Convenient analytical techniques are developed for use in preliminary design of systems and protocols for the delivery of fountain-coded files from a source node to a destination node with the assistance of a relay node. Each node has a half-duplex packet radio, and the time-varying disturbance on each link is represented by a lumpable finite-state Markov chain. The analytical techniques include the use of first passage times and recurrence times in the derivation of an exact expression for the completion time of file transfer over a radio link and the application of results on Markov-correlated Bernoulli trials to obtain exact expressions for completion times of relay-aided file transfer in wireless networks. In the development of analytical techniques, we employ capacity-achieving channel codes and ideal fountain codes; however, we present simulation results for packet radios that employ practical channel codes and for which the fountain code is a standard systematic raptor code.

We devise and evaluate five methods for fountain-coded broadcast distribution of a file from a source to multiple destinations in an ad hoc wireless network that consists of half-duplex packet radios. The methods differ in their use of intermediate nodes, their use of forwarding, and their reliance on a network spanning tree. All five methods employ continued fountain coding to prevent nodes from receiving duplicate fountain-coded packets. We derive an analytical approximation for the throughput of fountain-coded broadcast file distribution in a four-node network with time-varying radio links modeled by independent two-state Markov chains, and we show that our approach to fountain-coded file distribution gives throughput that is very close to the approximation. We employ simulations to examine larger networks in which each radio link has correlated Rayleigh fading and the radios use adaptive modulation and channel coding.

Fountain coding is a valuable tool for multicast transmissions in half-duplex packet radio networks if it is supported by an adaptive transmission protocol that compensates for fluctuations in the propagation losses on the radio links. Our goal is to devise low-complexity packet-by-packet adaptive modulation and channel coding protocols that provide high throughput for a broad range of multicast channels and operate with limited feedback and no knowledge of the fade levels or even the probability distribution for the fading on the radio links. The only control information for the protocols is derived from simple receiver statistics that are obtained by the demodulators and channel decoders in the receiving radios. Performance results are presented for practical fountain coding with low-complexity adaptive modulation and channel coding. Results on ideal fountain coding with adaptive transmission based on hypothetical perfect channel-state information are employed as performance benchmarks.

The papers in this special issue address the topic of capacity approaching codes. This issue reflects a further shift of interest in coding theory research, this time toward polar codes, a new class of capacity achieving codes introduced in 2008. Of the 17 papers appearing in this issue, 9 are devoted to various aspects of polar codes, with 6 papers devoted to LDPC codes, including 3 on spatially coupled (convolutional) LDPC codes, and 2 on other coding topics.

We examine the integration of adaptive modulation and channel coding protocols with fountain coding in a packet radio system. We present three modes of operation for the adaptive transmission system, each of which adapts the channel code in a way that accommodates the fixed-length packets produced by the fountain encoder. Each mode works with the fountain coding system to mitigate the effects of time-varying fading on the radio links and provide high throughput.

For time-varying fading, adaptation of the physical-layer channel code greatly enhances the throughput of a multicast transmission system, even if the system employs an application-layer fountain code for packet erasure correction. Performance evaluations for adaptive channel-coding protocols typically require extensive simulations of the fading channel, the iterative decoding process, and the generation of the control information that is used for the adaptation of the channel code. We present a method for the evaluation of such protocols that avoids a substantial amount of the computation required by traditional simulations, and we demonstrate that some important performance measures can be evaluated entirely by analysis. By the use of capacity-achieving channel codes in our investigation, we also decouple the performance of the adaptive coding protocol from the performance of a particular type of channel code and decoding method, which facilitates comparisons among different protocols. The application of our methods is demonstrated for two adaptive channel-coding protocols that are candidates for fountain-coded multicast transmission in packet radio systems.

If a frequency band has primary and secondary users, then the cognitive radios of the secondary users must monitor the band and be prepared to cease their transmissions if a primary user's radio begins to transmit. Traditional spectrum sensing requires the secondary radios to refrain from communicating while they check for the emergence of primary signals. We propose and evaluate methods by which the secondary radios can continue their communications while simultaneously monitoring the band to detect any transmissions that are initiated by the primary radios. Our methods for spectrum monitoring supplement traditional spectrum sensing and improve the communications efficiency of the secondary radios.

New distributed protocols for channel access and adaptive spreading are described and evaluated for use in direct-sequence spread-spectrum packet radio networks that have no central controllers, access points, or base stations. The protocols rely on demodulator statistics to provide the information needed for efficient sharing of the frequency band and compensation for changes in the communications environment in a network of half-duplex radios for which simultaneous two-way communications is not possible.

Protocols that were proposed recently for adapting the error-control code from packet to packet in a frequency-hop packet radio network are evaluated for use on channels for which the fading distribution has fixed or slowly varying parameters. The protocols do not require channel measurements or pilot signals; instead, the receiver derives the necessary adaptation control information from its decoder during of the reception of each packet. The throughput achieved by each adaptive-coding protocol when it is used with a family of turbo product codes is compared with the capacity limit and with the throughput that is obtained from a hypothetical ideal protocol that is given perfect channel state information.

Adaptation of the code rate and spreading factor for direct-sequence spread-spectrum packet radio transmissions provides much higher throughput than if the code rate and spreading factor are fixed. A low-complexity protocol for packet-by-packet adaptation can be obtained if receiver statistics that are developed during the demodulation of a packet are used to choose the code rate and spreading factor for the next packet. The design and evaluation of the protocol typically requires extensive simulations, especially for modern packet radio receivers that employ iterative decoding. We show that analytical methods based on Shannon capacity results greatly simplify the design of the adaptive protocol and provide good estimates of its throughput performance.

Information-theoretic limits on resource consumption are employed to obtain analytical methods for conducting tradeoffs between power, bandwidth, and time for cognitive radio transmissions in ad hoc dynamic spectrum access networks. A quantitative measure of resource consumption is applied to the design and evaluation of protocols for adaptive modulation and coding. The application of information theory to the minimization of resource consumption in cognitive radio networks is illustrated for binary phase-shift-key modulation with coherent demodulation.

Next generation packet radio networks will have far greater processing capabilities than current radio systems. We propose and evaluate decoding techniques that make use of such capabilities to increase the probability of successful decoding. We propose a metric derived from statistics collected during demodulation in a binary CDMA receiver. We investigate several methods to apply the proposed metric to the demodulator's soft-decision outputs prior to decoding. Our soft-decision decoding techniques are designed to mitigate the effects of interference from other signals in the frequency band. We compare the performance of our proposed metric to the log-likelihood ratio (LLR) metric, which requires that the mean signal level and noise variance are known for each bit position. Rather than attempt to estimate these parameters directly, our metric uses demodulator statistics and thus does not require pilot symbols or training sequences typically required by an LLR-based metric.

The one tutorial paper and eight contributed papers in this special issue focus on cooperative communications in MIMO cellular networks.

In many dynamic spectrum access networks, it is necessary for secondary users to monitor the frequency band in which they are communicating so that they can determine if the primary user has begun transmission. Traditional sensing methods require the transmitters of the secondary users to be silent while spectrum monitoring is performed. Statistics that are derived easily in a communications receiver have the potential to permit a level of spectrum monitoring while the receiver is demodulating and decoding a packet, so that it is not necessary to silence the secondary transmitters. The proposed techniques for spectrum monitoring can supplement existing methods and reduce the amount of time that secondary users must refrain from communicating.

We describe similarities and differences between complementary-code-key (CCK) modulation and modulation that is derived from biorthogonal signals, and we present performance results and other information that may be useful to those who have applications for CCK modulation that do not require IEEE 802.11b compliance. The properties and performance of the highrate IEEE CCK 802.11b modulation formats are investigated and compared with the properties and performance of alternative modulation formats that are based on biorthogonal signals. Several complementary properties are derived for the full-rate (11 Mb/s) CCK signal set, the half-rate (5.5 Mb/s) CCK signal set, a full-rate signal set obtained from biorthogonal signals, and a half-rate biorthogonal signal set. Each signal set is a complementary set, but each also has stronger complementary properties. We evaluate the performance of IEEE 802.11b standard CCK modulation, CCK with certain modifications that depart from the IEEE standard, and modulation that is derived from biorthogonal signals. Performance comparisons are presented for additive white Gaussian noise (AWGN) channels and for channels with specular multipath. In particular, for AWGN channels, we provide an accurate analytical approximation for the frame error probability for full-rate CCK modulation.

Alternative protocols are presented for adapting the code from packet to packet in a mobile, wireless, ad hoc network that employs frequency hopping, coherent or noncoherent demodulation, and soft-decision decoding on channels with time-varying propagation loss and time-varying partial-band interference. The protocols can be employed with a wide range of codes and decoding algorithms. No channel measurements are needed, and no external side information is supplied to the receiver. Performance results are provided for packet transmissions that employ turbo product codes. The protocol performance results are compared with capacity limits and with the performance for hypothetical ideal protocols that use perfect channel-state information to select the codes that maximize the expected throughput.

Results are presented on code performance and capacity bounds for channels with Gaussian, bi-level, block interference for binary and nonbinary modulation, noncoherent demodulation, and soft-decision decoding. Each transmitted block is corrupted by additive white Gaussian noise that has one of two power spectral densities. The smaller of the two is the power spectral density of the thermal noise, and the difference between the two spectral densities is the power spectral density of the interference noise. The average power in the interference is constant, so the power spectral density of the interference is inversely proportional to the average fraction of the blocks that have interference. This block interference channel has been used to model partial-band interference in frequency-hop communications and to model pulsed interference in a number of communication systems. Throughput results for turbo-product and low-density parity-check codes that are used on Gaussian block interference channels are compared with the capacity bounds for such channels. For some code rates, we show that the throughput of the codes and the capacity bounds are both nonmonotonic functions of the fraction of the blocks that have interference. Applications to adaptive-rate coding are discussed.

Cognitive radios that are employed in a network with dynamic frequency assignments must operate efficiently in the presence of uncertainties and variations in the propagation characteristics of the network's communication links. A low-complexity adaptive transmission protocol is described and evaluated for use in cognitive radio networks whose links have unknown and possibly time-varying propagation losses as a result of such phenomena as slow fading or variations in shadowing. The cognitive radios are required to derive only simple statistics in the receivers in order to provide the information that is needed by our protocol; no estimates or measurements of received power or channel gain are used. The protocol's primary mechanism for responding to changes in propagation loss is to adjust the modulation and coding. Because of disruptions that can be caused by higher levels of interference to other radios in the network, the transmitter power is increased only if the most powerful combination of coding and modulation is inadequate. We employ finite-state Markov models for slowly varying channels, and we demonstrate that for such channels our protocol performs nearly as well as an ideal protocol that is told the exact value of the propagation loss for each packet transmission. Thus, the additional complexity that is required to enable cognitive radios to obtain precise channel-gain estimates is not justified and would lead to only negligible improvement in throughput. The throughput of our adaptive transmission protocol is compared with an upper bound that is derived from information theory for a hypothetical ideal protocol that is given perfect channel-state information, and some preliminary results on learning the adaptation decision intervals are included.

Two classes of complementary signal sets are compared in terms of their complementary properties and their error probabilities for channels with thermal noise and multipath interference. One class consists of the high-rate (11 Mbps and 5.5 Mbps) signals employed in the IEEE 802.11b standard, and the other class includes full-rate (11 Mbps) complex signals derived from biorthogonal sequences and half-rate (5.5 Mbps) biorthogonal signals. We examine several types of complementary properties of each class of signals and give performance comparisons for the signals when employed on channels in which thermal noise is the only disturbance and channels with thermal noise and multipath interference. For standard IEEE 802.11b complementary-code-key (CCK) modulation, we find the performance is strongly dependent on the differential multipath delay. For systems that employ binary error-control coding, the signals that are based on biorthogonal modulation are superior to the two IEEE 802.11b CCK signal sets.

High-rate direct-sequence (DS) spread spectrum is a modulation technique in which most or all of the spreading is provided by nonbinary data modulation. For applications to mobile ad hoc wireless networks, the limited processing gain of high-rate DS spread spectrum gives only modest protection against multiple-access or multipath interference, which limits the applicability of the modulation technique to fairly benign channels. In this paper, we explore the increased interference-rejection capability that can be obtained from convolutional coding with Viterbi decoding, Reed–Solomon coding with errors-and-erasures decoding, and block product coding with iterative decoding. For channels with multiple-access or multipath interference, performance results are given for several soft-decision decoding metrics, the benefits of adaptive-rate coding are illustrated, and the accuracy and utility of the Gaussian approximation are described. We also show how to use the bit-error probability for a system without error-control coding to determine which modulation method will give the best packet-error probability in a system with error-control coding.

High-rate direct-sequence spread spectrum is a modulation technique in which most or all of the spreading is provided by nonbinary data modulation. For applications to mobile ad hoc wireless networks, the limited processing gain of high-rate direct-sequence spread spectrum gives only modest protection against multiple access or multipath interference, which limits the applicability of the modulation technique to fairly benign channels. In this paper, we explore the increased interference-rejection capability that can be obtained from convolutional coding with Viterbi decoding, Reed-Solomon coding with errors-and-erasures decoding, and block product coding with iterative decoding. For channels with multiple access or multipath interference, performance results are given for several soft-decision decoding metrics, the benefits of adaptive-rate coding are illustrated, and the accuracy and utility of the Gaussian approximation are described. We also show how to use the bit-error probability for a system without error-control coding to determine which modulation method will give the best packet-error probability in a system with error-control coding

A new protocol is presented for routing multimedia traffic in an energy-efficient manner in a frequency-hop, store-and-forward, packet radio network. The FH network employs an adaptive-transmission protocol integrated with a distributed, energy-aware routing protocol, based on least-resistance routing. Adaptive transmission gives rise to alternative paths through the network with different energy requirements. The adaptive routing and transmission protocols are designed to exploit the differences in the energy consumption of different routes and the service requirements of the different types of traffic. Results are provided that show that our energy-efficient routing protocol provides good service to the different types of media while conserving energy.

Wireless communication channels may change greatly from one transmission to the next, due to variations in propagation loss and interference. The use of fixed transmission parameters for such channels results in wasted energy when channel conditions are good. Adaptation of the power, code rate, and symbol rate reduces energy consumption and interference caused to other systems. Such adaptation requires information about the characteristics of the channel, which is more difficult to obtain in a packet radio network (PRN) or other mobile ad hoc network than in a typical cellular communication system. We develop methods for providing partial information about the channel state from three statistics that are derived by different subsystems in the receiving terminals of a direct-sequence spread-spectrum PRN. We present and evaluate a protocol that uses this information to adapt the transmission parameters in response to changes in interference and propagation conditions in the network. The performance of the new adaptive-transmission protocol is compared with a system with fixed transmission parameters and with an adaptive protocol that is furnished with perfect knowledge of the channel state at the completion of each transmission.

An adaptive transmission technique for frequency-hop packet transmission is described and its performance is evaluated for certain channels with unknown or time-varying parameters. The power in the transmitted signal and the rate of the error-control code are adapted in a way that provides energy-efficient communications. The slow-frequency-hop packet transmissions have several bits per hop and several hops per packet. Feedback is limited to a few bits in each acknowledgment packet, and the feedback for our adaptive transmission consists of only the counts of errors and erasures from the previous packet transmission. The performance of the adaptive transmission system is evaluated for channels with unknown but fixed partial-band interference and propagation loss and for certain channels with time-varying partial-band interference and propagation loss.

Alternative decoding methods are described and evaluated for use with a commercial turbo product code chip that is employed for error control on slow-frequency-hop spread spectrum wireless communications. One strategy is based on parallel decoding in two independent decoders, and another employs a single encoder with adaptive scaling of the sift decisions at its input. Performance results for such decoding strategies are compared for packet transmissions over channels with partial-band interference. When coupled with the development and use of side information in the frequency-hop receiver, these decoding strategies greatly enhance the performance of turbo product codes and make them competitive with parallel-concatenated turbo convolutional codes.

Information about the reliabilities; of the received symbols is very beneficial in frequency-hop communication systems. This information, known as side information, can be used to erase unreliable symbols at the input to an errors-and-erasures decoder. For slow-frequency-hop systems it is common that special redundant symbols, referred to as side-information symbols, are included in each dwell interval, and the demodulation of these symbols provides the side information. The corresponding decrease in the number of message symbols that can be sent in each dwell interval makes it desirable to develop alternative methods that do not require side-information symbols. In this paper, one such alternative is proposed, and its performance is evaluated for channels with partial-band interference. It is shown that staggered interleaving of Reed-Solomon code words and iterative errors-and-erasures decoding facilitates the erasure of unreliable symbols without the need for side-information symbols. The performance of this method is compared with the performance of systems that employ standard block interleaving and errors-only decoding or errors-and-erasures decoding with side information obtained from test symbols.

Hermitian codes are an attractive alternative to Reed-Solomon codes for use in frequency-hop spread-spectrum packet radio networks. For a given alphabet size, a Hermitian code has a much longer block length than a Reed-Solomon code. This and other considerations suggest that Hermitian codes may be superior for certain applications. Analytical results are developed for the evaluation of the packet error probability for frequency-hop transmissions using Hermitian coding. We find there are several situations for which Hermitian codes provide much lower packet error probabilities than can be obtained with Reed-Solomon codes. In general, as the code rate decreases or the symbol alphabet size increases, the relative performance of Hermitian codes improves with respect to Reed-Solomon codes. Performance evaluations are presented for an additive white Gaussian noise channel and for certain partial-band interference channels, and the packet error probability is evaluated for both errors-only and errors-and-erasures decoding.

A set of adaptive protocols for mobile wireless frequency-hop spread-spectrum communication networks is described. The primary elements of the protocol suite are the adaptive-transmission protocol, the adaptive-routing protocol, and the adaptive-forwarding protocol. Together, these protocols control the transmission of packets on each link in the network and the routing of packets through the network. Each protocol interacts with the other protocols and with elements of the physical layer in order to obtain information about the energy requirements and interference conditions of the alternative routes. The protocols adapt their responses to the observed changes in these energy requirements and interference conditions. No measurements of the signal-to-noise ratio or the received power are required by the adaptive protocols.

The terminals in a mobile store-and-forward wireless network must be able to react quickly to changes in propagation conditions and interference levels on the links in a network. Routing updates are often very slow in responding to changes in link quality, especially for the links that are not utilized frequently. The adaptive-forwarding protocol can assist the routing protocol by forcing some transmissions on less frequently utilized links, thereby updating the information about the states of these links. We say that alt-forwarding occurs for a given packet if that packet was originally scheduled for transmission on one link but the adaptive-forwarding protocol elects to transmit the packet on a different link. By forcing a packet on an alternative link, we allow the adaptive-transmission protocol to update the transmission parameters for the link, and we cause the adaptive-routing protocol to deliver the packet along a secondary route. The feedback gathered by utilizing an alternative link helps the networking protocols respond to dynamic conditions and discover more energy-efficient routes. We show that by designing the criteria for selecting an alternative link to account for the status of the link and the likelihood that the link leads to an efficient route, there is a significant increase in the energy efficiency of the network.

The performance is compared for slow-frequency-hop and direct-sequence spread-spectrum packet communication systems of similar complexity with doubly selective fading channels characterized by several different multipath delay profiles and Doppler spreads. The delay profiles are chosen to reflect experimental measurements of mobile-radio channels, and the Doppler spreads are chosen to represent the range of carrier frequencies and vehicle speeds encountered in common mobile communication systems.

The performance of an energy-efficient adaptive routing protocol is evaluated for a frequency-hop (FH) store-and-forward wireless network that must operate in the presence of partial-band interference. The routing protocol is based on least-resistance routing with a metric that accounts for link quality and energy consumption. The distributed routing protocol is integrated with the adaptive transmission and channel-access protocols. The performance of this protocol suite is demonstrated for a distributed FH network by use of a network simulation that includes multiple sources of partial-band interference. We find that the combination of energy-efficient routing and adaptive transmission improves the information throughput and energy efficiency of the network.

The receiver processing that is often employed for direct-sequence spread spectrum with quaternary data modulation operates separately on in-phase and quadrature components of the spread-spectrum signal. Previous results on complex quaternary sequences, which are also referred to as four-phase sequences, provide a strong motivation to employ alternative processing methods that permit the receiver to benefit from the correlation properties of these sequences. With this goal in mind we present receiver architectures that use complex processing and are capable of demodulating the signals proposed for the third-generation mobile cellular code-division multiple-access systems. The performance of the proposed receiver architecture with complex processing is shown to be determined by the complex aperiodic correlation functions for the spreading sequences. Comparisons are made with systems in which the quaternary sequences are derived from pairs of common binary spreading sequences and the receiver employs separate in-phase and quadrature processing. We find that in spite of their superior periodic crosscorrelation properties, the previously developed quaternary sequences do not provide significantly smaller error probabilities in multiple-access systems.

The characteristics of mobile wireless communication channels fluctuate for many reasons, including movement of the radios, changes in path attenuation, and variations in interference. Several adaptive signaling techniques have been proposed for use in wideband code-division multiple-access (CDMA) systems including adaptive data rates, adaptive spreading code rates, discontinuous transmission, and multicode CDMA. We introduce adaptive signaling techniques that use nonuniform phase-shift-key (PSK) modulation. These techniques have several advantages for use in CDMA communications, and they support multimedia transmission by simultaneously delivering different types of traffic, each with its own required quality of service. The signaling methods that we propose deliver a basic message at a specified error rate and simultaneously deliver an additional message by exploiting any extra capability that is available. We show that by adapting the location of the points in a PSK constellation, the throughput can be maximized for the additional message while maintaining an acceptable error rate for the basic message. Responses to larger changes in channel quality are accomplished by adapting the PSK constellation size, signaling rate, and error-correcting code. Examples of adaptive signaling schemes that employ nonuniform PSK constellations are presented, including an application to a cellular CDMA system.

A new method is described for routing multimedia traffic in a frequency-hop (FH) store-and-forward packet radio network. The method is illustrated for traffic of two types, each type having its own throughput, delay, and error-rate requirements. A typical application is the routing of voice and data packets in a distributed multiple-hop network. In such an application, voice packets cannot tolerate much delay, but they are allowed to contain a small number of frame erasures while data packets must be delivered error-free even if a moderate delay is required to do so. The fully distributed routing protocol presented in the paper takes into account the type of service required for each type of traffic, and it adapts to the interference as seen by the FH radio receivers in the network. Our approach to multimedia routing is based on least-resistance routing with different link and path resistance metrics for different message types. Each of the resistance metrics for a link reflects the ability of the link to provide the service required by the one of the message types. This includes, but is not limited to, a measure of the likelihood of successful reception by the FH radio receiver for that link. The route selection for a particular type of packet depends on the resistances of the links along the routes from that packet's source to its destination. In general, different routes may be selected for different types of packets. The primary conclusion of this paper is that the quality of service increases for each of the two types of multimedia traffic if the routing protocol accounts for the type of message that is being relayed.

It is a common requirement in a mobile wireless communication network that a radio must be capable of simultaneously transmitting a message to two or more neighbors in the network. Some of the intended recipients may be more capable than others in the sense that their communication links from the transmitter have less interference, fading, or attenuation. Because it is desirable that a multicast or broadcast transmission be received successfully by all radios for which it is intended, the usual approach is to limit the transmission rate to that which can be demodulated by the least capable among these radios. Nonuniform nonbinary phase-shift-key (PSK) signal constellations can be designed to increase the throughput of multicast transmissions by delivering additional information to more-capable receivers along with the multicast message. This additional throughput can be employed to transmit multimedia messages (e.g., voice and data) to the more-capable receivers. In this paper, we determine the error probabilities for coherent demodulation of nonuniform PSK signals and noncoherent demodulation of nonuniform differential PSK signals. Because the PSK constellations have a constant envelope, they are better for use in mobile wireless communication networks than the constellations based on quadrature-amplitude modulation that have been proposed in previous publications.

Broadcast or multicast signaling can be employed in a wireless communication network to transmit a message to multiple neighbors simultaneously. The capabilities of the intended recipients may vary in the sense that the communication links to some neighbors may have less interference or attenuation than the links to others. We have previously proposed the use of nonuniform phase-shift key (PSK) signal constellations to allow a transmitter to deliver a basic message to each of the intended receivers and an additional message to the more-capable receivers. In this paper, convolutional coding and nonuniform PSK modulation are combined to provide greater efficiency and increased flexibility. The primary goal of multicast transmission, which is for each designated neighbor to have an acceptable probability of receiving the multicast message correctly, is achieved in a way that permits inclusion of multimedia messages for the more-capable receivers. Performance results and tradeoffs are presented for hard- and soft-decision decoding of convolutionally encoded coherent M-ary PSK multicast transmissions. Our results show that convolutional coding can be used with nonuniform PSK modulation to transmit additional information in mobile communication systems with little degradation to the basic information.

Because of the variability of the channels in frequency-hop wireless systems and networks, the performance of error-control coding can be improved by adapting the rate of the code to the channel conditions. In this paper, adaptive-rate error-control coding is investigated for slow frequency-hop communications with Reed-Solomon coding. Two methods are investigated that use decoder side information as a means for selecting the code rate. These methods are based on counts of errors and erasures, which are provided by the demodulator and the decoder. The performance of the adaptive-rate coding system is evaluated for channels with Rayleigh fading, partial-band interference, and thermal noise.

Spread-spectrum modulation can provide protection from the selective fading that is typically encountered in mobile radio networks. Because the methods of combating frequency-selective fading are quite different for slow-frequency-hop (SFH) and direct-sequence (DS) spread spectrum systems, these two types of modulation perform very differently. The purpose of this paper is to compare the performance of SFH and DS systems under identical conditions for several models of the wide-band fading channel. Each system has the same bandwidth, transmits over the same frequency-selective Gaussian wide-sense-stationary uncorrelated-scattering channel, and uses error-correction coding to combat thermal noise and fading. The probability of bit error at the output of the decoder is determined for each system by a combination of analysis and simulation. Results are presented for systems with a single transmitter-receiver pair and for networks with multiple simultaneous transmissions (i.e., multiple-access communications). The multiple-access network is distributed, so that control of power by a central terminal, such as a base station, is not possible. The results illustrate the tradeoffs in performance between SFW and DS spread-spectrum systems as a function of the parameters of the signals and the channel model. The performance of the SFH system is shown to be less sensitive to the exact characterization of the channel delay spectrum than the DS system. For most of the channels considered in this paper, SFH spread spectrum gives better performance than DS spread spectrum.

The spectral efficiency is determined for a direct-sequence code-division multiple-access (CDMA) communications system that employs rapid closed-loop power control on a channel with doubly selective fading. The sensitivity of the spectral efficiency to the chip rate of the direct-sequence waveform and the number of taps in the RAKE receiver is considered. The effectiveness of the power-control method is also examined for different power-control delays, delay spectra, and Doppler spreads. The implications of the results for the design of personal communication systems are discussed.

The use of block coding and errors-and-erasures decoding can enhance performance in frequency-hop (FH) communication systems, provided that a good scheme is employed to determine which symbols to erase. The problem of making erasure decisions from collections of receiver outputs is investigated in this paper. Methods to determine which received symbols to erase are derived from Bayesian decision theory. Decision rules are developed for a system with M-ary orthogonal signaling, noncoherent demodulation, and frequency-selective fading. One result is a class of Bayesian schemes in which erasure decisions are made independently from symbol to symbol. Within this class is a rule that uses signal amplitude estimates for improved performance. A second result is a Bayesian technique in which erasure decisions are mutually dependent and are made collectively for each codeword. These techniques are analyzed and compared with the performance of receivers that use erasure techniques that require multiple applications of bounded distance decoding. The performance of the Bayesian techniques for dependent erasures are also compared with the performance of receivers that do not permit erasures. It is found that each of the Bayesian techniques offers substantial performance gains over errors-only decoding, and the dependent erasure scheme provides the best performance among the techniques of lower complexity.

Concatenated coding techniques are applied to slow frequency-hop packet radio communications for channels with partial-band interference. Binary orthogonal signaling (e.g., binary FSK) is employed with noncoherent demodulation, Reed-Solomon codes are employed for the outer code while both block and convolutional codes are considered for the inner code. Hard-decision and soft decision decoding methods are considered for the inner codes. A method is devised for estimating the reliability of the outer Reed-Solomon code symbols, and this estimate is used to determine which code symbols should be erased. Comparisons are made between the performance of concatenated codes and the performance of Reed-Solomon codes alone.

Error probabilities are evaluated for direct-sequence spread-spectrum communications and Rake reception over channels with doubly selective fading. The error probability for such a system depends on the spreading sequence, the autocorrelation function of the fading process, the received signal-to-noise ratio, and the number of taps in the Rake receiver. The focus of the paper is on the effect of the spreading sequence on the performance of each of two systems. One system employs noncoherent detection of differentially-encoded binary direct-sequence spread-spectrum signals and a post-detection diversity-combining Rake receiver which uses equal-gain combining. The other system employs coherent detection of binary direct-sequence spread-spectrum signals and a post-detection diversity-combining Rake receiver with perfect gain estimates for the channel. A simple sequence selection criterion is introduced, and the sensitivity of the performance of the system to the choice of the spreading sequence is examined. It is shown that significant performance differences result from different choices of the spreading sequence. It is also shown that, given a moderate range of delay spreads, sequences can be found that yield low bit error probabilities over that range. These are found to be robust with respect to the delay spectrum for the channel, the number of taps in the Rake receiver, the Doppler spread, and the signal-to-noise ratio.

The use of side information can provide increased coding gains in frequency-hop multiple-access communication systems. The internal generation of this side information by the receiver is investigated in the paper. Methods to determine which received signals to erase prior to decoding are derived from Bayesian decision theory. The performance of synchronous and asynchronous frequency-hop systems with Reed-Solomon coding is analyzed for channels with Rayleigh fading, multiple-access interference, and wideband Gaussian noise. The performance of the Bayesian technique is compared with that of receivers that make erasure decisions using the Viterbi ratio-threshold test. The Bayesian method is found to provide better performance.>

Acquisition of synchronism is considered for DS/SS CDMA systems. For large systems with large timing uncertainties, it has been shown previously that acquisition in the presence of multiple-access interference may impose a significant limitation on capacity. This leads the authors to consider a system in which timing uncertainties are relatively small and to propose an acquisition scheme which exploits this to reduce complexity and acquisition overhead. The proposal may be appropriate for a microcellular environment for personal communications in which CDMA packet transmission is employed for both voice and data. Packetized transmission would imply that the overhead available for acquisition is small, and the large number of microcells would restrict the cost of the acquisition scheme used in the receiver in each microcell. The acquisition time required for a simple serial search scheme may therefore be unacceptably large. On the other hand, while acquisition using a passive matched filter is fast, the filter length required for reliable acquisition is liable to be excessive in terms of cost and complexity. Motivated by these considerations, the authors propose a two-stage acquisition scheme which employs a short programmable matched filter for initial detection, followed by a correlator for verification. Numerical results based on an approximate analysis of acquisition performance in the presence of multiple access interference are employed to compare the scheme with conventional acquisition schemes.>

Error probabilities are evaluated for direct-sequence spread-spectrum communications and Rake reception over channels with doubly selective fading. The error probability for such a system depends on the spreading sequence, the autocorrelation function of the fading process, the received signal-to-noise ratio, and the number of taps in the Rake receiver. The focus of the paper is on the effect of the spreading sequence on the performance of each of two systems. One system employs noncoherent detection of differentially-encoded binary direct-sequence spread-spectrum signals and a post-detection diversity-combining Rake receiver which uses equal-gain combining. The other system employs coherent detection of binary direct-sequence spread-spectrum signals and a post-detection diversity-combining Rake receiver with perfect gain estimates for the channel. A simple sequence selection criterion is introduced, and the sensitivity of the performance of the system to the choice of the spreading sequence is examined. It is shown that significant performance differences result from different choices of the spreading sequence. It is also shown that, given a moderate range of delay spreads, sequences can be found that yield low bit error probabilities over that range. These are found to be robust with respect to the delay spectrum for the channel, the number of taps in the Rake receiver, the Doppler spread, and the signal-to-noise ratio.

A correction is presented in this note for an error which appears in the subject paper by M.B. Pursley and S.D. Sandberg [ibid., vol. 37, pp. 1105-1 112, Nov. 1989]. In addition, attached as an addendum is a proof that a modified version of an algorithm presented in the subject paper produces an optimal packet con6guration for variable-rate coding in meteor-burst communications. The proof of optimality for the original algorithm is quite tedious, and was not included in the subject paper.

The bit error probability for a direct-sequence code division multiple access (CDMA) system is determined as a function of the chip rate for communications over doubly selective fading channels. The effect the chip rate has on the performance of a CDMA system is considered for both a correlation receiver and a rake receiver. Several selective fading channels are employed as examples to illustrate that the choice of the best chip rate depends upon the characteristics of the channel and the number of taps in the rake receiver. The tradeoff between the number of taps and the bit error probability is investigated for different chip rates. Additionally, the effects of the Doppler spread on the performance of the system and the choice of chip rate are considered. The purpose of this paper is to examine some of the fundamental issues that influence performance of CDMA systems when employed for mobile cellular telephony and personal communication systems on channels with doubly selective fading.>

Reliable data distribution within spread-spectrum packet radio networks requires high performance from the network protocols. This paper describes research in forwarding and routing protocols that are designed specifically for slow-frequency hop (SFH) packet radio networks in which some of the radios are subjected to excessive interference. It is shown that information extracted from the decoder can be used to aid the network protocols. New metrics are introduced that use this information to give a quantitative assessment of the interference environment experienced by the receiver in an SFH radio. Forwarding protocols are developed that can react quickly to local sources of interference, and the metrics that are introduced permit the routing algorithm to react to changes in the interference conditions in the network.>

We consider binary orthogonal signaling over a nonselective Rician-fading channel with additive white Gaussian noise. The received signal over such a channel may have both a specular component and a scatter (Rayleigh-faded) component. If there is only a scatter component, the noncoherent receiver is optimal. If there is only a specular component, the optimal receiver is the coherent receiver. In general, the optimal receiver for a Rician channel depends on the strengths of the two signal components and the noise density, and the set of possible optimal receivers is infinite. We consider a system in which the noncoherent receiver and the coherent receiver are employed in a parallel configuration for a symbol-by-symbol demodulation of the received signal. Each sequence of transmitted symbols produces a sequence at the output of each of the parallel receivers. The task of identifying which of these received sequences is a more reliable reproduction of the transmitted sequence is the data verification problem. In this paper, we show that data verification can be accomplished by combining side information from the demodulators with a suitable error-control coding scheme. The resulting system is a universal receiver that provides good performance over the entire range of channel parameters. In particular, the universal receiver performs better than the traditional noncoherent receiver.>

The purpose of this paper is to illustrate the issues involved in designing the demodulator portion of a universal receiver for unknown or time-varying channels by means of a specific example. We consider the class of nonselective Rician fading channels with additive white Gaussian noise. The optimal receiver for a Rician channel depends on the parameters of the channel, and the collection of optimal receivers for channels in the class of interest forms an infinite receiver class. We find a finite number of receivers in this receiver class with the property that, regardless of the parameters of the channel in effect, at least one of these receivers provides a symbol error probability that is within a specified deviation from the optimal symbol error probability for the channel. These receivers are then used in parallel to perform a symbol-by-symbol demodulation of the received signal. The receiver output that gives the most reliable reproduction of the transmitted sequence is identified by means of a data verification mechanism. The resulting system is a universal receiver. Methods for data verification are developed in other papers. In this paper, we develop an algorithm for finding the required finite set of receivers. Typical issues, such as the tradeoff between the number of parallel receivers and the allowed deviation from optimality, are discussed.>

Error probabilities are evaluated for direct-sequence spread-spectrum communications over channels with doubly selective fading. The error probability for such a system depends on the spreading sequence, the autocorrelation function of the fading process, and the receiver signal-to-noise ratio. The focus of this paper is on the effect of the spreading sequence on the performance of differentially coherent detection of binary direct-sequence spread-spectrum signals using a correlator receiver. It is shown that significant performance differences result from different choices of spreading sequence. It is also shown that, given a moderate range of delay and Doppler spreads, sequences can be found which yield low bit error probabilities over the entire range. These are found to be robust with respect to a variety of shapes for the channel autocorrelation function and the full range of signal-to-noise ratios.>

Adaptive protocols that specify the ways in which a radio is permitted to modify its normal forwarding procedures based on information obtained locally in the network are considered. A computer program has been developed to simulate a frequency-hop (FH) packet radio network with partial-band jamming and interference due to other FH and narrowband radios. The radios in the network use time-slotted, receiver-directed, FH spread-spectrum signaling. Results on throughput, delay, and end-to-end probability of success are presented, and comparisons between different forwarding protocols are given for a static network topology with both static and mobile network jamming.>

Research in adaptive, decentralized routing for frequency-hop packet radio networks with mobile partial-band jamming. A routing technique called least-resistance routing (LRR) is developed, and various versions of this routing method are examined. LRR uses a quantitative assessment of the interference environment experienced by a radio's receiver to determine a resistance value for that radio. Two components for the interference environment are considered: transmissions from other radios and partial-band jamming. The resistances for each of the radios in a particular path are combined to form the path resistance, and packets are forwarded on the path with the smallest resistance. Comparisons are made between different versions of LRR and between LRR and previously developed adaptive routing techniques. It is found that LRR is an effective way for dealing with mobile jamming in a frequency-hop packet radio network. Significant increases in throughput and end-to-end probability of success are obtained with LRR.>

The effect of multiple-access interference on the acquisition of direct-sequence spread-spectrum (DS/SS) signals is studied. A passive matched filter approach is used, and the acquisition window length, which is the length of the matched filter, determines the complexity of the acquisition scheme. The acquisition-based capacity of a DS/SS system is defined to be the maximum number of simultaneous transmissions permissible while maintaining acceptable acquisition performance. The performance of the acquisition scheme is evaluated for large acquisition window length, and the asymptotic analysis yields the capacity as a function of the acquisition window length. If this length is linearly related to the processed gain, the acquisition-based capacity is smaller than that obtained by consideration of post-acquisition criteria only (e.g., bit-error probability for the demodulated signal). The results indicate the relative importance of the acquisition problem and suggest directions for further research.>

The erasure of unreliable symbols improves the performance of most types of error-control coding if a good method is used to decide which symbols should be erased. Bayesian decision theory is employed to obtain such a method for use in frequency-hop communications with Reed-Solomon coding and errors-and-erasures decoding. The performance of frequency-hop communications with Bayesian erasure insertion is analyzed for channels with both partial-band and wideband Gaussian noise. The Bayesian technique is compared with Viterbi's ratio-threshold test, and these are compared to receivers that do not erase and use errors-only decoding. Comparisons are also made with receivers that erase all the symbols that are affected by the partial-band interference. When interference is strong, large coding gains result from the Bayesian method, and error probabilities are reduced by several orders of magnitude.>

The authors introduce a form of automatic repeat request (ARQ), referred to as variable-rate type-I hybrid ARQ, in which the code rate varies in response to the fluctuations in the power received from a meteor trail. For one implementation, the source or the destination periodically obtains estimates of the signal power at the destination, and the source uses these estimates to select the rate of the code. For an alternative approach, the code rate is determined completely by the decoding successes and failures during previous transmissions. The performance measure is the throughput per trail, which is defined as the expected number of information bits received correctly for a given meteor trail. Numerical results for Reed-Solomon codes are included to illustrate the relative performance of the various schemes. It is shown that the throughput is larger for both implementations of variable-rate type-I hybrid ARQ than for fixed-rate type-I hybrid ARQ and ARQ without forward error correction.>

The performance of type-II hybrid automatic repeat request (ARQ) is compared to that of fixed-rate type-I hybrid ARQ for meteor-burst communications. Maximum throughput is obtained for meteor-burst communications by using a transmission scheme for which the information rate of the code, varies in response to the fluctuations in the power received from a meteor trail. For type-II hybrid ARQ, a variation in the code rate is inherent in the coding scheme. On the first transmission that is made for a data block, a code of relatively high rate is used, but if an additional transmission is required, only redundant symbols are sent, and this reduces the overall rate of the code. The performance measure is the throughput per trail, which is defined as the expected number of successfully received information bits for a given meteor trail. The authors also develop an approximation for the average value of the throughput, averaged over the parameters of the meteor trail. Numerical results for Reed-Solomon codes are included to illustrate the relative performance of the various schemes. It is shown that the throughput is larger for type-II hybrid ARQ than for either fixed-rate type-I hybrid ARQ or ARQ without forward-error-correction.>

The problem of communication over a channel with unknown characteristics is addressed. The true channel is from a known set of channels, but the transmitter and receiver do not know which of these channels is actually in effect. The goal of a universal receiver is to provide nearly optimal demodulation regardless of the channel that is actually in effect. A parallel receiver implementation is proposed for a universal scheme to cope with such uncertainty. The parallel system consists of a finite number of receivers with the property that, for each channel in the set, the performance of at least one of the receivers will be within a specified performance range. Data verification is accomplished by an appropriate coding system. Sufficient conditions for the existence of such a universal receiver for a prescribed set of channels are established, procedures are outlined for the receiver design, and an example is given to illustrate the applicability of the theory. For M-ary signaling it is shown that, from an information-theoretic viewpoint, the data verification can be achieved at no extra cost by use of the intrinsic side information that is provided by an appropriate coding scheme that also provides error correction.>

A novel acceptance criterion that is less stringent than previous criteria is developed. The criterion accepts the codeword that is closest to the received vector for many cases where previous criteria fail to accept any codeword. As a result, the performance of generalized minimum distance (GMD) decoding is better if the new criterion is used. For M-ary signaling, the weights used in GMD decoding are generalized to permit each of the possible M symbol values to have a different weight.>

The statistical dependence of hits due to multiple-access interference in an asynchronous slow-frequency-hop packet radio network in which the radios employ memoryless hopping patterns is described. Models in which hits are conditionally independent given the number of interfering packets are investigated. It is shown that if the conditional probability of a hit is chosen appropriately, the distribution function for the number of hits in a packet for these models can be used to compute upper and lower bounds on the true distribution function for the number of hits. Conditions are described for which these models can be used to compute upper and lower bounds on the codeword and packet error probabilities. It is shown that if the ratio of the number of interfering packets to the number of frequency slots is held constant, hits in the asynchronous frequency-hop network are asymptotically independent in the limit as the number of frequency slots increases. This result suggests that when the number of frequency slots is large, error probabilities can be closely approximated by using the distribution for the number of hits that results from assuming that hits are independent.>

The multiple-access capability of asynchronous frequency-hop packet-radio networks is analyzed. The only interference considered is multiple-access interference, and perfect side information is assumed. Bounds on the probability of error for unslotted systems are developed based on the distributions of the maximum and minimum interference levels over the duration of a given packet, and these are employed to develop corresponding bounds on the throughput. The idealized model makes possible the derivation of asymptotic results showing the convergence of these bounds for high traffic levels. The asymptotic performance of the system is seen to be the same as that of the corresponding slotted system. Results for the maximum asymptotic throughput are also obtained. These results show that the asymptotic sum capacity of the channel can be attained using Reed-Solomon coding. All these results are valid for either fixed or exponentially distributed packet lengths. The results indicate that the performance of frequency-hop networks is insensitive both to the distribution of packet lengths and to whether or not transmissions are slotted. It also demonstrates the efficacy of Reed-Solomon coding in combating multiple-access interference.>

The authors demonstrate that contrary to the claim made in the above named work (ibid., vol.36, Jun., p.720-3, 1988), the sequence of hits in an asynchronous frequency hop multiple-access system is not a Markov process. Comments of the use of a model in which the hits are independent are also given.>

The performance of binary frequency-shift-keyed communications over frequency-selective wide-sense-stationary uncorrelated-scattering Rayleigh fading channels is discussed. Previous analyses of FSK communications over frequency-selective channels have considered the average probability of error for specific models for the fading channel and typically assume that the two FSK signals are orthogonal. A technique for obtaining bounds on the average error probability for FSK in terms of one or two parameters obtainable from multipath spread or frequency correlation functions channel measurements is described.>

For pt.I see ibid., vol.COM-3, no.12, p.1320 (1987). Ratio-statistic combining is proposed for mitigating partial-band interference in systems with diversity transmission and frequency-hop signaling. Systems with noncoherent demodulation and binary orthogonal signaling are covered. The partial-band interference is Gaussian, and Gaussian quiescent noise is included in the analysis to account for wideband noise sources. The exact probability of error is found for a receiver using ratio-statistic combining, and this is compared to the exact error probabilities for receivers with optimum combining with perfect side information, clipped-linear combining, the ratio-threshold test with majority-logic decoding, and self-normalization diversity combining. Numerical results are also given for a frequency-hop system which uses ratio-statistic combining for channels with Rayleigh fading and partial-band interference. It is determined that ratio-statistic combining is an excellent diversity combining scheme for systems with partial-band interference and fading.>

The performance of variable-rate Reed-Solomon error-control coding for meteor-burst communications is considered. The code rate is allowed to vary from codeword to codeword within each packet, and the optimum number of codewords per packet and optimum rates for the codewords are determined as a function of the length of the message and the decay rate for the meteor trail. The resulting performance is compared to that obtained from, fixed-rate coding. Of central importance is the derivation of tractable expressions for the probability of correct decoding for bounded-distance decoding on a memoryless channel with a time-varying symbol error probability. A throughout measure is developed that is based on the probability distribution of the initial signal-to-noise ratio.>

The results of a simulation of a fully connect packet communication network are presented. The network employs the slotted ALOHA channel access protocol, and Reed-Solomon coding is used to correct errors and erasures in the received packets. The network has a fixed number of channels available for packet transmissions. In two of the transmission schemes considered, a given packet transmission occurs on a single channel only. One of these employs fixed assignment of terminals to the channels, and the other employs random assignment. A third method permits each transmitter to hop randomly over the set of channels during the transmission of a packet. The terminal transmits on one channel at a time, and it transmits a fixed number of symbols during each dwell interval. Delay and throughput are evaluated for all three transmission methods. The effects of code rate on the performance of the channel-hopping scheme are explored, and the improvement that can be obtained for the channel-hopping scheme by use of incremental-redundancy transmission is examined.>

The performance of binary differential phase-shift keyed (DPSK) communications over frequency-selective wide-sense-stationary uncorrelated-scattering fading channels is considered. A technique is described for obtaining bounds on the average error probability for DPSK in terms of one or two parameters obtained from multipath spread or frequency-correlation-function channel measurements. A method of approximating the performance of systems using various data-pulse shapes and systems where it is difficult to obtain a complete channel characterization is developed. Numerical examples and comparisons of the most interesting cases are given.>

Diversity combining techniques that employ a ratiothreshold test (RTT) are suggested for communications with fading and partial-band interference. We consider a system with binary orthogonal signaling and noncoherent demodulation. The fading channel is modeled as a group of independent narrow-band channels, each with nonselective Rician fading. We assume that the partial-band interference is Gaussian, and we include additive white Gaussian quiescent noise in the analysis to account for wide-band noise sources. The performance measures we use to evaluate the diversity combining schemes are the narrow-band interference rejection capability and the signal-to-noise ratio requirement over the entire range of partial-band interference duty factors. The performances of the RTT with square-law combining and the RTT with majority logic decoding are compared to each other and to the performance of the optimum diversity combining technique.

This paper is devoted to an examination of the key features of spread-spectrum signaling in packet radio networks. The multiple-access capability, capture, and anti-multipath capability of spread spectrum are the principal topics, and the basic features of spread spectrum that enable it to provide these capabilities are illustrated. The interaction between the spread-spectrum signaling and the network protocols is discussed. Methods for performance evaluation are reviewed, and analytical results on the multiple-access capability of spread spectrum are presented.

Clipped-linear diversity combining is analyzed for receivers without side information. Communication systems with noncoherent demodulation, binary andM-ary orthogonal signaling, and diversity transmission are considered. The main source of interference is additive Gaussian partial-band interference, but a nonzero quiescent noise level is also included in the analysis to account for wide-band noise sources. Some of the results apply to general (non-Gaussian) interference. The numerical results demonstrate that clipped-linear combining can perform well in terms of both narrow-band interference rejection capability and maximum signal-to-interference ratio requirement. A practical disadvantage of clipped-linear combining is that it relies on measurements of the signal output voltage.

Binary direct-sequence spread-spectrum multiple-access communications, an additive white Gaussian noise channel, and a coherent correlation receiver are considered. An expression for the output of the receiver is obtained for the case of random signature sequences, and the corresponding characteristic function is determined. The expression is used to study the density function of the multiple-access interference and to determine arbitrarily tight upper and lower bounds on the average probability of error. The bounds, which are obtained without making a Gaussian approximation, are compared to results obtained using a Gaussian approximation. The effects of transmitter power, the length of the signature sequences, and the number of interfering transmitters are illustrated. Each transmitter is assumed to have the same power, although the general approach can accommodate the case of transmitters with unequal powers.

The analysis of a multipath-combining receiver for directsequence spread-spectrum communications through a specular multipath channel is developed. The analysis applies to systems that use quadriphase-shift-keyed, offset quadriphase-shift-keyed, minimum-shiftkeyed, or binary phase-shift-keyed modulation. The measures of performance are the signal-to-noise ratio and approximations to the error probability involving the signal-to-noise ratio. The performance of a multipath-combining receiver is determined not only for the case of a single transmitter, but also for the case of multiple interfering transmit, ters. Furthermore, the performance of the system is determined in terms of parameters of the signature sequences. These parameters can be used as guides in selecting signature sequences for the system. Results are also given for the case of randomly generated signature sequences.

The use of convolutional coding in packet radio systems introduces problems in evaluating performance, since the errors out of the decoder are not independent. A new bound on the packet error probability out of a Viterbi decoder may be used to evaluate these systems. We present results on the packet error probability for frequencyhop and direct-sequence spread-spectrum systems. In addition, we show that the assumption of independent errors out of the decoder gives an upper bound that is not as tight as our new bound. Comparisons are made with frequency-hop systems using Reed-Solomon codes.

The performance of noncoherent reception in direct-sequence spread-spectrum communications over specular multipath fading channels is investigated. Analytical and numerical results on the average probability of error are presented for direct-sequence spread-spectrum systems employing binary orM-ary frequency-shift-keying modulation with noncoherent demodulation and differential phase-shift-keying modulation with differentially coherent demodulation.

The performance of frequency-hop transmission in a packet communication network is analyzed. Satellite multiple-access broadcast channels for packet switching and terrestrial packet radio networks are the primary examples of the type of network considered. An analysis of the effects of multiple-access interference in frequency-hop radio networks is presented. New measures of "local" performance are defined and evaluated for networks of this type, and new concepts that are important in the design of these networks are introduced. In particular, error probabilities and local throughput are evaluated for a frequency-hop radio network which incorporates the standard slotted and unslotted ALOHA channel-access protocols, asynchronous frequency hopping, and Reed-Solomon error-control coding. The performance of frequency-hop multiple access with error-control coding is compared with the performance of conventional ALOHA random access using narrow-band radios.

The performance of coherent direct-sequence spread-spectrum communications over specular multipath fading channels is investigated. The average probability of error of the correlation receiver is derived for an arbitrary number of paths with deterministic or random gain coefficients. The gain coefficients, delays, and phase angles of any two distinct paths are modeled as mutually independent random variables. Numerical results for several values of the system and channel parameters are presented.

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.

Nearly all previous analytical results on the performance of direct-sequence spread-spectrum multiple-access (DS/SSMA) communication systems are restricted to systems in which the periodpof the signature sequence is equal to the numberNof chips per data symbol. In many applications, however, it is necessary to employ signature sequences whose periodpis much larger thanN. Thus, successiveN-chip segments of the signature sequence are used to phase-code the carrier during the transmission of successive data symbols. The performance of such systems depends on the partial correlation properties of the signature sequences (rather than the aperiodic correlation properties as in the case whenN=p). In this paper, we consider the performance of a DS/SSMA system for arbitrary values ofpandN. As special cases of our results, we delermine the effects of partial correlation in three classes of systems: those for whichN =p, those for whichNandpare relatively prime, and those for whichNis a divisor ofp. We also provide two methods for the design of sequences for systems for whichNis a divisor ofp.

Approximations are obtained for the average probability of error in an asynchronous direct-sequence spread-spectrum multiple-access communications system. Both binary and quaternary systems are considered, and the chip waveforms are allowed to be arbitrary time-limited waveforms with time duration equal to the inverse chip rate. The approximation is based on the integration of the characteristic function of the multiple-access interference. The amount of computation required to evaluate this approximation grows only linearly with the product of the number of simultaneous transmitters and the number of chips per bit. The accuracy of the approximation is extremely good in most cases, but it can be improved, if necessary, by an application of a series expansion. Numerical results are presented for specific chip waveforms and signature sequences.

Bounds and approximations are obtained for the average probability of error in an asynchronous slow-frequency-hopped spread-spectrum multiple-access communications system with non-coherent binary frequency-shift-keyed (FSK) data transmission. Both nonselective fading and wide-sense-stationary uncorrelated-scattering fading are considered.

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.

New analytical results are obtained on the performance of quadriphase spread-spectrum multiple-access communications. The primary performance parameter considered is the signal-to-noise ratio at the receiver output. This parameter includes the effects of multiple-access interference and channel noise, and it has been shown to give a reliable estimate of the average probability of error.

Although the existence of universal noiseless variable-rate codes for the class of discrete stationary ergodic sources has previously been established, very few practical universal encoding methods are available. Efficient implementable universal source coding techniques are discussed in this paper. Results are presented on source codes for which a small value of the maximum redundancy is achieved with a relatively short block length. A constructive proof of the existence of universal noiseless codes for discrete stationary sources is first presented. The proof is shown to provide a method for obtaining efficient universal noiseless variable-rate codes for various classes of sources. For memoryless sources, upper and lower bounds are obtained for the minimax redundancy as a function of the block length of the code. Several techniques for constructing universal noiseless source codes for memoryless sources are presented and their redundancies are compared with the bounds. Consideration is given to possible applications to data compression for certain nonstationary sources.

This paper is concerned with the performance of biphase direct-sequence spread-spectrum multiple-access communication for a general class of fading channels. The channels considered are those for which the channel output consists of a strong stable specular signal plus a faded version of this signal. Such channels, which are referred to as Rician fading (or Rice fading) or specular-plus-Rayleigh fading, are the result of a transmission medium which gives rise to a major stable communication path and a number of additional weaker communication paths. The fading channel is modeled as a general wide-sense-stationary uncorrelatedscattering (WSSUS) channel-a model which is general enough to exhibit both time and frequency selectivity and to impose no restrictions on the fading rate. For the general WSSUS model, results are obtained on the average signal-to-noise ratio at the receiver output in terms of the spread-spectrum signature sequences and the covariance function for the fading process. These results are then specialized to each of two important classes of WSSUS channels: time-selective fading channels and frequency-selective fading channels. Numerical evaluations are presented for specific examples of each of these two types of channels. Analytical expressions are derived for a spread-spectrum multiple-access system with random signature sequences, and the use of these expressions in preliminary system design is discussed.

Correlation parameters that are important for spreadspectrum communications applications are evaluated. The optimal phases (with respect to autocorrelation) are obtained for certain binary shiftregister sequences, including all maximal-length sequences of periods 31, 63, 127, and 255. Selected Gold sequences of period 127 and Kasami sequences of period 255 are also considered. Examples are given to illustrate the use of these data in the selection of signature sequences for spread-spectrum multiple-access communications systems.

Tbe problem of transmission of separate messages to each of two receivers over a general binary-input broadcast channel is investigated. A new approach to a class of information-theoretic problems is developed and applied to obtain bounds on the cardinalities of auxiliary random variables. These bounds permit the calculation of two different regions of achievable rate pairs which are derived from the Cover-van der Meulen region{\cal R}of achievable rate triples. Numerical evaluation of these regions of rate pairs for two examples demonstrates that the region{\cal R}can be enlarged. This enlargement is accomplished by making{\cal R}internally consistent, as the true capacity region must be. The results display complex interactions between common and separate information in broadcast problems.

Variable-rate universal source codes are data compression schemes that are optimum for the coding of a collection of sources (e.g., a source with unknown parameters) subject to a fixed average distortion constraint. Existence of variable-rate universal source codes is demonstrated for very general classes of sources and distortion measures.

An analysis of an asynchronous phase-coded spread-spectrum multiple-access communication system is presented. The results of this analysis reveal which code parameters have the greatest impact on communication performance and provide analytical tools for use in preliminary system design. Emphasis is placed on average performance rather than worst-case performance and on code parameters which can be computed easily.

An analysis of the code sequence parameters that are most important to the communication performance of an asynchronous phase-coded spread-spectrum multiple-access communication system is presented. Previously known bounds and computational techniques for such parameters are surveyed. Some new results on mean-square correlation are included.

Discrete-time source coding theorems are established for more general reproduction alphabets than allowed in previous results on coding for a class of sources subject to a fidelity constraint. The two different alphabets considered are metric spaces for which every closed bounded subset is compact and separable Hilbert spaces. Potential applications of the Hilbert space results to continuous-time source coding are discussed.

The selection of sets of periodic sequences with good correlation parameters is an important problem in many areas of communication theory. Although algorithms have been proposed for selecting sets of sequences, the amount of computation required is often prohibitive. Several autocorrelation and cross-correlation parameters are investigated such as those which characterize the performance of asynchronous phase-coded spread-spectrum multiple-access communication systems. New analytical results are provided which permit significant reduction in the amount of computation needed to evaluate these correlation parameters.

This paper is concerned with two problems in the theory of source coding subject to a maximum average distortion constraint. The first problem involves the coding of a nonergodic discrete time source and the second involves coding for a class of ergodic discrete time sources. Coding theorems are given for both of these situations for very general source alphabets. The codes that are obtained here will, in general, be variable length codes so that average code rate and average distortion are the measures of performance.

In this paper we provide an alternate method of proving the existence theorem for the coding of discrete stationary ergodic sources subject to a fidelity constraint. This method differs from previously published proofs for sources with memory in that a random coding argument is obtained directly for the coding of sourcen-tuples. The main advantage of the technique employed in this paper is that it can easily be extended to yield the basis for the proof of the coding theorem for more general sources (e.g., nonergodic) and for sources with unknown parameters.