithm operating with a known channel response. A simplified channel estimation algorithm when the number of data alphabets is greater than 2 is also proposed. Fast convergence of the algorithm in estimating the channel is demonstrated for binary pulse amplitude modulation over a variety of channels. Convergence over a wide range of SNR occurs within 100 symbols. The channel estimation algorithm for multi-level signals converges within 500-1000 symbols. We finally present an application of this algorithm to the problem of sequence estimation in the presence of rapidly time-varying intersymbol interference. The algorithm provides reliable zero-delay decisions which results in a better channel tracking algorithm when compared to previously proposed schemes. >

Reduced complexity symbol detectors with parallel structure for ISI channels

Abstract: The problem of practical realization of the optimal fixed-delay symbol-by-symbol detection algorithm, which is optimum in the sense of minimizing the symbol error probability, given a delay constraint D, is investigated. A fully-parallel structure is developed, and through systematic reformulations of the algorithm, the computational requirements are reduced considerably. In addition, the problems associated with a large dynamic range such as overflow (or underflow) are (practically) removed. A number of approximations are applied to this simplified parallel symbol (SPS) detector that lead to the derivation of suboptimal detectors. One such suboptimal detector is shown to be the same as the minimum-metric Viterbi detector. A brief comparison of the SPS detector and the Viterbi detector shows that the former has a slightly better performance at low values of signal-to-noise ratio (SNR) and the latter performs a smaller number of computations (particularly) at higher values of SNR; otherwise, the two detectors are comparable in performance and complexity. >

Alarm correlation and fault identification in communication networks

Abstract: Presents an approach for modeling and solving the problem of fault identification and alarm correlation in large communication networks. A single fault in a large network may result in a large number of alarms, and it is often very difficult to isolate the true cause of the fault. This appears to be one of the most important difficulties in managing faults in today's networks. The problem may become worse in the case of multiple faults. The authors present a general methodology for solving the alarm correlation and fault identification problem. They propose a new alarm structure, propose a general model for representing the network, and give two algorithms which can solve the alarm correlation and fault identification problem in the presence of multiple faults. These algorithms differ in the degree of accuracy achieved in identifying the fault, and in the degree of complexity required for implementation. >

Further results in the fast estimation of a single frequency

Abstract: The author proposes a new frequency estimator for a single complex sinusoid in complex white Gaussian noise. The estimator is applicable to problems in communications requiring high speed, recursive frequency estimation. The estimator is computationally efficient yet obtains near optimum performance at moderate signal-to-noise ratios. >

On the ability of establishing real-time channels in point-to-point packet-switched networks

Abstract: There are numerous applications which require packets to be delivered within pre-specified delay bounds in point-to-point packet-switched networks. To meet this requirement, we define a real-time channel as a unidirectional connection between two nodes in such a network that guarantees every packet to be delivered before a user-defined, end-to-end deadline. The goal of this paper is to lay a mathematical basis for the problem of establishing real-time channels by (i) deriving a necessary and sufficient condition for the schedulability of a set of channels over a link, and (ii) developing an efficient method for calculating the minimum delay bound over a link for each channel. Given the traffic characteristics of a channel, our results can be used to check whether or not every packet will be delivered within a pre-specified delay bound. The results are also applicable to a wide variety of real-time task scheduling problems. >

Maximum-likelihood differential detection of uncoded and trellis coded amplitude phase modulation over AWGN and fading channels/spl minus/metrics and performance

Abstract: This paper derives metrics for maximum-likelihood differential detection of uncoded and trellis coded MPSK and QAM transmitted over Rayleigh and Rician fading channels. Receiver structures based on these metrics are proposed and their error probability performance analyzed and/or simulated. The results represent a generalization of the notion of multiple symbol differential detection, previously introduced by the authors for MPSK over an AWGN, to the fading channel and other modulations. For the coded cases, ideal interleaving/deinterleaving is assumed and furthermore the presence or absence of channel state information. An interesting side result is that for a constant envelope modulation transmitted over a fading channel with unknown but rapidly-varying phase error (the other extreme to the slowly-varying phase error case normally assumed for differential detection), under certain practical assumptions, it is shown that the optimum receiver is of the limiter-discriminator type. >

Adaptive trellis-coded multiple-phase-shift keying for Rayleigh fading channels

Abstract: An adaptive scheme for trellis-coded modulation of MPSK signals, called adaptive trellis-coded multiple-phaseshift keying (ATCMPSK), is proposed for slowly Rayleigh fading channels. The adaptive scheme employs a slightly modified rate 1/2 convolutional encoder and the corresponding Viterbi decoder to realize a family of codes of different rates which are employed according to channel conditions. During poor channel conditions, trellis-coded QPSK (TCQPSK) together with repetition schemes are employed. As channel conditions improve, higher rate schemes such as trellis-coded 16 PSK are used. An interleaving/ deinterleaving method suitable for the adaptive scheme is proposed. Theoretical bounds for the error performance and an exact expression for the throughput of the proposed adaptive scheme are derived, and are compared against simulation results. Simulations have been performed to measure the performance of the scheme for different parameters and some nonideal conditions. It is shown that ATCMPSK results in considerable improvement in bit-error-rate (BER) performance of MPSK signals. Under ideal conditions, gains in the range of 3-20 dB are achieved over conventional fixed rate pragmatic trellis-coded schemes.

Narrowband interference suppression in CDMA spread spectrum communications

Abstract: Spread spectrum (SS) communications offers a promising solution to an overcrowded frequency spectrum amid growing demand for mobile and personal communications services. The proposed overlay of spread spectrum signals on existing narrowband users implies strong interference for the SS system. The paper discusses how system performance can be improved by preprocessing to suppress narrowband interference. Linear prediction filters have been proposed since the 1980s for suppression of narrowband interference. Vijayan and Poor (1991) proposed nonlinear methods of suppressing the narrowband signal with significant increase in the SNR improvement. The present authors derive an enhancement to this nonlinear prediction and achieve further improvement by applying the technique to interpolating filter structures. Finally, they extend results to the case of multiple spread spectrum users and demonstrate how nonlinear filtering can dramatically outperform linear filtering. >

Optical orthogonal code-division multiple-access system .I. APD noise and thermal noise

Abstract: In an optical multiple-access system, overall system throughput efficiency add significant implementation cost-reduction would be achieved if many users could access a common optical channel at any time without control among users. Recently one such scheme, an optical orthogonal code division multiple-access system (OOCDMA), was introduced by Salehi et al. (1982) for the case of no noise. In this paper, some extensions of that work are presented, including the effects of avalanche photodiode (APD) noise and thermal noise as well as interference for the OOCDMA direct-detection receiver. Since it has been shown that an optical hard-limiter before the receiver correlator can reduce the interference effect for the OOCDMA system in the absence of noise, the hard-limiter role in the presence of thermal and APD noise is also examined. >

Analysis of switched diversity systems on generalized-fading channels

Abstract: The performances of switched diversity systems operating on generalized (Nakagami)-fading channels are analyzed using a discrete-time model. The average bit error rate (BER) of binary noncoherent frequency shift keying (NCFSK) on slow, nonselective Nakagami-fading channels is derived. Closed-form expressions that can be used to determine optimum switching thresholds (in a minimum error rate sense) are also derived. In addition, the use of optimum fixed thresholds is considered. It is found that a considerable amount of diversity gain can be obtained using an optimum fixed (rather than adaptive) switching threshold. Results are obtained for both independent and correlated Nakagami-fading branch signals. The effects of fading severity and the correlation coefficient on both the BER and on the optimum switching threshold are investigated. It is shown that useful diversity gain can be obtained with power correlation coefficients as high as 0.9 when the fading is strong. The results for a Rayleigh channel are obtained and presented as a special case of generalized-fading model. >

Detection of bandlimited signals over frequency selective Rayleigh fading channels

Abstract: Presents sequence estimation for the frequency selective Rayleigh fading channel. Maximum likelihood estimation using the Viterbi algorithm (MLSE-VA) and sequential sequence estimation (SSE) are developed. Both MLSE-VA and SSE consist of a set of Kalman filters which estimate the fading channel as time evolves. Computer simulations for two different channel models show that the error performance of the two approaches is essentially the same. SSE however has considerably less computational complexity than MLSE-VA. To improve the error performance, diversity is combined with both MLSE-VA and SSE. The simulations show that diversity results in a signal to noise ratio gain of greater than 10 dB. >

Packet combining systems based on the Viterbi decoder

Abstract: Type-I hybrid-ARQ protocols can be used to construct powerful adaptive rate algorithms through the use of packet combining techniques. In this paper several packet combining schemes are presented for use in conjunction with the Viterbi decoder over stationary and time-varying channels. The first technique presented is an averaged diversity combiner, which is shown to be identical in performance to an interleaved code combiner over an AWGN channel. The averaged diversity combiner is then generalized to make use of packet weights based on either ideal channel state information or weights derived from side information generated by the Viterbi decoder. It is shown that the weighted diversity combiner using decoder side information performs almost as well as the system using ideal channel state information. All of the packet combining schemes discussed in this paper provide improved throughput and reliability performance relative to that provided by the standard type-I hybrid-ARQ or EEC systems. This performance improvement is obtained at the expense of negligible to moderate modifications to the transmitter and receiver. Performance bounds are derived for each of the combining schemes and their tightness verified through simulation results. >

Multiuser detection in single-path fading channels

Abstract: The performance analysis of maximum likelihood sequence and decorrelating multiuser detectors is developed for the single-path Rayleigh fading channel. The received signal in this multipoint-to-point channel is additively composed of white Gaussian noise and independently faded waveforms from a finite number of asynchronous users. The optimum sequence detector consists of a bank of single-user matched filters followed by a dynamic programming algorithm, has a demodulation complexity per symbol which is exponential in the number of users, and requires the knowledge of the system as well of the fading parameters. The decorrelating detector has a complexity which is polynomial in the number of users, and does not require knowledge of the signal amplitudes, which are assumed to vary slowly relative to the symbol rate. The single-user error rates are presented for both detectors and compared to conventional detection and isolated transmission, and the notion of asymptotic multiuser efficiency is developed for this channel. In contrast to conventional detection; which suffers from near-far effects due to Rayleigh fading, it is shown that the aforementioned multiuser detectors exhibit performance which rivals that of isolated transmission for sufficiently small thermal noise power. The results of the analysis are illustrated with numerical examples and indicate that the near-far problem may be alleviated by a more sophisticated receiver design. >

Nonlinearity compensation in digital radio systems

Abstract: Digital radio links with bandlimited pulses exhibit a severe performance degradation when the transmitter high power amplifier operates near saturation. To cope with the increase of nonlinear intersymbol interference due to the amplifier nonlinearities, a discrete-time Volterra system can be used to process the transmitted data. We present an efficient technique for implementing adaptive data predistorters with memory based on a discrete-time Volterra system composed of digital linear filters and memoryless nonlinear devices working at the symbol rate. Third- and fifth-order structures are proposed and a system performance evaluation is presented for several realistic situations. >

Branch-exchange sequences for reconfiguration of lightwave networks

Abstract: Some of today's telecommunications networks have the ability to superimpose some form of logical connectivity, or virtual topology, on top of the underlying physical infrastructure. According to the degree of independence between the logical connectivity and the physical topology, the network can dynamically adapt its virtual topology to track changing traffic conditions, and cope with failure of network equipment. This is particularly true for lightwave networks, where a logical connection diagram is achieved by assignment of transmitting and receiving wavelengths to the network stations that tap into, and communicate over, an infrastructure of fiber glass. Use of tunable transmitters and/or receivers allow the logical connectivity to be optimized to prevailing traffic conditions. With rearrangeability having thus emerged as a powerful network attribute, this paper discusses the reconfiguration phase which is the transition between the current logical connection diagram and a target diagram. We consider here an approach where the network reaches some target connectivity graph through a sequence of intermediate connection diagrams, so that two successive diagrams differ by a single branch-exchange operation. This is an attempt at logically reconfiguring the network in a way that is minimally disruptive to the traffic. We propose and compare three polynomial-time algorithms that search for "short" sequences of branch-exchange operations, so as to minimize the overall reconfiguration time. For networks made of up to 40 stations, theoretical and simulation results show that, when a randomly selected diagram is to be changed to another randomly chosen diagram, the average number of branch-exchange operations required grows linearly with the size of the network. >

An adaptive maximum-likelihood sequence estimator for fast time-varying intersymbol interference channels

Abstract: This paper proposes an adaptive maximum-likelihood sequence estimator (MLSE), which is a suboptimum approximation to the adaptive maximum-likelihood detector and is capable of tracking fast time-varying intersymbol interference (ISI) channels. The adaptive MLSE consists of a channel estimator and an MLSE implemented by the Viterbi algorithm (VA). The novel feature of the proposed adaptive MLSE is a channel estimation scheme, where the channel estimation is accomplished for each state in the VA along the surviving path connected to each state. This MLSE makes it possible to estimate a channel impulse response without an influence of a decision delay inherent in the VA, and the performance and complexity of the proposed procedure is controlled by the memory length of the VA. The bit error rate performance of the proposed MLSE is confirmed by experimental results. It is shown that the proposed MLSE has a capability of excellent tracking performance in a severe environment caused by fast time-varying ISI, for example frequency selective multipath fading in digital mobile radio communications. >

ML-oriented NDA carrier synchronization for general rotationally symmetric signal constellations

Abstract: We point out that the nondecision-aided (NDA) carrier synchronizer, maximizing the low E/sub s//N/sub o/ limit of the likelihood function averaged over a general 2/spl pi//N-rotationally symmetric signal constellation, reduces to the familiar timing-aided Nth power synchronizer; this extends a result of D'Andrea, Mengali and Reggiannini (1988) where only M-PSK constellations have been considered. Whereas in the case of M-PSK the tracking error variance of this NDA ML synchronizer is known to converge to the Cramer-Rao bound (CRB) with increasing E/sub s//N/sub o/. We show that for other rotationally symmetric constellations (such as QAM) the tracking error variance is substantially larger than the CRB. >

Folding algorithm: a computational method for finite QBD processes with level-dependent transitions

Abstract: This paper presents a new computational method for steady state analysis of finite quasi-birth-death (QBD) processes with level-dependent transitions. The QBD state space is defined in two-dimension with N phases and K levels. Instead of formulating solutions in matrix-geometric form, the Folding-algorithm provides a technique for direct computation of /spl pi/P=0, where P is the QBD generator which is an (NK)/spl times/(NK) matrix. Taking a finite sequence of fixed-cost binary reduction steps, the K-level matrix P is eventually reduced to a single-level matrix, from which a boundary vector is obtained. Each step halves the matrix size but keeps the QBD form. The solution /spl pi/ is expressed as a product of the boundary vector and a finite sequence of expansion factors. The time and space complexity for solving /spl pi/P=0 is therefore reduced from O(N/sup 3/K) and O(N/sup 2/K) to O(N/sup 3/ log/sub 2/ K) and O(N/sup 2/ log/sub 2/ K), respectively. The Folding-algorithm has a number of highly desirable advantages when it is applied to queueing analysis. First, the algorithm handles the multilevel control problem in finite buffer systems. Second, its total independence of the phase structure allows the algorithm to apply to more elaborate, multiple-state Markovian sources. Its computational efficiency, numerical stability and superior error performance are also distinctive advantages. >

Call blocking performance of distributed algorithms for dynamic channel allocation in microcells

Abstract: We determine the call blocking performance of channel-allocation algorithms where every channel is available for use in every cell and where decisions are made by mobiles/portables based only on local observations. Using a novel Erlang-B approximation method, together with simulation, we demonstrate that even the simplest algorithm, the timid, compares favorably with impractical, centrally administered fixed channel allocation. Our results suggest that an aggressive algorithm, that is, one requiring call reconfigurations, could provide a substantially reduced blocking probability. We also present some algorithms which take major steps toward achieving the excellent blocking performance of the hypothetical aggressive algorithm but having the stability of the timid algorithm. >

Suppression of adjacent-channel, cochannel, and intersymbol interference by equalizers and linear combiners

Abstract: We describe the ability of a linear equalizer/combiner or decision-feedback equalizer to suppress all received adjacent-channel, intersymbol, and cochannel interference. The emphasis is on values among transmitter bandwidth, receiver bandwidth, carrier spacing, and antenna diversity which provide the best opportunities for interference suppression. Through analyses of the number of degrees of freedom and constraints in generalized zero-forcing equalizers, and partial comparisons to calculations of equalizer minimum-mean-square performance, four results are obtained. First, with one antenna and a linear equalizer, arbitrarily large receiver bandwidths allow for marginal improvements in spectral efficiency through decreased carrier spacing, because the carrier spacing cannot be reduced to a value below the symbol rate without incurring unsuppressible interference. Second, large receiver bandwidths assist multiple antennas in improving the spectral efficiency in that carrier spacing values may go below the symbol rate, even in the presence of cochannel interference. Third, the use of equalizers and linear combiners, together with large receiver bandwidths, allows large transmitter bandwidths to be used. Fourth, for cochannel interference and intersymbol interference, the number of interferers that may be suppressible by a generalized zero-forcing linear equalizer/combiner increases linearly with the product of the number of antennas and the truncated integer ratio of the total bandwidth to the symbol rate. >