This paper considers optimal multiband transmission under hostile jamming, where both the authorized user and the jammer are power-limited and operate against each other. The strategic decision making of the authorized user and the jammer is modeled as a two-party zero-sum game, where the payoff function is the capacity that can be achieved by the authorized user in the presence of the jammer. First, we investigate the game under AWGN channels. It is found that: either for the authorized user to maximize its capacity, or for the jammer to minimize the capacity of the authorized user, the best strategy for both of them is to distribute the transmission power or jamming power uniformly over all the available spectrum. The minimax capacity can be calculated based on the channel bandwidth and the signal-to-jamming and noise ratio, and it matches with the Shannon channel capacity formula. Second, we consider frequency selective fading channels. We characterize the dynamic relationship between the optimal signal power allocation and the optimal jamming power allocation in the minimax game, and then propose an iterative water pouring algorithm to find the optimal power allocation schemes for both the authorized user and the jammer.

In this paper, we study the bandwidth efficiency (throughput) and the energy efficiency of relay networks considering both the physical layer and the medium access control (MAC) layer. Due to wireless signal power attenuation with transmission distance, using a relay for packet transmissions can lead to more energy-efficient wireless networking at the expense of requiring multihop transmissions. To understand the potential benefits of using a relay, the energy-throughput tradeoff needs to be analyzed. In a decentralized wireless network, not only the physical layer but also the MAC layer should be considered. At the physical layer, the transmit power determines the area which contains nodes that might be contending for channel access at the MAC layer. At the MAC layer, gaining access to the channel entails transmitting various signals at the physical layer. This uses energy and takes time, which impacts the bandwidth efficiency. We analyze the energy consumption and the throughput of relay networks as a function of the transmit power. We determine the conditions in which wireless communication using a relay has better energy efficiency or bandwidth efficiency than direct transmission.

In this paper we investigate the bandwidth (throughput) and energy efficiency considering both the physical layer and the medium access control (MAC) layer in multi-hop relay wireless networks. For a given distance between the source and the destination, as the number of relays increases the overhead necessary to operate the MAC protocol increases. However, the energy needed for a given throughput decreases when the distance between relays decreases. Thus there is an optimal number of relays that optimizes both the throughput and the energy efficiency. We analyze how the number of relays used between the source and the destination affects the throughput and the energy consumption. The energy-throughput relationship incorporating both the physical layer and the MAC layer was considered in the analysis and optimization of the number of relays. Based on the analysis we provide general criteria for the optimal number of relays.

We consider the problem of channel estimation for ultrawideband communication in a multipath channel using compressed sensing techniques. The receiver when using a compressed sensing approach consists of a number of correlators processing the received signal with random projection vectors. The theory is based on Gaussian distributed vectors. We have compared the performance of using orthogonal Hadamard vectors with that of using a random projection matrix in compressed sensing procedures. We have also compared the performance of systems with different parameters for Gaussian and Hadamard projections vectors such as number of pilots, number of projection vectors and different coding schemes. Moreover, we are investigating different receiver structures resulting in different complexity of the receivers. We show that the sampling rate can be reduced significantly with only a slight degradation in the performance.

This paper considers a MIMO multi-hop network and analyzes the relationship between its energy consumption and bandwidth efficiency. Its minimum energy consumption is formulated as an optimization problem. By taking both transmit antennas (TAs) and receive antennas (RAs) into consideration, the energy-bandwidth efficiency tradeoff in the networks is investigated. Moreover, the minimum energy of an equally-spaced relaying strategy is investigated for various numbers of antennas. In addition, the minimum energy over all possible antenna pairs is derived. Finally, the effect of the number of hops on the energy-bandwidth efficiency tradeoff is considered. For a fixed antenna pair, the minimum energy over all possible rates and hop numbers are obtained. Generally, the routes with more hops minimize the energy consumption in the low effective rate region. On the other hand, in the high effective rate region, the routes with fewer hops minimize the energy consumption.

We investigate the error exponent of exclusive-or multiple-access channels (XMAC) where the receiver wants to reconstruct the exclusive-or of incoming messages from two transmitters. We consider both the multiple access channel (MAC) strategy and the network coding (NC) strategy. In our analysis, the cutoff rate is used as a performance measure. Assuming a Gaussian XMAC and binary phase-shift keying (BPSK) modulation at each node, we show that the MAC strategy performs better than the NC strategy in the low rate region while the NC strategy performs better in the high rate region.

In this paper, energy-constrained wireless multihop networks with a single source-destination pair are considered. A network model that incorporates both the energy radiated by the transmitter and the energy consumed by the circuits that process the received signals is proposed. The rate of communication is the number of information bits transmitted (end-to-end) per coded symbol transmitted by any node in the network that is forwarding the data. The tradeoff between the total energy consumption and the end-to-end rate of communication is analyzed. The performance (either energy or rate) depends on the transmission strategy of each node, the location of the relay nodes, and the data rate used by each node. Communication strategies include the rate of transmission on each link, the scheduling of links, and the power used for each link. Strategies that minimize the total energy consumption for a given rate are found. Two communication strategies that capture the inherent constraints of some practical networks are also considered and compared with the optimum strategies. In the case of equispaced relays, analytical results for the tradeoff between the energy and the end-to-end data rate are provided. The minimum energy over all possible data rates is also obtained. Low rates incur a significant penalty because the receiver is on for a long time period while high rates require high transmission energy. At high rates routes with fewer hops minimize the energy consumption while at lower rates more hops minimize the energy consumption.

A new union bound on the bit error probability of bit-interleaved space–time (BI-ST) coded systems is derived. Unlike existing performance analysis tools for BI-ST systems, the new bound provides a general framework for analysing the performance of BI-ST systems employing finite interleaver sizes. The derivation is based on the uniform interleaving assumption of the coded sequence prior to transmission over multiple antennas. The new bound is a function of the distance spectrum of the code, the signal constellation used and the space–time (ST) mapping scheme. The bound is derived for a general BI-ST coded system and applied to two specific examples, namely, the BI space–time coded modulation and the BI space–time block codes. Results show that the analysis provides a close approximation to the BI-ST performance for a wide range of signal-to-noise ratios. The analysis can also accurately characterise the performance differences between different interleaver sizes, which is a breakthrough in the analysis of BI-ST coded systems.

In this paper, we present analytical bit error probability results for M-ary modulation concatenated with Reed Solomon (RS) codes. The analysis of bit error probability is nontrivial as the number of bits per symbol for the RS codes may not be an integer multiple of the number of bits per symbol for a modulation symbol. We propose a Markov chain technique which allows analytical evaluation of the bit error probability for such cases. The performance of RS coding with coherent biorthogonal, coherent/non-coherent orthogonal modulation over an additive white Gaussian noise (AWGN) channel is evaluated. Simulation of the bit error probability of RS code concatenated with a Nordstrom Robinson (NR) code as an inner code is performed and compared with the case of biorthogonal modulation. From the results, we notice that a stronger inner code gives better bit error probability. In addition, the throughput of the coded system with biorthogonal modulation over an AWGN channel is discussed. For a Rayleigh flat fading and block fading channel, we analyze the bit error probability of RS codes concatenated with biorthogonal modulation. From the result, we notice that a stronger outer code gives a better bit error probability for the case of Rayleigh flat fading channel.

In this paper the tradeoff between energy and delay for wireless networks is studied. A network using a request-to-send (RTS) and clear-to-send (CTS) type medium access control (MAC) protocol is considered. A generic framework is developed that allows us to obtain the joint statistics of energy and delay through their joint generating function, when the effects of an imperfect channel are incorporated in the model. Several energy and delay tradeoffs are studied using the joint generating function. These include the average energy vs. average delay, average delay with energy constraint, etc. The proposed analytical method is verified through simulations.

Outage probability is an important performance measure of wireless communication systems operating in a fading environment. In this paper, we study the outage probability of low-density parity-check (LDPC) coded systems for slow fading channels (nonergodic channels) under the assumption that the transmitter knows only the channel statistics while the receiver has perfect or imperfect channel side information (CSI). The fading coefficient is assumed to be random but stays constant over a LDPC codeword. We define the outage event as the set of channel realizations which disables successful decoding. Based on a density evolution algorithm and stability condition, closed- form outage probabilities are derived for both Rayleigh and Rician fading channels. The effect of channel estimation error on the outage probability is also investigated assuming Gaussian estimation error.

We propose a low complexity frequency domain channel estimator for pilot-symbol-assisted (PSA) orthogonal frequency division multiplexing (OFDM) systems in a low mobility environment. We consider a situation where the receiver needs to estimate multipath channel with low complexity when only limited channel information is available. The proposed scheme relies on a recently proposed model, the Slepian basis expansion model, where Slepian sequences are used to exploit channel correlation in time. However, in slow fading channels, the length of the required Slepian sequence is very long and thus decoding complexity increases. To achieve accurate channel estimation with low complexity, we propose to utilize the Slepian sequences to exploit the frequency correlation of the channel. Simulation results show that the proposed channel estimator outperforms the channel estimator based on the exponential basis expansion model where the channel is approximated as a linear combination of complex exponential functions.

In this paper a union bound on the bit error probability of bit-interleaved space-time (BI-ST) coded systems is derived. The derivation is based on the uniform interleaving assumption of the coded sequence prior to transmission over the multiple antennas. The performance of a BI-ST coded system is a function of how the bit errors are distributed over the signals in the codeword. In this paper, we derive this distribution as well as the corresponding pairwise error probability. The bound is a function of the distance spectrum of the code, the signal constellation used and the space-time (ST) encoding scheme. The bound is derived for a general BI-ST coded system and applied to two specific examples; namely, the BI space-time coded modulation (BI-STCM) and the BI space-time block codes (BI-STBC). Results show that the analysis provides a close approximation to the performance for a wide range of signal-to-noise ratios (SNR).

This paper aims to lay a solid foundation for the application of ultra-wideband (UWB) radio in vehicle environments by exploring the characteristics of UWB channels within a vehicle. A comprehensive measurement campaign was conducted to gather a set of channel impulse responses of UWB links within and outside an armored vehicle. Based on the experimental data, the channel's temporal characteristics, path loss, and capacities are analyzed. The distributions of delay spread and amplitudes of multipath signals are also studied, showing correspondence with the IEEE 802.15.3a UWB channel model. The UWB channels within the vehicle are then modeled by extracting relevant cluster and ray arrival rates and cluster and ray decay factors.

In this letter, a union bound on the error probability of coded multi-antenna systems over block fading channels is derived. The bound is based on uniform interleaving of the coded sequence prior to transmission over the channel. Using this argument the distribution of error bits over the fading blocks is computed and the corresponding pair wise error probability (PEP) is derived. We consider coded systems that concatenate a binary code with a space-time block code (STBC). Coherent detection is assumed with perfect and imperfect channel state information (CSI) at the receiver, where imperfect CSI is obtained using pilot-aided estimation. Under channel estimation environments, the tradeoff between channel diversity and channel estimation is investigated and the optimal channel memory is approximated analytically. Results show that the performance degradation due to channel memory decreases as the number of transmit antennas is increased. Moreover, the optimal channel memory increases with increasing the number of transmit antennas.

In this paper a union bound on the bit error probability of bit-interleaved coded modulation (BICM) is derived. In the derivation we assume that the bit errors in a codeword are uniformly distributed over the transmitted symbols. We derive the bound for BICM systems over AWGN, Rician and Nakagami fading channels. The proposed bound is general to any signal constellation and coding scheme with a known distance spectrum

In this paper, we investigate link adaptation and incremental redundancy (IR) retransmission schemes over correlated wireless channels. While computer simulations have been used to study the performance of these techniques, a numerically tractable analytical approach is more desirable to analyze generic protocols, and to reveal insights into the performance tradeoffs. An error-recursion approach is developed in this paper to mathematically analyze the throughput, delay, and energy efficiency of rate-adaptation techniques over fading channels with arbitrary correlations between retransmissions. Using Reed-Solomon codes as an example, we quantitatively predict the performance tradeoff of throughput and latency for IR schemes and the performance dependency on the channel correlation. Numerical results also show that reactive rate-adaptation schemes with IR retransmission outperform proactive rate-adaptive schemes, even with perfect channel side information, in terms of throughput and energy efficiency.

In this letter, we investigate the fundamental relationship between the performance of a maximum ratio diversity combining scheme and the normalized mean square covariance (NMSV) over wide-sense stationary uncorrelated scattering channels. In particular, we show that the reliability achieved by diversity combining is closely related to the value of NMSV of the channel under consideration.

A set of parameters collectively called recentered normalized mean square correlation (RC-NMSR) are introduced to characterize the quality of multipath fading channels with nonzero specular components. The consideration of nonzero specular components requires nontrivial generalization of the parameters previously introduced for wide-sense stationary uncorrelated scattering (WSSUS) channels. The new parameters are obtained by studying the principles of diversity combining. We illustrate the effectiveness of these parameters by theoretical and empirical study of a simple diversity combining scheme and frequency hopping spread spectrum systems.

A set of second-order statistics collectively called normalized mean square covariance (NMSV) are defined to characterize the frequency and/or the time selectivity of wide-sense stationary uncorrelated scattering (WSSUS) channels. Normalized frequency mean square covariance (NFMSV) quantifies the frequency selectivity, while normalized time mean square covariance (NTMSV) characterizes the time selectivity. Normalized frequency-time mean square covariance is defined to characterize the combined effect of frequency and time selectivities. The NMSVs of a WSSUS channel can be computed easily from the scattering function. We show that there is a very close relationship between the NMSV of a WSSUS channel and the performance of various diversity combing schemes. Also we discuss, with practical system design problems, how useful the parameters are for efficient system design.

In this work, we investigate the tradeoff between energy and delay for wireless networks utilizing the IEEE 802.11 standard for medium access control. The proposed analysis provides the joint distribution of the energy and delay of a transmitted data packet, which is then used to evaluate the corresponding average values. Our analysis takes into account the effect of the channel noise on the transmission of the RTS, CTS, data, and ACK packets. Furthermore, channel coding is incorporated in the analysis by estimating the packet error probability using error-exponent-based bounds under a memoryless channel. Using these analysis tools, the code rate and the signal-to-noise ratio per dimension are optimized to achieve minimum average delay per information bit.

A union bound on the error probability of coded multi-antenna systems over block fading channels is proposed. The bound is based on uniform interleaving of the coded sequence prior to transmission over the channel. Using the uniform interleaving argument the distribution of error bits over the fading blocks is computed. The pair-wise error probability is derived for a specific distribution pattern of the error bits over the fading blocks. We consider coded systems that concatenate a binary code with a space-time block code (STBC). The tradeoff between channel diversity and channel estimation is investigated assuming pilot-aided channel estimation and the optimal channel memory is approximated analytically. Results show that the optimal channel memory increases with increasing the number of transmit antennas.

The performance of a single-user, ultra-wideband (UWB) communication system employing binary block-coded modulation with pulse-position modulation (PPM) or on-off keying (OOK) and operating in indoor multipath channels is considered. We examine the tradeoff between receiver complexity and performance for the case of RAKE receivers with maximal-ratio combining (MRC). The derived expressions are evaluated numerically with measured UWB channel data for various cases.

This paper concerns with the minimum mean-squared error (MMSE) detection of synchronous multicarrier CDMA systems. Maximal-ratio combining (MRC) MMSE detection schemes are proposed for the multicarrier CDMA systems. In the proposed MRC MMSE receiver, the MMSE detection is first performed separately for each carrier, and then the outputs of each MMSE detector are combined in such a way that the resulting signal-to-noise ratio (SNR) is maximized. The performance of the considered MRC MMSE schemes is compared with the conventional MMSE receivers of both jointly and separately designed MMSE filters. It is found that when the system is lightly loaded, the MRC MMSE detection scheme performs comparably to the jointly optimized MMSE detection in the presence of slow frequency-nonselective independent Rayleigh fading for each carrier.

Optimal multilevel codes (MLC) with QAM constellations are considered with focus on both AWGN and Rayleigh fading channels. With the proposition of three novel set partitioning rules for QAM constellations, a new MLC scheme with a very simple MSD (multistage decoding) structure comes into being, which is operated on the capacity rule. Compared with traditional MLC scheme the new MLC structure greatly reduces the calculation of the individual capacities in the MLC system because the new set partitioning rules ensure the independency of two dimension symbols. Furthermore the new system cannot cause any performance loss and the time delay is just 1/2 of that with traditional partitioning rules. As an example 64QAM constellation with three new set partitioning rules are provided. Their performance is simulated over AWGN and Rayleigh fading channels by choosing BCH codes as the component codes.

In this paper some nonstandard partitioning rules for 16QAM constellation are proposed. With these nonstandard partitioning rules a new MSD structure is generated. For the fixed component codes length the new structure can greatly reduce the complexity of MLC(Multilevel codes) system. The time delay is just 1/2 of that with traditional partitioning rules. Simulation results show that the new partitioning rules and the new MSD structure do not create any performance loss. Furthermore for the fixed time delay the new MLC system is better than the traditional MLC system and the performance improvement is about 0.25 dB with BER equal to 10/sup -5/.

The performance of a single-user ultra-wideband (UWB) communication system employing binary block-coded pulse-position modulation (PPM) and suboptimal receivers in multipath channels is considered. The receivers examined include a RAKE receiver with various diversity combining schemes and an autocorrelation receiver, which is used in conjunction with transmitted reference (TR) signaling. A general framework is provided for deriving the performance of these receivers in multipath channels corrupted by additive white Gaussian noise (AWGN). By employing previous measurements of indoor UWB channels, we obtain numerical results for several cases which illustrate the tradeoff between performance and receiver complexity.

This paper examines the asymptotic (M/spl rarr//spl infin/) performance of M-ary frequency-shift keying (M-FSK) in multi-channels, or multiple frequency-nonselective, slowly fading channels, with coding, side information, and diversity reception. In particular, Reed-Solomon (RS) coding is considered in conjunction with the ratio-threshold test (RTT), which generates side information regarding the reliability of received symbols. The asymptotic performance of orthogonal signaling in multichannels with maximal ratio combining (MRC), postdetection equal gain combining (EGC), hybrid selection combining (H-SC), and selection combining (SC) is derived for an arbitrary statistical fading model and diversity order. The derivations reveal that coherent and noncoherent implementations of diversity combining schemes yield the same performance asymptotically. In addition, the asymptotic results are evaluated assuming a Nakagami-m fading model, and the effect of fading severity, diversity order, code rate, and side information upon the performance of the various diversity combiners is investigated. The minimum signal-to-noise ratio (SNR) required to achieve arbitrarily reliable or error-free communication, as well as the associated optimal RS code rate, are determined for various cases.

This paper considers the bit error probability analysis of direct-sequence code-division multiple access with offset quadrature phase-shift keying (OQPSK) modulation and random signature sequences. A statistical characterization of the decision variable at the output of the correlation receiver is obtained, and several techniques for evaluating the error performance, previously derived for binary phase-shift keying (BPSK)-modulated systems, are then extended to the case of OQPSK. This includes exact bit error evaluation, as well as various approximation methods based on Gaussian modeling of the multiple-access interference terms. These techniques, known as the standard and improved Gaussian approximations, have increasing complexity depending on the level of accuracy required. For BPSK, the standard approximation is typically found to be inaccurate, unless the number of users becomes large, and only the improved approximation yields sufficient accuracy in general. But for the case of OQPSK, the relative performance comparison developed in this paper shows that, for all practical purposes, the simple standard approximation is surprisingly very accurate even with a small number of users.

An iterative receiver structure Is proposed for turbo-coded frequency-hop multiple access (FHMA) systems. In FHMA systems, the adjacent channel interference (ACI) is the major contributor of multiple access interference (MAI) if orthogonal hopping patterns are used. The ACI is a function of the tone spacings of the adjacent subchannels and the rolloff factor of the pulse-shaping filter. The calculation of the ACI for a square-root raised-cosine pulse-shaping filter in an FHMA system is presented in this paper. In addition, a low complexity iterative multiuser detector is developed to mitigate the degradation caused by ACI in the FHMA systems. The iterative receiver structure is based on a modified turbo decoding algorithm which makes use of the a posteriori log-likelihood ratio (LLR) information of the systematic bits to obtain the a posteriori information of the turbo-encoded parity bits. Iterations of the receiver/decoder are used as the mechanism to estimate and mitigate the MAI in the FHMA system. The properties of both soft and hard interference suppressors based on the modified turbo decoding algorithm are examined and an efficient recursive implementation is derived. Compared to maximum-likelihood multiuser detection, the proposed system is more practical and its complexity is only a linear function of the number of users. Simulation results show that the proposed iterative receiver structure offers significant performance gain in bandwidth efficiency and the required signal-to-noise ratio (SNR) for a target bit-error rate (BER) over the noniterative receiver structure. Moreover, the single user performance can be achieved when imperfect power control exists.

In this paper, we analyze the effects of a nonlinear amplifier on the performance of convolutionally coded multicarrier spread-spectrum systems in the presence of multipath fading. Two performance measures, bit-error rate (BER) and adjacent channel power ratio (ACPR) are considered to assess the effects of in-band interference and out-of-band interference (spectral regrowth) from the nonlinear amplifier, respectively. A memoryless polynomial model is used to represent the bandpass amplifier amplitude nonlinearities (AM/AM) and a slow frequency-nonselective Rayleigh fading channel is assumed for each modulated carrier. Analytical results for the BER for uncoded systems and upper bounds on the BER for coded systems are presented. The optimum amplifier output power backoffs for both systems, which yield the smallest system power consumption, are also determined. The obtained ACPR shows its slow (inverse linear) falloff with the amplifier output backoff.

Iterative algorithms are an attractive approach to approximating optimal, but high-complexity, joint channel estimation and decoding receivers for communication systems. We present a unified approach based on factor graphs for deriving iterative message-passing receiver algorithms for channel estimation and decoding. For many common channels, it is easy to find simple graphical models that lead directly to implementable algorithms. Canonical distributions provide a new, general framework for handling continuous variables. Example receiver designs for Rayleigh fading channels with block or Markov memory, and multipath fading channels with fixed unknown coefficients illustrate the effectiveness of our approach.

This paper examines the asymptotic performance of M-ary orthogonal modulation with noncoherent square-law detection and combining in Rayleigh fading. The analysis takes into consideration Reed-Solomon coding and evaluates the gain provided by the ratio-threshold test (RTT) which generates side information regarding the reliability of received symbols. The minimum received signal-to-noise ratio (SNR) required for error-free communication and the optimal code rate are derived for arbitrary orders of diversity. These asymptotic results are then extended to a direct-sequence code division multiple access (DS-CDMA) system with frequency-selective fading.

An iterative receiver structure is proposed for turbo-coded FHMA systems. In frequency-hop multiple access (FHMA) systems, the adjacent channel interference (ACI) is the major contributor of MAI if orthogonal hopping patterns are used. The ACI is a function of the tone spacings of the adjacent subchannels and the rolloff factor of the pulse-shaping filter. A low complexity iterative multiuser detector is developed to mitigate the degrading effect of ACI in the FHMA systems. Iterations of the demodulator and decoder are used as the mechanism to estimate and mitigate the MAI in the FHMA system. In addition, an iterative decoder structure based on a modified turbo decoding algorithm is proposed. Compared to maximum-likelihood multiuser detection, the proposed system is more practical and its complexity is only a linear function of the number of users. Simulation results show that the proposed iterative receiver structure offers significant performance gains in bandwidth efficiency and the required signal-to-noise ratio (SNR) for a target BER over a noniterative receiver structure.

Modified ARQ (automatic-repeat-request) techniques based on turbo coding are investigated for asynchronous DS-CDMA (direct-sequence code-division multiple-access) data networks under shadowing and frequency selective fading channel conditions. The throughput, delay, and energy efficiency performance of standard ARQ, metric combining, and RCPT (rate compatible punctured turbo) coded ARQ schemes are compared via simulations. The RCPT/ARQ schemes are shown to outperform the other two schemes in terms of both throughput and energy efficiency at the cost of larger delay and complexity. In addition, maximum network throughput is investigated for different ARQ schemes under energy constraints.

For pt.I see ibid., vol.47, no.1828-36 (1999). In Part I, a class of multicarrier systems was proposed to study the effect of the method of diversity allocation on the performance of coherent multiuser communication systems operating over fading channels. In this paper, optimization over the proposed class of systems is considered for a fixed number of users per unit bandwidth. The first case studied is a system where the only noise not attributable to users in the system is additive white Gaussian noise. It is observed that either a system employing exclusive allocation, where users are allocated time-bandwidth resources that are not simultaneously shared with other users, or a system employing maximum resource sharing, where all users simultaneously share time-bandwidth resources, is optimal. Next, the preferable of these two extreme forms of resource allocation is determined. For any reasonable signal-to-noise ratio (SNR) and user density, it is shown that the system employing exclusive resource allocation is optimal in a single-cell environment with perfect subchannel separation at the receiver. Finally, the optimization is repeated in the presence of partial-band interference (PBI). Once again, either a system employing exclusive resource allocation or a system employing a maximum resource sharing scheme is observed to be optimal. The presence of the PBI increases the range of user densities and SNRs where a system employing a maximum resource sharing scheme is optimal, particularly when the probability of a particular time-bandwidth slot experiencing interference is high.

The performance of turbo codes is investigated in a frequency-hopped spread-spectrum (FH-SS) system with full-band thermal noise and Rayleigh fading. For cases where the data rate exceeds the hopping rate (i.e., there exists multiple bits per hop) and fading side information (SI) does not exist, our approach is to iteratively estimate the fading levels. Simulation is performed for coherent and noncoherent reception, variable number of bits per hop, and cases where fading SI is available or unavailable to the decoder. It is shown that iterative channel estimation performed in conjunction with iterative decoding can improve the overall decoding performance. Finally, the performance of an FH-SS system using standard fading assumptions is compared to the performance of a measured fading channel. Due to flaws in the assumptions, the measured fading channel yields several decibels of performance loss relative to the ideal fading channel.

Summary form only given. A hybrid trellis-tree search algorithm, the H-PTCQ, which has the same storage requirement as PTCQ and, is presented. We assume 2 survivor paths are kept at each state. It is straightforward to extend the algorithm to the cases where n/spl ges/2. Simulation is conducted over 20-second speech samples using DPCM, PTCQ and H-PTCQ. The data sequence is truncated into blocks of 1024 samples. The optimal codebooks for a memoryless Laplacian source are used. Predictor coefficients for the 1st-order and 2nd-order predictors are {0.8456} and {1.3435, -0.5888}, respectively. Simulation results indicate that both PTCQ and H-PTCQ have about 3 dB gain over DPCM. H-PTCQ with 8-state convolutional code has about 0.2 to 0.3 db gain over PTCQ for the same trellis size; H-PTCQ with 256-state convolutional code has 0.05 to 0.1 dB gain over the PTCQ counterpart. Compared with a 2M-state PTCQ, the M-state H-PTCQ has the same computational complexity and uses half of the path memory. Since the performance improvement of an an 8-state PTCQ over a 4-state PTCQ is about 0.4 dB for a similar set of data, the 0.2 to 0.3 dB gain obtained by using H-PTCQ is quite remarkable. Notice that H-PTQ enables a transmitter to adapt performance according to the resource constraints without changing PTCQ receivers. It is also interesting to observe that the 0.1 dB gain of an 8-state TCQ against a 4-state TCQ plus the 0.3 dB gain of H-PTCQ is about the gain of an 8-state PTCQ over a 4-state PTCQ. The results for 256-state quantization also agree with this observation. Therefore, we conclude that most of the gain of a 2M- over M-state PTCQ comes from the better internal TCQ quantizer, and mostly from the better prediction by keeping more paths.

The decision to attempt or suspend transmission is cast as a stochastic control problem with imperfect state information. By employing a dynamic programming formulation, the tradeoff between high throughput and energy efficiency is resolved in a flexible cost structure over which the optimization is performed. The optimal policy is derived and shown to be a threshold rule that varies with the memory present in the error process. A suboptimal implementation of the policy indicates that the protocol always favors attempting transmissions when the memory is low. As the channel memory increases, the protocol suspends transmission for longer durations after a packet failure.

A trellis-based multiuser detection algorithm called bias compensated matched filter decision feedback sequence estimation (BCMFDFSE) is considered for DS-CDMA systems under frequency-selective fading environments. The development of the wideband DS-CDMA standard demands the consideration of frequency selectivity in designing systems. In this paper, we propose BCMFDFSE as a possible receiver structure that has nice performance/complexity tradeoffs. We compare BCMFDFSE with other algorithms such as successive interference cancellation (SIC) and parallel interference cancellation (PIC).

A class of multiuser multicarrier communication systems is introduced to study the influence of resource allocation on the performance of multiuser communication systems operating over fading channels. This class of systems includes both systems that employ exclusive allocation schemes, where users are allotted time-bandwidth slots without interference from other users, and systems that employ shared allocation schemes, where users are allotted time-bandwidth slots that are also employed by other users. The optimal weighting factors used in the combining of the received signals from the slots of a single user for the conventional receiver is derived, and the performance of systems in the class is characterized. For each of a number of popular multiuser architectures, it is shown that there exists a system in the class with nearly identical performance. Based on these relations, it is concluded that a class of systems has been introduced that allows the study of the merits of different types of time-bandwidth allocation under a single framework.

This paper investigates the effect of chip waveform shaping on the error performance, bandwidth confinement, phase continuity, and envelope uniformity in direct-sequence code-division multiple-access communication systems employing offset quadrature modulation formats. An optimal design methodology is developed for the problem of minimizing the multiple-access interference power under various desirable signal constraints, including limited 99% and 99.9% power bandwidth occupancies, continuous signal phase, and near-constant envelope. The methodology is based on the use of prolate spheroidal wave functions to obtain a reduced-dimension discrete constrained optimization problem formulation. Numerous design examples are discussed to compare the performance achieved by the optimally-designed chip waveforms with other conventional schemes, such as offset quadrature phase-shift keying, minimum-shift keying (MSK), sinusoidal frequency-shift keying (SFSK), and time-domain raised-cosine pulses. In general, it is found that while the optimized chip pulses achieved substantial gains when no envelope constraints were imposed, these gains vanish when a low envelope fluctuation constraint was introduced. In particular, it is also shown that MSK is quasi-optimal with regard to the 99% bandwidth measure, while the raised-cosine pulse is equally good with both the 99% and 99.9% measures, but at the expense of some envelope variation. On the other hand, SFSK is quasi-optimal with regard to the 99.9% bandwidth occupancy, among the class of constant-to-low envelope variation pulses.

The asymptotic performance of Reed-Solomon coded M-ary orthogonal signaling with ratio-threshold test (RTT) type demodulation in a Rayleigh fading channel is considered. We show that the minimum E~/sub b//N/sub 0/ needed for error-free communication is eln2 (2.75 dB) with RTT, and 4.79 (6.8 dB) with hard decision. The optimum code rate that minimizes the required E~/sub b//N/sub 0/ is e/sup -1/ with RTT and 0.46 with hard decision, and the optimum ratio threshold approaches 1 for large M. Next, we investigate the fundamental limit in direct-sequence spread-spectrum multiple-access (DS/SSMA) system employing an M-ary orthogonal code of length N=Mm, which is obtained by spreading every row of an M/spl times/M Hadamard matrix with a user-specific random sequence of length N. We derive the minimum E~/sub b//N/sub 0/ for error-free communication as a function of the number of users, the optimum code rate that minimizes E~/sub b//N/sub 0/, and the maximum limit on the total information transmission rate.

Decision feedback sequence estimation (DFSE), which is a reduced-complexity alternative to maximum likelihood sequence estimation (MLSE), can be used effectively for equalization of intersymbol interference (ISI) as well as for multiuser detection. The algorithm performs very well for whitened (minimum-phase) channels. For nonminimum-phase channels, however, the algorithm is not very effective. Moreover, DFSE requires a noise-whitening filter, which may not be feasible to compute for time-varying channels such as a multiuser direct-sequence code division multiple access (DS-CDMA) channel. Noise-whitening is also cumbersome for applications that involve bidirectional equalization such as the global system for mobile communication (GSM) system. In such conditions, it is desirable to use the Ungerboeck (1974) formulation for sequence estimation, which operates directly on the discrete-time unwhitened statistic obtained from conventional matched filtering. Unfortunately, DFSE based on matched filter statistics is severely limited by untreated interference components. We identify the anticausal interference components, using an error probability analysis. This leads us to a modified unwhitened decision feedback sequence estimator (MUDFSE) in which the components are canceled, using tentative decisions. We obtain approximate error probability bounds for the proposed algorithm. Performance results indicate that the modified algorithm, used on unwhitened channels with relatively small channel correlations, provides similar performance/complexity tradeoffs as the DFSE used on the corresponding whitened minimum-phase channels. The algorithm is especially attractive for multiuser detection for asynchronous DS-CDMA channels with long spreading codes, where it can achieve near-MLSE performance with exponentially lower complexity.

Turbo codes are investigated in a slow frequency-hopped spread spectrum (FH-SS) system with partial band jamming. In addition, full-band thermal noise is present. The channel model is that of a partial-band jammer in which a fraction of the frequency band is jammed and the remaining fraction is unjammed. This paper focuses on the implementation and performance of a modified turbo decoder for this model. We refer to the knowledge that each transmitted bit is jammed as channel state information. We consider cases of known or unknown channel state and variable number of bits per hop. Our approach is to modify the calculation of branch transition probabilities inherent in the original turbo decoder. For the cases with no side information and multiple bits per hop, we iteratively calculate channel state estimates. Analytical bounds are derived and simulation is performed for noncoherent demodulation. The performance of turbo codes is compared with a Reed-Solomon and a concatenated code comprised of a convolutional inner code and Reed-Solomon outer code.

The asymptotic performance of Reed-Solomon (RS)-coded M-ary orthogonal signaling with ratio-threshold test (RTT) type demodulation in a Rayleigh-fading channel is considered. We show that the minimum E~/sub b//N/sub 0/ needed for error-free communication is eln2 (2.75 dB) with RTT, and 4.79 (6.8 dB) with hard decisions. The optimum code rate that minimizes the required E~/sub b//N/sub 0/ is e/sup -1/ with RTT and 0.46 with hard decision, and the optimum ratio threshold approaches 1 for large M. Next, we investigate the fundamental limit in a direct-sequence spread-spectrum multiple-access (DS/SSMA) system employing an M-ary orthogonal code of length N=Mm, which is obtained by spreading every row of an M/spl times/M Hadamard matrix with a user-specific random sequence of length N. We derive the minimum E~/sub b//N/sub 0/ for error-free communication as a function of the number of users, the optimum code rate that minimizes E~/sub B//N/sub 0/, and the maximum limit on the total information transmission rate. Then, we consider a multirate DS/SSMA system, where a population of users simultaneously transmit at different power levels a variety of traffic types of different information rates. We derive the minimum required E~/sub B//n/sub 0/ and the optimum code rate for each traffic type.

The performance of different coding schemes for direct-sequence spread-spectrum (DS-SS) with multiple-access (MA) interference in a nonselective Rayleigh fading channel is considered. A conventional 64-ary orthogonal code (M/sub 64/) transmitting 6 bits of information is examined first. Each of the 64 code symbols in the M/sub 64/ code is assumed to be spread by a random sequence of length N, and the channel is assumed to be interleaved every N chips. We consider a M/sub 64/ DS-SS code concatenated with a (63, k) Reed-Solomon (RS) outer code and varying the amount of spreading and the code rate for a fixed data rate and bandwidth. Our analysis based on Gaussian approximation shows that when the number of users is reasonably large, an optimal value k* to achieve the minimum bit error probability of the (63, k) RS code can be found. Furthermore, we extend the results by substituting the M/sub 64/ code with the trellis coded Nordstrom-Robinson code (TCNR), and the trellis coded Reed-Muller code (TCRM), which have the same data rate as that of the M/sub 64/ code. An optimal value k* to achieve minimum bit error probability can also be found when the TCNR code or the TCRM code is concatenated with a (63, k) RS outer code.

The performance of a countermeasure technique in the presence of the optimal follower multitone jammer is evaluated for frequency-hopped spread spectrum (FHSS) communications. It is shown that, with a certain probability, the optimal jammer will have dual tones in a frequency channel.

The phenomenon of hard handoffs (as applicable to FDMA- and TDMA-based networks) as well as soft handoffs (as applicable to DS/CDMA-based networks) is formulated as stochastic optimization problems. The signals received by a mobile user are treated as stochastic processes with associated rewards, which are functions of some measurable characteristics of the received signals, while the handoff is associated with a switching penalty. This formulation captures the trade-offs involved in handoffs in a flexible manner and captures many facets of popular cellular communication systems in use currently. Using dynamic programming, necessary and sufficient conditions for determining the optimal base station(s) the mobile should be associated with during each decision epoch are derived. For the cases where the above-mentioned necessary and sufficient conditions fail to determine an optimal decision, "limited lookahead" arguments are used for determining handoff decisions. The decisions are taken in a decentralized manner, which makes its implementation easier compared to centralized algorithms. Simulation results show that for the hard handoffs, performance gain by the proposed algorithm over the simpler threshold algorithms proposed in the literature is small; however, for the case of soft handoffs, the proposed algorithm offers considerable improvement over the algorithm proposed in the IS-95 standard.

Considers the problem of optimal scheduling of soft handoffs as applicable to DS/CDMA based cellular networks. The authors have formulated the phenomenon of soft handoffs as a reward/cost stochastic optimization problem wherein the reward is a function of some measurable characteristics of the received signal, and cost can be associated with different factors such as multiple simultaneous active connections, connection set-up and termination overheads. Using dynamic programming, a maximum net reward policy that specifies the optimal base stations the mobile should be associated with during each time slot, is determined. The authors also extend their results to the case when there are more than two base stations. Furthermore, the decisions are taken in a decentralized online manner. Simulation results show that the proposed algorithms offer considerable improvement over the policy proposed in the IS-95 standard.

The effect of chip waveform shaping on the power efficiency and spectral occupancy of DS-CDMA communication systems is investigated assuming random sequences and coherent reception. A method for designing optimum chip waveforms that minimise the average power of the multiple access interference at a given bandwidth occupancy is derived. The performance improvements of the optimally designed chip waveforms are illustrated by comparing the achieved SIR gain and capacity increase with the figures of some known examples of modulation schemes (such as OQPSK and MSK) that employ conventional chip shaping pulses.

The performance of a frequency-hop spread-spectrum system employing carrier jitter against one-dimensional tone jamming (n=1 band multitone jamming) is investigated. First, noncoherent BFSK signaling under continuous-wave (CW) tone interference with arbitrary frequency offset is analyzed. A closed-form expression is derived for the error probability when there is one interfering CW tone and the background noise is negligible. When the background noise is significant, an expression involving one numerical integration is derived for the probability of error. It is shown that an interfering CW tone with power less than that of the signal can still cause errors with significant probability for certain ranges of carrier offsets. Next, the authors apply these results in analyzing the performance of a FHSS communications system under one-dimensional tone jamming when the communicator pseudorandomly jitters his carrier frequency from hop to hop. Two different methods of carrier jittering are considered. It is found that one of the schemes offers approximately a 3 dB gain in signal-to-noise ratio over a system without carrier jittering while the other scheme offers no significant gain.>

We consider a direct-sequence spread-spectrum multiple access communication system with convolutional coding and hard decision decoding. We calculate the packet error probability and throughput of this system. Previous bounds on packet error probability have relied on the worst case assumption of phase and chip synchronous interference. We present new bounds on packet error probability and throughput for the case of both slotted and unslotted systems. These new bounding techniques are based on two advances: an improved Chernoff bound on the error event probability of a convolutional code, and the use of moment space techniques. Numerical results indicate that these new bounds on packet error probability improve on previously reported bounds by more than an order of magnitude. We also examine the problem of choosing the optimum code rate which maximizes throughput. We compare the optimum code rate which results from the bounding technique to the optimum code rate derived from an approximation technique. Although the bounding technique and approximation technique yield very different results for throughput, the resulting choice of optimum code rate is similar.

Decoding that uses soft-decision information but with multiple low-complexity decoders are investigated. These decoders correct only errors and erasures. The structure of the receiver consists of a bank of z demodulators followed by errors- and erasures-correcting decoders operating in parallel. Each demodulator has a threshold for determining when to erase a given symbol. We assign a cost f(/spl theta/) to the noise for causing an erasure when the receiver uses a particular threshold /spl theta/ and a (larger) cost f(/spl theta.>

This paper considers the application of trellis coding techniques to direct-sequence spread-spectrum multiple-access (DS/SSMA) communication. The unique feature of the trellis codes considered is that they are constructed over the set of possible signature sequences rather than over some standard 2-D signal constellation. The resulting codes have a small number of signals per dimension. We present several examples of these trellis codes, and suggest possible methods of implementation. We also present a detailed error analysis for this system, which employs techniques developed by Lehnert and Pursley (1987, 1989)) to accurately model the multiple access interference. We generate numerical results for several examples and conclude that the proposed trellis coded systems yield significant performance improvements over binary antipodal DS/SSMA systems. In addition, the new trellis codes perform better than standard error control techniques with the same complexity and code rate. Analytic results are verified with simulations.>

The performance of robust metrics (metrics that can be computed from the outputs of the matched filters only) with convolutional coding and diversity under worst-case partial-band noise jamming is analyzed. Both binary and dual-k convolutional codes employing these metrics with diversity are compared via Union-Chernoff bounds. The performances of metrics considered in the literature that assume perfect side-information are given for comparison purposes. It is found that there exist very good robust metrics that provide performance comparable to metrics using perfect side-information. Among the robust metrics considered, the self-normalized metric offers the best performance and achieves performance practically identical to that of the square-law-combining metric with perfect side-information for M=8.>

The performance of Reed-Solomon codes in an asynchronous frequency-hop spread-spectrum multiple-spectrum (FHSS-MA) network is discussed. When q denotes the number of frequency slots available to the network and r denotes the rate of the Reed-Solomon code, optimal (q,r) pairs that meet a given performance criterion with minimum bandwidth expansion (q/r) for a given number of active users are obtained. It is shown that the optimal code rate rapidly converges to a constant value and the optimum number of slots increases approximately linearly as the number of active users increases. This suggests that one should fix the code rate and increase the number of slots to accommodate the increasing number of users in the network under a given performance criterion with minimum bandwidth expansion.>

A countermeasure to a partial-band follower jammer is proposed for frequency-hopped spread-spectrum communications. This technique randomizes the transmission technique used by the transmitter (and receiver). Either the information is carried by M tones which are transmitted in a frequency slot, or by M frequency slots which contain signal energy. As a counter-countermeasures, the jammer randomizes between jamming the same frequency slot being used by the communicator, or jamming a subset of the slots not being used by the communicator. The performance for randomized strategies for the communicator and jammer is investigated. It is shown that the proposed technique enhances the system's performance.>

Expressions are developed for the probability of error for asynchronous frequency-hop spread-spectrum multiple-access networks using Markov hopping patterns and binary frequency shift keying (BFSK) with one symbol transmitted per hop. The expressions are exact when there is one interfering user and orthogonal BFSK is used. They provide excellent approximations when there are more than one interfering user. It is also shown that the error probability when Markov hopping patterns are used is a good approximation to the error probability when memoryless hopping patterns are used. By computing the channel capacity and the associated throughput, a simple hard decision receiver is shown to perform much better than a receiver using perfect side-information to erase the symbols transmitted on hops that were hit when all the users have the same power and one binary symbol is transmitted per hop.>

A simple, exact calculation is presented of the probability distribution of the number of hits in a block of n symbols in a frequency-hopped, spread-spectrum, multiple-access communication system. While the sequence of hits is not Markovian, there is an underlying Markovian structure that allows the probability distribution of the number of hits to be calculated in a recursive fashion. Knowing the probability distribution of the number of hits makes it possible to calculate the probability of error for a system employing error correcting codes for several different types of receivers, including receivers with both errors and erasures. The numerical results show that both the approximation obtained by assuming the actual sequence of hits is Markovian and the approximation obtained by assuming the hits are independent are very good. When the number of frequency slots is not too small (less than five), calculations show that assuming the independence of hits gives an error probability accurate to within 1% of the actual error probability. Assuming the hits are Markovian gives error probabilities which are accurate to within 0.001%.>

The information theoretic capacity is considered. In order to account for independent encoding and decoding and private (to the sender and receiver) hopping patterns, an interference channel model is adopted with K sender-receiver pairs with the ith receiver only interested in the message transmitted by the ith sender. Both synchronous and asynchronous hopping patterns are investigated. Although the channel exhibits memory in the latter case, it is possible to compute the capacity region. The asymptotic normalized sum capacity is also computed.>

The correcting properties of concatenated codes with parallel decoding over an additive channel are investigated. The ith inner decoder's output is a codeword if the Euclidean distance between the received vector and some codeword is less than Delta /sub i/ and an erasure otherwise. The outer decoders correct errors and erasures. The error-correcting capability, which is taken to be the minimum length of any noise vector that can cause an error, is obtained for a bank of z inner and outer decoders as a function of the thresholds used. The set of thresholds that maximize the error-correcting capability is also found. It is shown that for a small number of branches, the error-correcting capability is nearly as large as any decoder.>

The authors consider a multiple-access frequency-hopped spread-spectrum communication system with Reed-Solomon codes. The performance measures of interest are an achievable region and the channel throughput. The achievable rate region is the set of all pairs of code rate and number of users for which communication is possible with error probability below a fixed value. The throughput measures the expected number of successful codeword transmissions per unit bandwidth. Two models of interference are considered. For these two models, the authors determine the optimal number of users for a given bandwidth and the optimal rate Reed-Solomon code that maximize the throughput. They also determine the achievable region for these models.>

The process of communicating in the presence of interference that is unknown or hostile is modeled as a two-person zero-sum game with the communicator and the jammer as the players. The objective function considered is the rate of reliable communication. The communicator's strategies are encoders and distributions on a set of quantizers. The jammer's strategies are distributions on the noise power subject to certain constraints. Various conditions are considered on the jammer's strategy set and on the communicator's knowledge. For the case where the decoder is uninformed of the actual quantizer chosen, it is shown that, from the communicator's perspective, the worst-case jamming strategy is a distribution concentrated on a finite number of points, thereby converting a functional optimization problem into a nonlinear programming problem. Moreover, the worst-case distributions can be characterized by means of necessary and sufficient conditions which are easy to verify. For the case where the decoder is informed of the actual quantizer chosen, the existence of saddle-point strategies is demonstrated. The analysis is also seen to be valid for a number of situations where the jammer is adaptive.>

It is shown that for worst-case partial-band jamming, the error probability performance (for fixed E/sub b//N/sub I/) becomes worse with increasing M for (M>16). The asymptotic probability-of-error is not zero for any E/sub b//N/sub I/(>ln 2), but decreases inverse linearly with respect to it. In the fading case, the error-probability performance (for fixed E/sub b//N/sub 0/) improves with M for noncoherent detection, but worsens with M for coherent detection. For large E/sub b//N/sub 0/ the performance of the Rayleigh fading channel asymptotically approaches the same limit as the worst case partial-band jammed channel. However, for values of M at least up to 4096, the partial-band jammed channel does better. While it is unlikely that an M-ary orthogonal signal set with M>1024 will be used in a practical situation, these results suggest an important theoretical problem; namely, what signal set achieves reliable communication.>

The capacity of channels with block memory is investigated. It is shown that, when the problem is modeled as a game-theoretic problem, the optimum coding and noise distributions when block memory is permitted are independent from symbol to symbol within a block. Optimal jamming strategies are also independent from symbol to symbol within a block.>

This paper is concerned with the performance of a Communications system which utilizes frequency-hop spread spectrum, diversity transmission, Reed-Solomon coding, and parallel error-correction and erasure-correction decoding. Both binary signaling andM-ary orthogonal signaling are considered. The goals are twofold. First, it is desirable to provide good performance in partial-band Gaussian noise interference by use of coding and diversity with an efficient error-correction algorithm. Second, it is necessary to totally neutralize narrow-band interference (regardless of the power level or statistical distribution of the interference) in order to have an effective spread-spectrum system. Through an analysis of the effects of partial-band interference on a frequency-hop spread-spectrum system with diversity, it is shown that the use of ReedSolomon coding with a parallel errors and erasures decoding algorithm accomplishes these goals. The paper also investigates the accuracy of the Chernoff bound as an approximation to the true performance of a frequency-hop spreadspectrum communication system with diversity; side information,M-ary orthogonal signaling, and Reed-Solomon coding. The performance results presented in the paper are based on analysis and computer evaluation. Approximate results based on the Chernoff bound are also given. It is shown that the Chernoff bound forM-ary orthogonal signaling gives a very poor approximation for many cases of interest. This is largely due to the looseness of the union bound.

The performance of optimal codes on frequency-hopped channels with partial-band interference is investigated. The performance measures considered are channel capacity and cutoff rate. Worst-case partial-band Gaussian noise interference is assumed with the interference independent of the transmitted signal. The capacity and cutoff rate are calculated as a function of the signal-to-noise ratio. We consider soft decision receivers and hard decision receivers with and without side information. Optimal code rates are found for each of the above cases. The required signal-to-noise ratio for reliable communication when codes are used is determined as a function of the code rate.

The performance of codes in a frequency-hopped spreadspectrum communication system with partial-band interference is investigated. The performance measure considered is the decoded bit error probability. A simplified interference model and worst-case partial-band Gaussian noise interference model is considered with the interference noise statistically independent of the transmitted signal. We consider soft decision receivers with side information and hard decision receivers with and without side information.

The capacity and cutoff rate of frequency-shift keying (FSK) modulation and noncoherent reception when the signal is subject to Rician fading are calculated. Both hard and soft decisions with maximum likelihood combining are considered, as well as soft decisions with square-law combining. Optimal code rates are found that minimize the required signal-to-noise ratio for reliable communication.

A new class of channel models with memory is presented in order to study various kinds of interference phenomena. It is shown, among other things, that when all other parameters are held fixed, channel capacityCis an {\em increasing} function of the memory length, while the cutoff rateR_{0}generally is a {\em decreasing} function. Calculations with various explicit coding schemes indicate thatCis better thanR_{0}as a performance measure for these channel models. As a partial resolution of thisCversusR_{0}paradox, the conjecture is offered thatR_{0}is more properly a measure of coding delay rather than of coding complexity.

Upper and lower bounds on the average probability of error are obtained for direct-sequence spread-spectrum multiple-access communications systems with additive white Gaussian noise channels. The bounds, which are developed from convexity properties of the error probability function, are valid for systems in which the maximum multiple-access interference does not exceed the desired signal and the signature sequence period is equal to the duration of the data pulse. The tightness of the bounds is examined for system with a small number of simultaneously active transmitters. This is accomplished by comparisons of the upper and lower bounds for several values of the system parameters. The bounds are also compared with an approximation based on the signal-to-noise ratio and with the Chernoff upper bound.