This paper presents an improved soft-output trellis/tree M-algorithm (SOTTMA) (Wong and McClane, 2006) for reduced-complexity equalization of a high-order modulated MIMO system undergoing equal-power, Rayleigh frequency-selective fading. This improved version reduces the amount of computation by approximately half through the utilization of a mapping scheme with multi-level bit-mapping properties (de Jong and Willink, 2002). The complexity of the improved SOTTMA no longer increases with the constellation size and therefore can be applied to equalize systems with high- order modulation (such as 64-QAM).

Two reduced-complexity soft-input soft-output trellis decoding techniques are presented in this paper for equalizing single-input single-output intersymbol interference (ISI) channels and multiple-input multiple-output (MIMO) frequency selective fading channels. Given a trellis representing an ISI channel, the soft-output M-algorithm (SOMA) reduces the complexity of equalization by retaining only the best M survivors at each trellis interval. The remaining survivors are discarded. The novelty of the SOMA is the use of discarded paths to obtain soft-information. Through a simple update-and-discard procedure, the SOMA extracts reliable soft-information from discarded paths which enables a large trellis to be successfully decoded with a relatively small value of M. To decode a trellis representing a MIMO frequency selective fading channel, two challenges are faced. Not only that the trellis has a large number of states, the number of branches per trellis interval is also enormous. The soft-output trellis/tree M-algorithm (SOTTMA) expands each trellis interval into a tree-like structure and performs the M-algorithm twice: once at each trellis interval to reduce the number of states and the other at each tree sub-level to remove unwanted branches. With the proposed technique, high-order trellises with million of branches per interval can be decoded with modest complexity.

This paper presents a reduced-complexity soft-input soft-output trellis/tree multiuser equalizer for an iterative DS-CDMA system undergoing Rayleigh frequency selective fading. The algorithm first expands the equalizer-trellis to an equivalent trellis/tree structure. Then it applies the M-algorithm to the equivalent structure twice, once to reduce the number of states in the trellis and the other to reduce the number of branches emanating from each state. To compute soft-information, the algorithm utilizes not only those fully-extended paths reaching the end of the trellis but also paths that are traversed and discarded in the pruned trellis. Through a simple update-and-discard procedure, reliable soft-information is extracted from discarded paths which enables an extremely large trellis to be successfully decoded with modest complexity. BER performance is presented for a convolutional-coded DS-CDMA system employing random spreading sequences. Our results demonstrate that the proposed algorithm is capable of achieving single-user performance with a much reduced complexity. The proposed algorithm can also be applied to reduce the complexity of multiuser detection where the transmission channel is frequency flat. Single-user performance can also be achieved with the proposed technique.

We propose code hopping-direct sequence spread spectrum (CH-DSSS) with binary phase shift-keying (BPSK) modulation to compensate for intersymbol interference (ISI) in an ultra-wideband system. The central idea is that code hopping (CH) affects ISI amplitudes that are produced by both the cross- and the auto-correlation properties of spreading codes for codewords; not just by the latter as occurs without CH. We also propose a low complexity CH pattern search algorithm to find good CH patterns. To evaluate the performance of the CH-DSSS system, a bit error rate (BER) expression is derived for a Rake receiver by applying the Beaulieu series method. Computational results show that significant gains can be obtained by CH for both the average BER and the outage probability (e.g. a 6 dB gain in outage probability for a non-line of sight channel).

A general framework for the design of low complexity timing error detectors (TEDs) for orthogonal space-time block code (OSTBC) receivers is proposed. Specifically, we derive sufficient conditions for a difference-of-threshold-crossings timing error estimate to be robust to channel fading. General expressions for the S-curve, estimation error variance and the signal-to-noise ratio are also obtained. As the designed detectors inherently depend on the properties of the OSTBC under consideration, we derive and evaluate the properties of TEDs for a number of known codes. Simulations are used to assess the system performance with the proposed timing detectors incorporated into the receiver timing loop operating in tracking mode. While the theoretical derivations assume a receiver with perfect channel state information and symbol decisions, simulation results include performance for pilot-symbol-based channel estimation and data symbol detection errors. For the case of frequency-flat Rayleigh fading and QPSK modulation, symbol-error-rate results show timing synchronization loss of less than 0.3 dB for practical timing offsets. In addition it is shown that the receiver is able to track timing drift with a normalized bandwidth of up to 0.001.

We analyze the properties of a class of low complexity timing error detectors for the purpose of timing error tracking in orthogonal space-time block coding receivers. For symmetrical signal constellations, under the assumptions of ideal data decisions and channel knowledge at the receiver, expressions for the S-curve, estimation error variance and the detector signal-to-noise ratio are derived. Simulations are used to confirm the analytical results and to evaluate the effects of data decision errors on the estimator properties. Symbol-error-rate performance is evaluated for a system operating in a frequency-flat Rayleigh fading environment, where the timing synchronization loss is found to be less than 0.3 dB. In addition to receiver with perfect channel state information, results for pilot-based channel estimation are included in order to examine the effects of channel estimation errors on timing synchronization.

Design and analysis of low complexity timing error detectors (TEDs) for quasi-orthogonal space-time block coding systems are presented. The detectors operate on data symbols and approximate decision variables, producing timing error measurement robust to channel fading. In addition to the estimator S-curve, we obtain the estimation error variance and TED SNR, with the analysis carried out under the assumptions of perfect data and channel knowledge at the receiver. Simulations are used to examine the effects of decision errors on the detector characteristics, and to evaluate the overall system performance, where the proposed TEDs are incorporated into the receiver timing loop. Receivers with perfect channel knowledge and pilot-based channel estimation are considered. Symbol error rate results show timing synchronization loss of less than 0.5 dB for a receiver with perfect channel information.

Abstract In this paper, we study the use of channel coding in a direct‐sequence code‐division multiple‐access (DS‐CDMA) system that employs space‐time adaptive minimum‐mean square‐error (MMSE) interference suppression over Rayleigh fading channels. It is shown that the employment of adaptive antenna arrays at the receiver can assist in attenuating multiuser interference and at the same time speeds‐up the convergence rate of the adaptive receiver. In this work, we assess the accuracy of the theoretical results developed for the uncoded and convolutionally coded space‐time multiuser detector when applied to the adaptive case. It is found that the use of antenna arrays brings the receiver performance very close to its multiuser counterpart. Using performance error bounds, we show that a user‐capacity gain of approximately 200% can easily be achieved for the space‐time adaptive detector when used with a rate 1/2 convolutional code (CC) and a practical channel interleaver. This capacity gain is only 10% less than the gain achieved for the more complicated multiuser‐based receiver. Finally, we perform a comparison between convolutional and turbo coding where we find that the latter outperforms the former at all practical bit‐error rates (BER). Copyright © 2006 John Wiley & Sons, Ltd.

This paper presents a reduced-complexity soft- output trellis/tree multiuser equalizer for an iterative DS-CDMA system undergoing Rayleigh frequency selective fading. The algorithm first expands the equalizer-trellis to an equivalent trellis/tree structure. Then it applies the M-algorithm to the equivalent structure twice, once to reduce the number of states in the trellis, and the other to reduce the number of branches emanating from each state. To compute soft-information, the algorithm utilizes not only those fully-extended paths reaching the end of the trellis, but also paths that are traversed and discarded in the pruned trellis. We show a simple and effective method of using these discarded paths without having to store them. BER performance is presented for convolutional-coded CDMA system employing random spreading sequences. Our results demonstrate that the proposed algorithm is capable of achieving single-user performance with a much reduced complexity.

We propose code hopping - direct sequence spread spectrum (CH-DSSS) with binary phase shift-keying (BPSK) modulation to compensate for intersymbol interference (ISI) in an Ultra-wideband system. The central idea is that code hopping (CH) affects ISI amplitudes that are produced by both the cross-and the auto-correlation properties of spreading codes for codewords; not just by the latter as occurs without CH. We also propose a low complexity CH pattern search algorithm to find good CH patterns. To evaluate the performance of the CH-DSSS system, an exact bit error rate (BER) expression is derived for a Rake receiver, and the computational speed to evaluate it is further increased by applying the Beaulieu series method (BSM) without sacrificing accuracy. Computational results for Gold and Walsh-Hadamard codes show that significant gains can be obtained by CH for both the average BER and the outage probability (e.g. a 6 dB gain in outage probability for a non-line of sight channel).

This paper presents a reduced-complexity soft-output trellis/tree equalizer for a high-order modulated MIMO system undergoing equal-power, Rayleigh frequency-selective fading. The algorithm reduces the complexity of trellis decoding by applying the M-algorithm twice, once to reduce the number of states in the trellis, and the other to reduce the number of tree branches emanating from each state. For soft-information, the algorithm utilizes not only those fully-extended paths reaching the end of the trellis, but also paths that are traversed and discarded in the pruned trellis. Our results demonstrated that the proposed algorithm is capable of achieving near-optimal performance with a much reduced complexity.

We present a method for the design of low complexity timing error detectors in orthogonal space-time block coding (OSTBC) receivers. A general expression for the S-curve of timing error detectors is derived. Based on this result, we obtain sufficient conditions for a difference of threshold crossings timing estimate that is robust to channel fading. A number of timing error detectors for 3- and 4-transmit antenna codes are presented. The performance is evaluated by examining their tracking capabilities within a timing loop of an OSTBC receiver. Symbol-error-rate results are presented showing negligible loss due to timing synchronization. In addition, we study the performance as a function of the timing drift and show that the receiver is able to track up to the normalized timing drift bandwidth of 0.001

This paper investigates the use of convolutional coding in space-time minimum mean-square-error (MMSE) multiuser-based receivers over asynchronous multipath Rayleigh fading channels. We focus on the performance gain attained through error control coding when used with binary-phase-shift-keyed modulation (BPSK) and multiuser access based on direct sequence-code-division multiple access (DS-CDMA). In our analysis, we derive an approximation for the uncoded probability of bit-error in multipath fading channels. This bit-error rate (BER) approximation is shown to be very accurate when compared to the exact performance. For a convolutionally coded system, we obtain a closed form expression for the bit-error rate upper bound. This error bound is noted to be tight as the number of quantization levels increased beyond eight. Using our theoretical results, we obtain an estimate for the achieved user-capacity that accrues due to error control coding. It is found that using convolutional coding with 3-bit soft-decision decoding, a user-capacity gain as much as 300% can easily be achieved when complete fading state information plus ideal channel interleaving are assumed.

This paper describes a low-complexity turbo equalizer for coded sparse multipath channels whose length can span hundreds of symbol intervals. First, for single-input-single-output (SISO) systems, an existing parallel-trellis framework, which consists of a bank of identical regular trellises, is exploited to construct the maximum a posteriori (MAP) equalizer in the turbo equalizer. This MAP equalizer, when combined with prefiltering, can equalize a broad selection of sparse multipath channels, including those with nonminimum phase, by using only M-state trellises, where M is the constellation size. For multiple-input-multiple-output (MIMO) systems, a MIMO prefilter and a bank of M-state parallel-trellis MAP equalizers are deployed according to a layering structure. The total number of states needed is only NTM, where NTis the number of transmit antennae. For both SISO and MIMO systems, a class of binary convolutional and turbo codes having sparse generator polynomials are chosen as the coding schemes. These codes partially integrate channel interleaving with encoding, which allows a simple channel interleaver with low latency and memory storage requirement to be employed. The MAP decoders for these codes can also be implemented with the same parallel-trellis framework as the MAP equalizers. Overall, parallel processing is supported throughout the turbo equalizers. The amount of computational time reduction when compared to a turbo equalizer using a single-trellis MAP equalizer and decoder is proportional to the number of trellises in the parallel-trellis MAP equalizer and decoder. The performance of the parallel-trellis turbo equalizers is evaluated on static and Rayleigh fading sparse multipath channels via Monte Carlo simulations

We analyze the properties of a robust timing error detector for nT= 2 orthogonal space-time block coded M-PSK systems with an arbitrary number of receive antennas. The algorithm uses maximum-likelihood detection variables to estimate the timing error by examining the difference in threshold crossings. The S-curve of the detector is shown to be independent of the channel state, thus making it very robust in poor channel conditions. Furthermore, we derive a closed form expression for the variance of the estimator, and show that the estimation SNR peaks in the timing error region the receiver usually operates in. We evaluate the tracking performance in 1-, 2- and 4-receive antenna systems with randomly distributed timing drift. Complete channel state estimation is assumed throughout the paper

We propose a very low complexity timing error detector for n/sub T/ = 2 orthogonal space-time block coded M-PSK systems with an arbitrary number of receive antennas. The algorithm uses maximum-likelihood detection variables to estimate the timing error by examining the difference in threshold crossings, similarly to the Mueller and Muller detector. We show that the timing error estimation is independent of the channel state, thus making it very robust in poor channel conditions. The decision directed version of the detector is used to evaluate the tracking performance for BPSK and QPSK signaling in 1-, 2- and 4-receive antenna systems. Symbol error rate as well as mean square estimation error results are presented. We examine the performance as a function of the timing drift and show that the receiver is able to maintain lock up to a normalized timing bandwidth of B/sub T/T = 0.001. Complete channel state estimation is assumed throughout the paper.

A low-complexity space-time turbo equalization algorithm, the soft-output M-algorithm (SOMA), is proposed for frequency-selective time-varying MIMO channels. The SOMA is a soft-output version of the M-algorithm known in sequential decoding. It reduces the complexity of trellis-decoding by retaining only M states per trellis depth. For the log-likelihood ratio computation, the algorithm includes not only survivor paths that reach the end of the trellis but paths that are traversed and discarded. The complexity of the SOMA is independent of the trellis size and increases linearly with M. The algorithm is evaluated in a convolutional-coded system that employs transmit-diversity. Simulation results show a reduction from 4096 states to 96 states with negligible performance loss is possible using the SOMA-equalizer for a 4-tap, equal-power, Rayleigh channel. For a version of a 4-tap, EDGE-like channel, 64 states are sufficient.

e analyze the performance of a joint timing epoch tracking and PSAM-based channel estimation system in a frequency-flat Rayleigh fading MIMO channel. The receiver tracks a random timing drift via a timing error detector developed for nT= 2 orthogonal space-time block coded MPSK systems with an arbitrary number of receive antennas. The detector's S-curve has recently been shown to be independent of the channel state, resulting in system very robust in poor channel conditions. We evaluate the receiver's tracking capabilities in conjunction with channel estimation and study the effects of the delay inherent to PSAM interpolation systems. Symbol error rate performance for a QPSK system is presented, with the results showing negligible performance degrad.

This paper investigates the use of convolutional coding in space-time minimum mean-square-error (MMSE) multiuser-based receivers over asynchronous multipath Rayleigh fading channels. We focus on the performance gain attained through error control coding when used with binary-phase-shift-keyed modulation (BPSK) and multiuser access based on direct sequence-code-division multiple access (DS-CDMA). In our analysis, we derive an approximation for the uncoded probability of bit-error in multipath fading channels. This bit-error rate (BER) approximation is shown to be very accurate when compared to the exact performance. For a convolutionally coded system, we obtain a closed form expression for the bit-error rate upper bound. This error bound is noted to be tight as the number of quantization levels increased beyond eight

A method to produce soft-outputs is proposed for the M-algorithm. The soft-output M-algorithm (SOMA) reduces the complexity of trellis decoding by retaining only M states per trellis depth. Its complexity increases with M rather than with the number of states in the trellis. We also propose an improved SOMA that is based on bi-directional decoding. The performance of the SOMA and the bi-directional SOMA (bi-SOMA) are assessed in decoding a turbo code and in turbo equalization. Simulation results show negligible performance loss when a 16-state turbo code is decoded by the SOMA with M = 12. For turbo equalization, near-optimal performance can be achieved by retaining only a small number of equalizer states as long as the. number of states retained by the decoder is sufficiently large. For a BPSK turbo equalization system with 16 states in both trellises, a SOMA-equalizer with M = 4 and a bi-SOMA decoder with M = 8 suffices. For a QPSK system with 256 equalizer states and 16 decoder states, a SOMA-equalizer with M = 16 and a SOMA-decoder with M = 12 suffices.

An effective method for joint timing and channel estimation for receive diversity systems in a frequency-flat Rayleigh fading environment is presented. We implement nonsynchronous timing recovery using Gardner's timing error detector, whose insensitivity to phase errors allows for timing recovery prior to pilot symbol based channel estimation. By employing a polyphase filter bank in the timing loop, we are able to simultaneously carry out matched filtering and data interpolation, thus eliminating the need for a separate interpolation filter. In addition, selection diversity combining is used to select the input to the timing loop, thus improving the reliability of the signal used for timing recovery. Pilot assisted channel estimation is performed on the recovered data strobes. For normalized Doppler frequency of 0.01 the system's bit error rate (BER) performance is within 1 dB from the ideal timing and channel estimation error bound, with an additional drop of 1.5 dB for a nonoptimum channel interpolator. In deep fades, the receiver timing is held fixed. We show that the receiver maintains timing lock over such fades up to a normalized timing bandwidth of 1/spl times/10/sup -4/for normalized Doppler frequency up to 0.05.

We propose a simple method to construct a good space-time trellis codes. As with any trellis code, the space-time trellis codes can be realized with a convolutional encoder followed by a mapping rule. Herein, we devise an improved space-time trellis codes by optimizing the convolutional code and mapper for the Jakes time correlated flat fading model. This new, simple method can be used to construct both non-recursive and recursive space-time codes where the latter is essential for serial concatenation. A simple encoding system is presented which is 1.8 dB away from the channel capacity for the 2-input/2-output fully interleaved MIMO channel.

This paper presents the results for the performance of serial concatenation of space-time block code (STBC) or differential STBC (dSTBC) with various channel codes, including convolutional codes (CCs) and turbo codes (TCs). These serially concatenated codes provide diversity gain as well as coding gain. The bandwidth efficiency is 1 bit/s/Hz for all the codes studied. The serial concatenation with TC not only provides coding gain over the serial concatenation with CC, but also mitigates the effects of spatial cross-correlation between fading channels. The serial concatenation of STBC and 1/2 rate TC with quaternary phase-shift keying (QPSK) modulation is 3.7 dB from the channel capacity at the BER of 10/sup -5/ in a 2 transmit and 2 receive antennae system, where a modified Jakes' time-correlated flat fading model is used. The cost for the absence of channel state information (CSI) is approximately 3 to 4 dB while dSTBC is used.

In this letter, we consider the application of an iterative interference cancelation (IC) scheme to improve the speed of convergence of the adaptive minimum mean-squared error (MMSE) receiver for the reverse-link of a direct-sequence code-division multiple-access (DS-CDMA) system. Our aim is to reduce the overhead introduced during the receiver's training period. This will be achieved using an iterative interference cancelation algorithm such as the parallel interference cancelation (PIC) algorithm. The proposed iterative algorithm makes use of the available knowledge of all users' training sequences at the base-station receiver to jointly cancel multiple-access interference (MAI) and adapts to the MMSE optimum filter taps using the combined adaptive MMSE/PIC receiver. We employ the proposed iterative algorithm to both the least mean square and the recursive least squares algorithms where we show that a significant improvement in terms of convergence speed is achieved. Moreover, we demonstrate the near-far resistance of the proposed receiver.

Analytical expressions that explicitly indicate the tap values and tap positions of infinite-length, T-spaced tapped-delay-line (TDL) equalizers for sparse multipath channels are derived. Simple design rules for allocating taps to finite-length, minimum mean-square error, nonuniformly spaced TDL equalizers (NU-Es) are formulated based on the derived results. The design-rule-based methodology demonstrates a better tradeoff between accuracy and efficiency than existing tap-allocation schemes. The resultant NU-Es also achieve a lower overall computational complexity than conventional, uniformly spaced TDL equalizers (U-Es) of the same span for both directly adaptive and channel-estimate-based implementations. Moreover, a square-root raised cosine (SRRC) receive filter matched to a SRRC transmit filter is better than a matched filter when used to precede a NU-E.

A novel coding and turbo equalization scheme for sparse multipath channels is presented in this paper. A burst-error-correcting convolutional code, which coding and interleaving via a sparse encoder and a convolutional interleaver, is selected as the channel code. A previously-proposed parallel-trellis framework is adopted for implementing the maximum a posteriori (MAP) equalizer and decoder in the turbo equalizer. Such a system exhibits a similar level of performance to a conventional system using a random-error-correcting convolutional code together with a row /column (R/C) or random block interleaver. Yet, the proposed system has the advantages of low latency and low memory requirements when compared to those conventional systems. This is due to (i) the elimination of the block-type interleavers and deinterleavers and (ii) the parallelism achieved in the turbo equalizer. One disadvantage of the proposed system is to decrease in throughput, as more tail symbols are required for proper termination of all sub-trellises in the decoder. Extension of the proposed system to turbo codes is considered. Also, the effect of prefiltering on a nonminimum-phase, high definition television (HDTV) channel is examined. Results indicate that using the feedforward filter (FFF) of a nonuniformly-spaced decision feedback equalizer (NU-DFE) performs almost as good as using one with a large number of uniformly-spaced taps. However, far fewer computations are needed to find the optimum tap values of the sparse prefilter.

Performance comparisons between the conventional decision feedback equalizer (DFE) and an alternative design, known as the decision directed feedback equalizer (DDFE), are conducted with nonuniform spacings on sparse multipath channels. The optimum feedforward filters (FFF) of the DDFE and its variant under the minimum mean square error (MMSE) criterion are derived with the constraint of a nonuniformly spaced feedback filter (NU-FBF), and relationships regarding the optimum tap values and the resultant MMSE between FFF with uniform and nonuniform spacings are established. While the bit error rate (BER) results obtained confirm previous claims that the T-spaced NU-DDFE exhibit prominent improvement over the T-spaced NU-DFE in equalizing long sparse channels such as those encountered in high definition television (HDTV) systems, the gain is only minimal, if any, when applied on simpler sparse channels with fewer multipath terms. Moreover, using a T/2-spaced FFF in the NU-DDFE demands a T/2-spaced FBF to mitigate additional intersymbol interference (ISI) caused by the T/2-spaced channel samples, and a better method than the commonly-used thresholding scheme may be required to accurately determine the tap positions of the T/2-spaced NU-FBF.

In this paper, we consider the estimation of Gallager's (1968) random coding exponent (RCE) for a peak power constraint at the transmitter for the two-dimensional fading channel with additive white Gaussian noise (AWGN) and with perfect channel estimation at the receiver. Despite the fact that many wireless channels are peak-power-limited, the RCE for such channels has not been considered previously in the literature. Such a problem has only been partially solved for the AWGN case due to the difficulty in finding an input signal distribution that yields the RCE. In this paper, we adopt a different approach in which we develop upper and lower bounds to the RCE with the hope of trapping it in a narrow region. Our quest is successful as we can estimate the RCE to an error of only 0.72 bit per modulation symbol. Furthermore, we find that the RCE for the peak-power-limited channel does not represent a severe degradation relative to that attained for the average-power-limited channel. Thus, good modulation and coding schemes at reasonable complexity should exist for a peak-power-constrained fading channel.

We consider the application of iterative interference cancellation (IC) schemes to improve the convergence speed of the linear adaptive minimum mean-squared error (MMSE) receiver in a direct-sequence code-division multiple-access (DS-CDMA) system. Our aim is to reduce the overhead introduced during the training period. This will be achieved using an iterative interference cancellation algorithm such as the parallel interference cancellation (PIC) algorithm. The proposed system makes use of the available knowledge of the training sequences for all users (i.e., at the base station) to jointly cancel the multiple access interference (MAI) and adapts to the MMSE optimum filter taps using the combined adaptive MMSE/PIC. An examination of the adaptive MMSE/PIC receiver reveals that it is near-far resistant. Moreover, it is shown that using the least-mean-square (LMS) as a simple form of the adaptive MMSE receiver, the proposed algorithm requires only a few tens of symbols for convergence as compared to a few hundred training symbols needed for the conventional adaptive LMS receiver. Also employing a more complex, yet faster, a recursive-least squares algorithm (RLS) convergence is reached with few training symbols when PIC is used.

The problem of designing nonuniformly-spaced tapped-delay-tine equalizers (NU-E) for sparse multipath channels is addressed. First, analytical expressions that explicitly indicate the tap positions and tap values of the infinite-length, T-spaced linear equalizers (LE) and decision feedback equalizers (DFE) under the zero-forcing (ZF) and minimum mean square error (MMSE) criteria are derived using the conventional matched receive filter (MF) and a square root raised cosine (SRRC) receive filter that is matched to a SRRC transmit filter. For both receive filter systems, the ZF-LE and the MMSE-LE for sparse multipath channels are nonuniformly-spaced with identical tap positions, but the ZF-DFE and MMSE-DFE are uniformly-spaced. Next, two suboptimum tap allocation algorithms based on the positions of large magnitude taps in the infinite-length, T-spaced equalizers are proposed for designing finite-length, T- and T/2-spaced MMSE NU-LE and NU-DFE. Results have shown that the proposed NU-E exhibit superior performance over uniformly-spaced tapped-delay-line equalizers (U-E) for the same number of taps, and only a small loss in SNR when compared to U-E with a large number of taps. Moreover, the SRRC receive filter is found to be a better front-end receive filter than the MF when used together with an appropriately-designed NU-E. A simple method that assigns extra T/2-spaced taps to improve the timing insensitivity of the proposed NU-E is also included.

The performance of minimum mean squared error (MMSE) multiuser detection (MUD) using array processing and Reed-Solomon (RS) coding is analyzed for binary, direct sequence code division multiple-access (DS-CDMA) systems used over multipath channels. Wang and Poor (1999) discussed the performance of the space-time MMSE MUD in multipath channels with no FEC coding. In this paper we investigate the performance of a base station receiver that combines space diversity, multipath diversity MUD, and RS channel decoding. The improvement in the bit-error rate (BER) using channel coding is evident in our simulation results. It is shown that employing RS codes with space-time MMSE-MUD improves the system performance significantly compared to both the uncoded space-time MMSE-MUD and the coded space-time RAKE receiver. We also present the Gaussian approximation for MMSE-MUD used in multipath channels. This Gaussian approximation gives accurate results when compared to our simulation results. Based on the validity of this approximation, we define upper bounds for the coded system BER. These upper bounds, which are shown to be tight, can be a helpful tool in predicting the system performance with different system parameters.

In this paper we investigate the performance of a minimum mean square error (MMSE) multi-user detector (MUD) using antenna array processing and forward error correction channel codes (FEC) in a synchronous direct-sequence code-division multiple access (DS-CDMA) system over both additive white Gaussian noise (AWGN) and flat Rayleigh fading channels. Two different channel codes are considered in a binary phase shift-keyed (BPSK) modulation system; Reed-Solomon (RS) and convolutional codes. Through computer simulations, a comparison between the two codes shows that convolutional codes and soft decision decoding can offer at least 2 dB coding gain over the hard decision RS decoding in an AWGN channel and approximately a 5 dB gain in a flat fading channel at a BER of 10/sup -4/. In the paper, such results are compared with these in the text (Wicker 1995) for the single user case and AWGN channels.

We compute the random coding error exponent for memoryless flat fading channels with ideal channel state information (CSI) and inputs drawn from a discrete alphabet. The signal sets we consider here are standard signal constellations commonly used in digital coded modulation. In addition, estimates of the code lengths required to achieve a certain error probability are determined and compared to those required for the AWGN channel. Finally, the effect of receiver diversity combining on improving communications reliability over the fading channel is considered. The results we obtain here shed light on the achievable performance over the fading channel with coded modulation.

There has been a considerable interest in determining the limits to communications over multipath fading channels. However, most studies have assumed that the channel is perfectly known at the receiver. In this paper, the random coding error exponent for flat fading channels with realistic channel state information (CSI) is studied. It is assumed that the CSI is obtained via some practical technique which utilizes a linear estimation scheme. Two commonly used techniques for channel estimation are considered in this paper, namely pilot tone extraction and pilot symbol transmission. The degradation in the achievable performance due to partial CSI is assessed and comparison of the different channel estimation methods is made. The focus of this paper is on the Jake's mobile Rayleigh flat fading model. Although Jake's model does not have a Markov property, such as that found in the commonly used exponential correlation model, which is usually attractive from the mathematical tractability point of view, Jake's model has a physical basis. Also, this model is considered herein from the standpoint of the random coding exponent. The results in this paper shed light on the amount of degradation in the achievable performance that is expected when the receiver has partial CSI. Finally, the sensitivity of the loss in achievable performance for the various channel estimation techniques with respect to channel parameters, such as Doppler spread and signal-to-noise ratio (SNR), is studied.

We compute the random coding error exponent for coded modulation transmitted over a flat, memoryless, Rayleigh fading channel. In addition, estimates of code lengths required to achieve a certain error probability are determined and compared to those required for the additive white Gaussian noise channel. Finally, the effect of receiver antenna diversity is also considered as a method to compensate for fading and is shown to have a significant, positive impact on the error exponent. The results we obtain represent an information theoretic view that complements the existing literature on the performance of coded modulation over fading channels with receiver diversity.

There has been much interest in wireless communications and thus it is appropriate to determine the Shannon limit for such systems. There have been a number of papers that consider channel capacity and also the random coding error exponent for various scenarios, In this paper, we consider Gallager's random coding error exponent for flat fading channels with antenna (or space) diversity employed at the receiver. Receiver antenna diversity is well known to be a fundamental technique for combating fading in wireless communications. The random coding error exponent is also well known to be a key quantity in assessing the ultimate, or achievable, performance over communications channels. We derive the random coding error exponent for various fading scenarios for which diversity combining is used. The cases we consider include memoryless fading channels with complete channel state information (CSI) at the receiver as well as time-correlated fading channels with complete CSI at the receiver. We also present results for time-correlated channels with partial CSI at the receiver via some practical channel estimation technique. The results we present in this paper shed light on the achievable performance over fading channels with receiver diversity combining and provide insight regarding the amount of coding complexity required for reliable communications over such channels.

In this correspondence, we consider the random coding error exponent for nondispersive two-dimensional (2-D) (quadrature) fading channels for which the channel state information (CSI) is perfectly known at the receiver and the input to the transmitter is constrained in its average power. Also, the effect of space diversity on improving the performance is demonstrated. The results obtained in this correspondence shed light on the effect of fading on communications reliability as well as the amount of coding complexity required to achieve a certain decoding error rate. A treatment for the random coding error exponent for time-correlated flat fading channels with Rayleigh fading and Bessel function correlation (the Jake's model) is also provided.

Adaptive array processing is seen as one possible solution to the severe bandwidth and power restrictions in a communications system between a geostationary satellite and a mobile terminal. This paper considers the use of an offset parabolic reflector with an array feed, referred to as a multiple beam antenna (MBA), as a way of combining the high gain of the reflector with the spatial filtering ability of the antenna array. A signal model is developed in which the key quantity is the steering vector which represents the response of the antenna array to a plane wave arriving from a given angle. The steering vector for the MBA is found numerically by finding the secondary field of each of the antenna elements, and then using the principle of reciprocity to relate this field to the received amplitude. Statistically optimum beamforming on the MBA is demonstrated followed by a simulation of the direct matrix inversion (DMI) algorithm.

The ATM performance over fiber-optic terrestrial networks is known to achieve high quality-of service (QoS) classes supporting different traffic types, and very low probability of bit errors, A probability of cell-loss on the order of 10/sup -10/ and a bit-error-rate (BER) on the order of 10/sup -8/ for data services are made possible on fiber-optic links. In contrast to the fiber-optic case, satellite transmission is often subjected to a large number of channel errors due to atmospheric noise and channel interference. Therefore, in order to achieve a fiber-optic like performance on the satellite channel, forward-error-correction (FEC) codes are essential for both the header and data fields of the ATM cell. This paper discusses two different FEC coding schemes for the ATM cell header. In addition, a FEC code design for data services (corresponding to AAL5) is presented. In the analysis we assume that there are no significant burst errors problem on the SATCOM link, and errors due to channel transmissions are mostly random errors.

The error probability of the cross-correlator receiver for binary digital frequency modulation (FM) detection is studied using theoretical analysis and computer simulations. The index of performance is taken as the bit-error rate (BER). The BER results obtained permit the selection of an optimum combination of modulation index and receiver bandwidth. This selection is carried out and is compared for analysis based on both computer simulation and theoretical calculation. The performance of the cross-correlator is also compared to that of the limiter-discriminator, and is found to be similar. This is noteworthy because the general I/Q demodulator structure of the cross-correlator is ideally suited to DSP chip implementation, and furthermore, severe amplitude limiting does not have to be performed on the input signal to the receiver. Input signal amplitude variations of up to 20% of the average signal value can be tolerated with only a 1-dB loss in performance, and the receiver is completely independent of the rate of amplitude variation. The theoretical analysis of the receiver uses a Fourier series approach which takes into account the effects of FM distortion and intersymbol interference (ISI). Theoretical and simulation results are found to agree within 0.5 dB in E/sub b//N/sub o/. We also address the issue of timing recovery. Results obtained indicate that losses due to timing error can be reduced to less than 0.5 dB in E/sub b//N/sub o/.

The uplink channel from a terminal to a regenerative satellite repeater is considered in which a digital transmultiplexer (TMUX) is used as a frequency-division multiple-access (FDMA) to time-division-multiplexed (TDM) converter for group demodulation. Linear modulation techniques were considered to determine which would make the most efficient use of this on-board processing (OBP) satellite system. The modulation techniques examined were quadrature phase-shift keying (QPSK), /spl pi//4-QPSK, and offset QPSK (OQPSK), all with Nyquist pulse shaping, and minimum-phase keying (MSK). The search for the optimum linear modulation technique took into account the performance criteria of power efficiency, bandwidth efficiency, and especially the complexity of the TMUX algorithm for OBP.

Due to the interest in wireless personal communications, there has been a lot of research on the performance of receivers with diversity. Most analyses assume the diversity branches are independent. This paper presents an analysis of the bit-error probability for receivers in which the diversity branches are correlated. Noncoherent orthogonal digital modulation (NCODM) with Rician and Rayleigh slow, nonselective fading models are assumed. Through the use of the diagonalization of quadratic forms, most of the calculations of the bit-error probability can be reduced to a two-dimensional numerical integration. For some cases for dual diversity, a closed-form expression for the error probability is given. A number of diversity combining laws, including square law and maximum likelihood, are considered. We find that Rician fading can be worse than Rayleigh fading in correlated diversity environments, a situation quite different from the independent diversity case. Also, for the Rayleigh fading model with correlated branch diversity, we find that an equal-weight, square-law combiner usually has the same error performance as the more complex maximum-likelihood combiner. However, this is not the case for a Rician fading model with the same correlation environment. Simple diagonalization methods that compensate for the lossy effect of correlation are specified and found to be effective when the dominant noise and interference have almost the same correlation distribution as the fading signals.

Efficient series that are used to calculate the bit error probabilities for biphase spread and quadriphase spread, BPSK modulated, asynchronous DS CDMA systems are derived. These series are then used to investigate the degradation in the performance of both systems due to synchronization errors. The analysis requires the characteristic functions of the multiple access interference and of the self interference and these functions have been expressed in terms of the special functions of mathematical physics. It is found that both systems have comparable performance when synchronization errors are considered. Thus, as far as the system capacity is concerned, quadriphase spreading does not offer any advantage relative to the simpler biphase spread system.

Four methods that can be used to approximate the distribution function (DF) of a sum of independent lognormal random variables (RVs) are compared. The aim is to determine the best method to compute the DF considering both accuracy and computational effort. The investigation focuses on values of the dB spread, σ, valid for practical problems in wireless transmission, where σ is between 6 dB and 12 dB. Contrary to some previous reports, our results show that the simpler Wilkinson's approach gives a more accurate estimate, in some cases of interest, than Schwartz and Yeh's 1982 approach.

In mobilesat communications, offsets in frequency are important to estimate before further processing and decoding of the received signal. We devise a straightforward technique for coarse frequency acquisition through FFT computation of a set of special preamble schemes suitable for any Nyquist pulse. We have considered the noise samples model when such samples are assumed to be uncorrelated, as in most of the literature. We also show how to approximate the analysis when the receiver's narrowband LPF is taken into account, which results in noise attenuation and correlation. The former is more important and results in relatively improved performance. The presented results are obtained through theory and verified by computer simulation.>

In the analog cellular environment there is a need for a faster more robust data modem. This paper presents the findings of an investigation into the feasibility of using a fractionally spaced equalizer with a burst noise detector as a means of achieving the above goal. The equalizer input is a discriminator detected radio signal whose output is the QAM baseband signal plus noise that has been further distorted by a telephone circuit. The performance of a T/4 and a T/2 spaced equalizer is compared with the performance of a symbol spared equalizer for low to medium signal to noise ratios (SNRs) commonly encountered in the analog cellular regime. Performance criteria are minimum mean square error, timing sensitivity, SNR after equalization, signal to interference ratio (SIR) after equalization and peak distortion (PD) after equalization. By means of simulation the convergence aspects of the T/2 spaced equalizer were investigated under differing burst and correlated noise scenarios. A noise detection plus equalizer control scheme is proposed and evaluated to maintain operation of the equalizer under burst noise conditions. A standard equalizer without burst noise detection and control fails under normal analog cellular operating conditions. However, the noise detected equalizer maintains operation through the burst at a level of error performance that is suitable for error control procedures to work well.>

A two-stage Doppler-phasor correction algorithm for mobile satellite, DSP-based modems is presented. The modulation considered is trellis-coded, differential phase-shift keying (DPSK) involving eight signal points. The Doppler phasor rather than the Doppler frequency is corrected as it leads to easy realization in DSP-based software. The Doppler phasor correction algorithm that is presented has a setup mode where the data are known and a data mode where the data are unknown. As such, it is intended for stream data or digital speech transmission. Both computer simulation and analytical techniques are used in the performance analysis.>

The symbol-aided (SA) synchronization concept developed by Moher and Lodge (1989) is applied to the MSAT channel modeled with a shadowed Rician process. Simulation data demonstrate that it can track the severe phase jitter encountered on the fading channel free of the false lock which plagues conventional techniques. The algorithm multiplexes known symbols into the data stream, establishing an absolute reference free of decision errors that is used to estimate the fading phase. An improvement to the SA algorithm which extracts phase information from the data-bearing symbols is proposed. It is found that the new technique is more effective for larger K. The improved algorithm is referred to as symbol-aided plus decision-directed (SADD) phase estimation. A system employing SADD phase estimation, trellis-coded modulation, interleaving, and amplitude weighting within the Viterbi decoder yielded the best BER performance on the shadowed MSAT channel considered.>

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 frequency-hopped spread-spectrum signal is modeled as a sinusoid that has one of N random frequencies. Coherent and noncoherent interception receiver structures based on Neyman-Pearson detection theory are determined. Under the assumption that there is a single hop per detection period, the optimum receiver structure is shown to consist of a bank of matched filters called the average likelihood (AL) receiver. A suboptimum structure called the maximum likelihood (ML) receiver is also analyzed. It is shown that AL and ML receivers have essentially the same performance. Simple formulas that relate the probability of detection, P/sub D/, to the probability of false alarm, P/sub F/, and the signal-to-noise ratio (SNR) for large N are derived. Receiver structures are also derived and analyzed for the case where the signal hops a number of times in one detection interval. This may correspond to the detection of a multihop signal in one symbol interval or to detection based on integration over a number of symbol intervals. The relationships of P/sub D/ to P/sub F/, for both coherent and noncoherent multiple-hop receivers, are examined.>

G. Ungerboeck's (1982) design rules for a class of bandlimited codes called trellis codes are reviewed. His design of the trellis is based on a set partitioning of the signal constellation, and he realized these trellis codes by a convolutional encoder followed by a mapping rule from the coder output to modulation symbols. R. Calderbank and J.E. Mazo (1984) showed how to realize trellis codes for one-dimensional signal sets in a single-step, easily derived, nonlinear transformation with memory on a sliding block of source symbols. The design rules that give a signal (state) specification in a trellis that yields the Calderbank-Mazo transformation with the smallest number of terms are presented. This gives a minimal transmitter complexity design. It is shown how to realize the Ungerboeck from the Calderbank-Mazo form, and as a result a step-by-step, search-free design procedure for trellis codes is presented. Two additional design rules are presented and applied to two examples by analytically designing two trellis codes. A simple procedure for converting an analytic code expression to a convolutional encoder realization is discussed. The analytic designs of a 4-D code and a 2-D code are presented.>

The performance of 8-PSK and 8-DPSK trellis codes is presented for a class of fast fading, land mobile satellite communication channels. The fading model is Rician but, in addition, the line-of-sight path is subjected to a fast lognormal attenuation that represents tree shadowing. The fading parameters used in this study represent the degree of shadowing and are based on measured data. The primary application considered is for digital speech transmission and thus, bit error probabilities in the order of 10/sup -3/ are emphasized. Sensitivity of the bit error probability to amplitude fading, amplitude and phase fading, and decoding delay is presented. Performance is determined via digital computer simulation. Optimal four- and eight-state codes are determined and optimality is found to be dependent on the presence of lognormal shadowing.>

The performance of trellis codes is examined for a class of intersymbol interference (ISI) channels that occur in high-frequency radio systems. The channels considered are characterized by in-band spectral nulls and by a rapid time variation. The baseline modulation technique is 4QAM (four-point quadrature amplitude modulation). When spectral nulls are absent, performance of fractionally spaced linear equalizers and trellis decoders is found to be near ideal and to be better than using symbol-spacing in the equalizer. However, error propagation in the feedback path, resulting from equalizer-based decisions, ruins the performance of the combination of decision-feedback equalizers and trellis decoders when spectral nulls are present. Their performance can be improved by using fractionally spaced feedforward equalizer sections and by designing the decoder to compensate for ISI. Rate 2/3 codes are found to outperform rate 1/2 codes in error performance.>

A comparison of different classes of encoded continuous phase modulation (CPM) schemes is presented. In terms of joint power-bandwidth performance, it is found that coded eight-level systems are better than coded four-level systems and that partial-response signalling is better than full-response signalling. In general, the price paid for better performance is increased receiver complexity. Heuristic design rules have been used to find good codes for CPM. In most cases the coding gains found are identical to published results that were generated by exhaustive search, indicating that the choice of design rules is quite appropriate. In the present study bandwidth efficiency is considered from both the 99% and 99.9% power-bandwidth points of view. It is found that partial-response signalling is even more jointly power and bandwidth efficient for the latter than for the former bandwidth criterion.>

Differential detection of duobinary CPFSK is analyzed to determine its performance as an alternative to other incoherent bandwidth efficient detection schemes. It is shown that a BPSK differential receiver can correctly detect a duobinary MSK signal when precoding (differential encoding) is employed at the transmitter. The effects of intersymbol interference due to IF filtering at the receiver are analyzed for a Gaussian and a 4th-order Butterworth IF filter. Furthermore, nonredundant error correction is shown to be feasible for differential detection of duobinary MSK and a method of analyzing the performance of the error correction receiver is presented.

This paper describes the theory, design, and testing of a Viterbi processor for a digital communication system with intersymbol interference over fading time-dispersive channels. The requirement is to implement the Viterbi algorithm for a channel memory of 9 baud at a data rate of 2400 bits/s. The processor is partitioned into three subprocessors corresponding to the correlation, state metric evaluation, and state decision-making operations. For prototype evaluation, each subprocessor is being implemented as a separate chip using4-5 \mum CMOS technology. The architecture, circuit design, and subsystem characterization of the correlator chip are described in some detail. The chip is required to evaluate 1024 state transition metrics in each baud interval (about 400 ns) using a pipeline architecture. Simulation and initial test results verify the correct operation of the chip with an adequate-speed safety margin. The theory of operation and architecture of the state metric chip are described. With off-chip memory for state metric storage, the state transition metrics from the correlator chip are used to determine the winning (optimal) path in the Viterbi trellis and to calculate the corresponding 16-bit state metric for each baud interval. Implementation of the third chip which is required to make a state decision regarding the bit sequence sent is presently being investigated.

The performance of cross-coupled,M-ary quadrature amplitude modulation (QAM) systems is determined when bandwidth efficient trellis codes are used to combat interference. Performance with and without compensation for cross-coupled interference is presented. It is found that simple trellis codes can maintain the error probability at an acceptable level for cross-coupling parameters that render uncoded systems unusable. Up to two-dimensional trellis codes are considered for four-dimensional QAM signals, and possibilities of obtaining diversity advantages in the form of higher total system throughput by prolonged availability of the two signals are explored. This is accomplished through joint coding over two different constellations. The probability of the most likely error events is calculated by using the method of moments. The results are applicable to any digital communication system using multidimensional quadrature amplitude modulation, e.g., voiceband modems, cross-polarized radio systems and, to some extent, optical systems. In the paper the analysis is restricted to nondispersive cross-coupling models. In most cases the coding gain is larger than in the absence of cross-coupling interference. Specifically, it is found that simple codes have coding gains increased by at least 2 dB with cross-coupling interference relative to that obtained on the additive white Gaussian noise channel.

Phase tracking capability is incorporated into two sequence estimation decoders for continuous phase modulations. One decoder employs the Viterbi algorithm; the other uses a reduced-survivor approach proposed earlier by one of the authors [11] for the more bandwidth efficient of these modulations. Computational complexity with the simplest of the joint data/phase algorithms is only marginally greater than that required for the equivalent decoding algorithm employing an externally derived carrier phase reference as supplied by a conventional carrier recovery circuit. Simulations with representative partial response modulations demonstrate the phase synchronization and tracking capabilities of the decoders. High SNR losses relative to an optimal receiver having perfect phase knowledge are found to be small (∼ 1 dB).

By using an analysis technique based on the concept of transfer function bounds, we show that the Viterbi demodulator for correlative encoded CPFSK modulation is sensitive to carrier reference errors. To compensate for this sensitivity, we introduce a few extra phase states into the demodulation algorithm; this has been suggested earlier by Jackson and Omura. However, their demodulator is more complex than ours, as it is intended to compensate for rapidly varying phase offsets. Ours requires considerably fewer decoder states but uses a combination of external and internal phase estimation relative to the Viterbi demodulation algorithm, and is intended to track slowly varying phase offsets. We test the performance of our hybrid demodulation procedure, using an approximate analysis and a digital computer simulation which involves a simple vector structure and is based on orthogonal basis functions for the signal space under consideration. Our demodulation algorithm results in a modest increase in the number of Viterbi decoder states and no increase in the number of receiver matched filters. To track time-varying phase offsets, a truncated metric version of the Viterbi demodulation algorithm is introduced and tested.

It has previously been shown that MSK modulation with correlative encoded symbols, using first- and second-order encoding polynomials, can give rise to signals with excellent bandwidth efficiency. In this paper we specify and analyze the Viterbi receiver for such signals. The receivers are not very complex as they either require four or eight states to be stored and processed during each symbol interval. Our analysis concerns the bit error rate and the transfer function bound technique is utilized. Perfect coherent operation of the receiver is assumed in the error analysis.

The use of Butterworth and Chebyshev low-pass filters in suboptimum in-phase (I) and quadrature phase (Q) receivers is considered for several bandwidth efficient modulations. These modulations are: minimum shift keying (MSK), tamed frequency modulation with rectangular pulse shaping (TFMREC), and MSK with duobinary encoding of the source bits (DMSK). The sensitivity of the modulations with theirIandQreceivers to a noisy phase reference and to timing errors is also investigated. It was found that standard, passive low-pass filter receive filters performed quite well when compared to other nonstandard filters. The use of standard filters should thus be considered in any system design. The modulations, with their simple receivers, can be ranked in order of increasing sensitivity to timing errors as follows: MSK, DMSK, TFMREC. This ranking is the reverse to the one obtained when it is done in order of best bandwidth efficiency.

In this paper we extend the probability of error analysis for Viterbi detectors for PAM data transmission to include the effects of steady-state carrier reference errors. It has earlier been found that the Viterbi detector is sensitive to the effects of constant carrier phase errors. However, for two reasonably complicated voiceband pulses taken from the literature, we find that the Viterbi detector is no more sensitive to random carrier phase errors than is a standard quantizing detector.

The problem of the joint optimization of transmitting and receiving filters is considered for a data transmitting system in which the channel may he represented during transmission by any element of an ensemble of system functions. It is shown that for any reasonable measure of performance such a system has an optimum receiving filter of a specific structure which, in the joint solution, leads to the existence of minimum total mean-square error filters which are bandlimited to a generalized Nyquist interval.

The Viterbi algorithm has been proposed for the symbol-by-symbol detection of discrete pulse amplitude modulated signals transmitted over noisy time-dispersive channels. The resulting detector has considerable complexity, requiring the storage of2^{m}state variables for binary signaling. A truncated-state detector assumes the channel memorymis much less than it really is and as such neglects some of the channel's intersymbol interference. An upper bound is prescribed for the detector's bit error probability due to this neglected interference in the case of binary signaling. This interference degrades the detector's performance in the same functional manner that intersymbol interference degrades the performance of the standard quantizing detector. This degradation can be considerably reduced for troublesome channels by optimally choosing the state variables for truncated-state detection.

The parameter optimization of practical filters for baseband equivalents of linear and nonlinear BPSK transmission systems is investigated. An estimate of system error rate is defined and this is minimized. Here the received signal is detected in the presence of intersymbol interference and white Gaussian noise. A closed form expression for receiverBTproduct minimizing mean-square distortion on a simple channel is developed. The numerical optimization scheme introduced in this paper minimizes the error rate estimate. This method only requires the transfer functions of the various system components and the data spectrum. The optimization is applied to linear systems which include four and six pole Butterworth and four pole Chebyshev receive filters for a channel with a fixed four pole Chebyshev filter as a channel filter. A joint transmit/receiver filter optimization is considered with practical constraints introduced on the transmit filter. The numerical optimization is also applied to a bandlimited nonlinear satellite channel with high uplink SNR.

This paper generalizes some aspects of Jain and Blachman's analysis of the error probability for binary PSK transmission over a two-link channel having a hard-limiting repeater. In the present analysisM-ary PSK transmission through a repeater having both nonlinear amplitude and phase characteristics is considered. The error probability is given in terms of an infinite series whosenth term must be obtained by a one-dimensional numerical integration. A practical amplitude and phase characteristic from the literature is treated. Also presented is a study of the effect on error probability of "backing-off" the repeater from saturation.

In this paper we specify an optimal receiver filter for 2phase PSK transmission over a channel consisting of the tandem connection of a linear filter and a bandpass nonlinearity, with thermal noise added at the channel output. This filter minimizes the bit estimation error subject to the constraint that it be a linear filter. Our main aim is to consider satellite communication channels and as such the system nonlinearity is taken to have both AM/AM and AM/PM conversions. In these systems we assume the up-link signal-to-noise ratio is large and thus our work relates to large transmit terminal applications. In an example the probability of error performance of the optimal received filter is found to be 2 dB better in terms of the effective output SNR as compared with that of a standard choice for the receiver filter.

A simple method is presented for computing upper and lower bounds for binary PAM signaling over channels with phase jitter. Other impairments to reliable communication are taken to be additive thermal noise and intersymbol or cochannel interference. The important cases of binary and quadrature phase shift keying are cases for which the analysis presented is valid. The method consists of finding upper and lower bounds conditioned on the phase jitter, φ, in a form in which the auguments of theQ-functions involved are linear in\cos \phiand\sin \phi. When these functions are represented by a piecewise linear approximation, the average of these bounds can be given in closed form. In most cases 5 piecewise linear segments provides an error rate estimate that is accurate to at least 1 dB in system signal-to-noise ratio (SNR).

The problem of designing and evaluating the performance of a maximum likelihood sequence receiver for binary PSK transmission over bandlimited nonlinear channels is considered in this paper. The effects of intersymbol interference followed by AM/AM and AM/PM conversions are taken into account while optimizing the performance in the presence of white Gaussian noise. A new representation for the output of a bandpass nonlinearity is given when the input consists of a carrier signal modulated by a sum of binary overlapping pulses. The structure of a maximum likelihood sequence receiver for a bandlimited nonlinear channel is derived using this representation. The receiver uses a modified Viterbi algorithm to determine the most likely sequence of data symbols transmitted. An upperbound on the probability of symbol error for this receiver is obtained. Numerical results illustrating the applicability of the present work to optimizing the performance of a digital satellite communications link are also presented.

This paper presents simple and general lower bounds for error rates in digital communication systems. The information bearing signal is taken to be impaired by additive interference and carrier phase jitter. The former is taken to be composed of two components; one component is peak-limited while the other is not. Intersymbol and cochannel interference are examples of peak-limited interference while additive thermal noise is an example of a nonpeak-limited interference. The novelty of the paper is in the generality of the results and in obtaining a simple error bound for transmission in the presence of cochannel interference and carrier phase jitter.

The theory of decision-aided carrier tracking loops as developed by Lindsey and Simon is extended to include the effects of intersymbol interference. A major theoretical result is the solution of the Fokker-Planck equation for the probability density function (pdf) of the phase error for a first-order tracking loop. This function is used to average upper and lower bounds on the demodulator error rate so that an estimate of the overall system error rate may be obtained. The modulation technique analyzed is double-sideband-pulse-amplitude pulse-amplitude modulation. Curves are presented which display the threshold performance of the system error rate at low modulation index.

Some simple lower bounds for the probability of error for band-restricted digital communication are presented. The bounds revolve two values of the complementary error function, the system SNR, the peak value, second moment, and sometimes, the fourth moment of the intersymbol interference. Contrary to other available lower bounds, no parameter searches or infinite series computations are required. The bounds hold when the system "eye" is open and in some cases when the source symbols are correlated.

This paper presents an upper bound on error-pattern probabilities for digital pulse-amplitude modulation transmission in a bandrestricted and additive white noise environment. The bound involves the computation of exponential and hyperbolic cosine functions. For two examples from the literature it yields a result that is an improvement on previously known results. For the case of double errors it is not as restrictive as a recently published bound.