The synchronization of clocks at physically separated network nodes requires timed signal exchanges between the nodes. Ultra-wideband (UWB) impulse signals potentially provide the means for doing this very accurately, but unlike narrowband signals, pulse signals are more naturally suited to time-division multiple-access (TDMA) schemes. In this work, we describe TDMA time-transfer schemes that estimate the mappings from a master node's clock time into slaves' clock times based on specific wireless measurements. We propose an optimal approach to distribution of UWB transmissions between those that perform alignment of nodes' clock rates and those that determine clock offsets. Analytical equations for the timing error variances are derived and our results suggest a possible lower bound for time-transfer error using UWB impulse signals.

To establish a secure communications link between any two transceivers, the communicating parties require some shared secret, or key, with which to encrypt the message so that it cannot be understood by an enemy observer. Using the theory of reciprocity for antennas and electromagnetic propagation, a key distribution method is proposed that uses the ultrawideband (UWB) channel pulse response between two transceivers as a source of common randomness that is not available to enemy observers in other locations. The maximum size of a key that can be shared in this way is characterized by the mutual information between the observations of two radios, and an approximation and upper bound on mutual information is found for a general multipath channel and examples given for UWB channel models. The exchange of some information between the parties is necessary to achieve these bounds, and various information-sharing strategies are considered and their performance is simulated. A qualitative assessment of the vulnerability of such a secret sharing system to attack from a radio in a nearby location is also given.

The optimality of the cross-correlation receiver for ultra-wideband (UWB) transmitted-reference (TR) systems is first justified as the optimal linear combiner with a noisy reference. In light of the observation that combining all the available paths with a noisy reference may lead to inferior performance to that of combining just some of them, a weighted cross-correlation receiver is proposed based on the output detection signal-to-noise ratio (SNR) maximization. The similarity between this weighted cross-correlation receiver and that suggested by the average likelihood ratio test (Chao et al. (2004)) is also addressed.

This work derives the average likelihood ratio test (ALRT) receiver for ultra-wideband transmitted reference systems in multipath environments with Rayleigh path strength models. A theoretical weighting function is obtained by approximating the ALRT receiver structure, and can be applied to correlation receivers. Compared to a simple correlation receiver, results show that theoretical weighted correlation receivers are more robust to different environments, and can reduce bit error probabilities even for IEEE 802.15.3a ultra-wideband channel models with lognormal path strength models.

An important set of applications for ultra-wideband radio involves high data rate communication in indoor, and thus highly cluttered, multipath environments. Hence the statistical model of the multipath channel is an important factor in the evaluation of radio designs. The model should be realistic enough to provide accurate performance estimates, while also simple enough to facilitate rapid simulation and tractable analysis. In this paper we present two simplifications to the standard multipath model and show that both closely reproduce the performance of the standard model for a variety of radio configurations, thus providing lower complexity alternatives for radio simulation or analysis. The characteristics of each model are then compared to gain some insight into the impact of different channel metrics on radio performance.

The multiple access (MA) performance of an ultra-wideband differential transmitted reference (UWB DTR) system and an ultra-wideband transmitted reference (UWB TR) system in multipath environments is investigated through analysis. The Gaussian assumption of the multiple access interference is verified by simulation and used in the analysis. Numerical examples are also given in this paper according to the analytical results and the channel models proposed by IEEE P802.15 working group. Results show that the MA performance of these two systems depends on the multipath situation, and the MA capacity of an UWB DTR system is twice that of an UWB TR system. A transmission strategy for these two systems is also proposed to improve the MA performance.

The optimal receiver for an ultra-wideband transmitted reference (UWB TR) system in a single user multipath environment is derived, based on knowledge of channel properties. The performances of this optimal receiver and other crosscorrelation receivers are analyzed and compared. The usual crosscorrelation receiver which is often used in UWB TR systems is shown to be suboptimal. In addition, an UWB differential transmitted reference (UWB DTR) system is also proposed and its performance is evaluated.

This paper explores a correlation timing detector for tracking of Ultra-Wide-Band (UWB) monocycle signals. We seek to examine the optimal relationship between the received and reference UWB monocycle waveforms considering timing jitter and the ability to acquire lock. We modeled the received UWB monocycle waveform as the n/sup th/ order derivative of the Gaussian function. We are able to obtain a good fit using the UWB model with n=4 to both UWB impulses measured in an anechoic chamber and UWB impulses obtained in an indoor office environment. The UWB monocycle model, though an idealized representation, allows us to derive a closed form expression for the slope of the characteristic function of the TLL when both the received and reference monocycle are of arbitrary and different orders n and m. Using this compact formula, we can analyze the timing jitter of the error-tracking TLL in an additive white Gaussian noise (AWGN) channel. Computer simulation is also used to examine the dynamics of the tracking process when the loop is second order. Notably the phase plane plot is examined that gives us an indication of the ability of the TLL to acquire lock. The analysis allows us to make informed choices of the order of the monocycle waveform considering trades-off between timing error variance due to AWGN in the channel and the ability of the TLL to acquire lock. We conclude this paper by discussing a possible automatic gain control (AGC) scheme, whose main purpose is to remove the dependence of the TLL on variations in input signal amplitude.

This paper investigates three different performance metrics for three candidate combinations of multiple access and modulation schemes in ultra wideband radio. The schemes are compared for a single user, multipath channel at a fixed data rate. First, semianalytic expressions are developed for the probability of error with arbitrary multiple-access coding and amplitude or pulse position modulation, which are then reduced for the special cases of time hopped with bit flipping modulation, time hopped with pulse-position modulation and direct sequence with bit flipping modulation. Using Monte-Carlo simulation the bit error rate, probability of outage and probability of best performance are found. The results show that the bit flipped schemes have a consistently lower average bit error rate and outage probabilities and the direct sequence, bit flipped, scheme has highest probability of outperforming both other schemes. In addition, the effect of multipath arrival clustering in channel models was examined and it was found that the same performance curves could be generated with nonclustered arrivals, and hence channel models with nonclustered arrivals can safely be used in performance prediction.

A time-of-arrival (ToA)-based ranging scheme using an ultra-wideband (UWB) radio link is proposed. This ranging scheme implements a search algorithm for the detection of a direct path signal in the presence of dense multipath, utilizing generalized maximum-likelihood (GML) estimation. Models for critical parameters in the algorithm are based on statistical analysis of propagation data and the algorithm is tested on another independent set of propagation measurements. The proposed UWB ranging system uses a correlator and a parallel sampler with a high-speed measurement capability in each transceiver to accomplish two-way ranging between them in the absence of a common clock.

An ultra-wide bandwidth (UWB) signal propagation experiment is performed in a typical modern laboratory/office building. The bandwidth of the signal used in this experiment is in excess of 1 GHz, which results in a differential path delay resolution of less than a nanosecond, without special processing. Based on the experimental results, a characterization of the propagation channel from a communications theoretic view point is described, and its implications for the design of a UWB radio receiver are presented. Robustness of the UWB signal to multipath fading is quantified through histograms and cumulative distributions. The all RAKE (ARAKE) receiver and maximum-energy-capture selective RAKE (SRAKE) receiver are introduced. The ARAKE receiver serves as the best case (bench mark) for RAKE receiver design and lower bounds the performance degradation caused by multipath. Multipath components of measured waveforms are detected using a maximum-likelihood detector. Energy capture as a function of the number of single-path signal correlators used in UWB SRAKE receiver provides a complexity versus performance tradeoff. Bit-error-probability performance of a UWB SRAKE receiver, based on measured channels, is given as a function of the signal-to-noise ratio and the number of correlators implemented in the receiver.

The challenges related to the deployment of ultrawideband (UWB) radios are posed in terms of interference issues that UWB radio systems will encounter. The problem of coexistence with a Global Positioning System (GPS) receiver is used as an experimental example. Calculation of an upper bound to the UWB transmitter power illustrates the effect of one possible type of regulation for a given UWB antenna system. The interference environment for a UWB receiver is used to lower bound the UWB transmitter power necessary for a given data rate. Sample measurements are provided.

A noncentralized fully distributed mobile communication network with directive/adaptive antennas is proposed. The spatial and temporal synchronization of transmitting and receiving antenna beams is accomplished by employing the global positioning system information and a synchronized spatial search algorithm. The link setup between a communication transmitter (CT) and a communication receiver (CR) depends on the success of both forward and reverse links. A two-way communication link protocol is defined as a basic agreement for the link activation in the network. Two link search algorithms, for additive white Gaussian noise channels, are proposed for use in hostile communication environments as follows: (1) a sequential ascending search power algorithm using an optimal set of link power levels and (2) a sequential Bayesian search algorithm (SBSA) using Bayes rule to update the CR location information. The optimal SBSA can be obtained by using dynamic programming, but the computational complexity is unfeasibly high. The experimental results in which the CT uses a noncoherent matched filter receiver for spread-spectrum code acquisition and the unfriendly interceptor uses a wide-band energy detector for both link search algorithms are presented.

The process of communication jamming can be modeled as a two-person zero-sum noncooperative dynamic game played between a communicator (a transmitter-receiver pair) and a jammer. We consider a one-way time-slotted packet radio communication link in the presence of a jammer, where the data rate is fixed and (1) in each slot, the communicator and jammer choose their respective power levels in a random fashion from a zero and a positive value; (2) both players are subject to temporal energy constraints which account for protection of the communicating and jamming transmitters from overheating. The payoff function is the time average of the mean payoff per slot. The game is solved for certain ranges of the players' transmitter parameters. Structures of steady-state solutions to the game are also investigated. The general behavior of the players' strategies and payoff increment is found to depend on a parameter related to the payoff matrix, which me call the payoff parameter, and the transmitters' parameters. When the payoff parameter is lower than a threshold, the optimal steady-state strategies are mixed and the payoff increment constant over time, whereas when it is greater than the threshold, the strategies are pure, and the payoff increment exhibits oscillatory behavior.

Attractive features of time-hopping spread-spectrum multiple-access systems employing impulse signal technology are outlined, and emerging design issues are described. Performance of such communications systems in terms of achievable transmission rate and multiple-access capability are estimated for both analog and digital data modulation formats under ideal multiple-access channel conditions.

One of the potential benefits of the UWB radio is its multipath resolution. The implications are multipath components which might not be resolved as distinct arrivals in more narrowband systems, may be separately identified in UWB systems. This paper explores some of the propagation characteristics associated with UWB signals, based on measured data.

Personal communications services (PCS) promise to provide a variety of information exchanges among users with any type of mobility, at any time, in any place, through any available device. To achieve this ambitious goal, two of the major challenges in the system design are: (i) to provide a high-speed wireless subsystem with large capacity and acceptable quality-of-service (QoS) and (ii) to design a network architecture capable of supporting multimedia traffic and various kinds of user mobility. A time-hopping spread-spectrum wireless communication system called ultra-wide bandwidth (UWB) radio is used to provide communications that are low power, high data rate, fade resistant, and relatively shadow free in a dense multipath environment. Receiver-signal processing of UWB radio is described, and performance of such communications systems, in terms of multiple-access capability, is estimated under ideal multiple-access channel conditions. A UWB-signal propagation experiment is performed using the bandwidth in excess of 1 GHz in a typical modern office building in order to characterize the UWB-signal propagation channel. The experimental results demonstrate the feasibility of the UWB radio and its robustness in a dense multipath environment. A ATM network is used as the backbone network due to its high bandwidth, fast switching capability, flexibility, and well-developed infrastructure. To minimize the impact caused by user mobility on the system performance, a hierarchical network-control architecture is postulated. A wireless virtual circuit (WVC) concept is proposed to improve the transmission efficiency and simplify the network control in the wireless subsystem. The key advantage of this network architecture and WVC concept is that the handoff can be done locally most of the time, due to the localized behavior of PCS users.

A statistical characterization of the complexity function of the Verdu optimum multiuser detection (VOMD) algorithm is presented for a communication system employing a finite number of randomly accessed orthogonal channels and a finite number of simultaneous users. Multichannel code-division multiple-access (CDMA) systems are proposed. It is proved that the probability, in which the individual channel complexity is greater than A/sup r(1+/spl alpha/)/, approaches zero exponentially fast as the average number of simultaneous users in each channel increases, where A is the modulation alphabet size and /spl alpha/>0. When the number of simultaneous users is large, the complexity of applying the VOMD algorithm to each individual channel is negligible when compared with the complexity of applying the same algorithm directly to the traditional single-channel CDMA system supporting the same number of simultaneous users. The probability distribution of the joint complexity function of the aggregate system is found. It is shown that when the number of simultaneous users is large, the joint complexity function is negligible compared with applying the VOMD algorithm directly to the traditional single-channel CDMA system supporting the same number of simultaneous users. Therefore, a multichannel CDMA communication system can support a comparable population of simultaneous users to the traditional single-channel CDMA system of comparable bandwidth, while reducing the complexity of optimum multiuser detection to a practical level.

Delay-and-sum beamforming is applied to both ideal and measured ultra-wideband (UWB) signals. The results of propagation measurements are also used directly to estimate the performance of an UWB communication system and to characterize design tradeoffs.

A non-centralized fully distributed mobile communication network with directive or adaptive antennas is proposed. Every node uses directive or adaptive antennas for transmitting and receiving communication signals. The spatial and temporal synchronization of the transmitting and receiving antenna beams is accomplished by employing the Global Positioning System (GPS) information and a double-ended spatial search algorithm. This research focuses on the problem of how a communication transmitter (CT) establishes the communication link with a communication receiver (CR). Two link search algorithms, (1) a sequential ascending search power algorithm using an optimal set of link power levels and (2) a sequential Bayesian search algorithm using Bayes rule to up date the CR location information, for additive white Gaussian noise (AWGN) channels, are proposed for a CT to search for its intended CR. A probability of interference, used as performance measurement for link search algorithms, is defined as the ratio of expected number of interfering event to the total number of the un-intended CRs per transmission. Examples and asymptotic analyses of the two link search algorithms employing a realistic antenna pattern are presented.

The use of time-hopped block waveform encoding PPM signals sets for multiple access communications is studied. The multiple access performance is analyzed in terms of the number of users supported by the system for a given bit error rate and bit transmission rate. The analysis shows that this technique is potentially able to provide multiple-access communications with a combined transmission capacity of over 500 Megabits per second at bit error rates in the range 10/sup -4/ to 10/sup -8/ using receivers of moderate complexity.

In order to estimate the performance of impulse radio communication systems, a characterization of the channel is required. In particular, knowledge of the multipath angle and time-of-arrival distributions is useful for predicting the performance of diversity reception schemes. In this paper, the CLEAN algorithm is applied to ultra-wide bandwidth (UWB) signals received on an array of sensors in order to resolve the incident signal components.

Attractive features of time-hopping spread-spectrum multiple access systems employing impulse signal technology are outlined and emerging design issues are described. Performance of such communications systems in terms of multiple-access capability is estimated for both analog and digital data modulation formats under ideal multiple access channel conditions.

An ultra-wide bandwidth (UWB) signal propagation experiment is performed in a typical modern office building in order to characterize the UWB signal propagation channel. The bandwidth of the signal used in this experiment is in excess of one GHz. The robustness of the WVB signal to fades is quantified through histogram and cumulative distribution of the received energy in various locations of the building. The results show that UWB signal does not suffer fades.

A new /spl Sigma/-/spl Sigma/-/spl Delta/ modulation algorithm for A/D & D/A converter is proposed which requires a much lower sampling rate than /spl Sigma/-/spl Delta/ modulation. The key feature of the proposed /spl Sigma/-/spl Sigma/-/spl Delta/ modulation is that the encoder recursively encodes the analog input sample with the fewest number of bits according to the Shannon-Elias method.

Theoretical analysis is formulated for a solid state laser based optical phase-locked loop (OPLL) disturbed by shot noise, amplitude modulated noise, and frequency noise. The frequency noise spectral density of solid state lasers is modeled to contain a white component, a 1/f component, and a strong 1/f/sup 2/ component at the laser output. This model is verified and the spectral content of each component is measured using an open-loop RF frequency discriminator. The choice of loop filter is made by considering the frequency noise components, transient effects, and the loop damping factor /spl zeta/. The total phase error variance as a function of loop bandwidth is displayed for several values of carrier signal-to-noise ratio for the measured frequency noise spectrum. Optimal loop bandwidth is also calculated as a function of carrier signal-to-noise ratio. An OPLL experiment is performed, and measured phase error variance is compared with the theoretical predictions using the measured frequency noise spectrum. The results show that the measured phase error variance closely matches the theoretical predictions.>

This paper presents a technique for computing the probability that f of m transmissions will be collision-free at a given receiver in a spread-spectrum multiple-access (SSMA) radio network in which all transmitters employ identical wideband symbol waveforms for signalling. Separation of signals (collision-freedom) is based on the fine time-resolution characteristics of pulse compression receivers operating on wideband waveforms. A taxonomy of collision-free reception events is presented for a low-complexity sampling receiver operating in the absence of significant resolvable multipath, and combinatorial techniques are used to count collision-free reception events. A method for embedding this calculation in receiver performance analyses is given.>

The paper presents a random spreading code assignment scheme for enhancing channel efficiency in centralized DS-SS packet radio networks which employ a multiple-capture receiver for each code channel. Compared to the common code case, this approach requires a modest increase in receiver complexity, but the number of distinct spreading codes being used is considerably less than the number of radios in the network. A general theoretical framework for evaluation of collision-free packet performance in each code channel is described, in which the possibility of collision-free transmission is conservatively estimated using a combinatorial method, and the effects of asynchronous multiple-access interference are characterized in terms of the primary and secondary user interferences. At the link level, the capture and throughput performances are evaluated for a proper set of codes, and compared with the results from the common code scheme. It is shown that the use of a random assignment scheme with more than one code results in a higher performance gain, and most of this gain can be achieved with just two distinct spreading codes.>

The main concern of this article is to find linear codes which will correct a set of arbitrary error patterns. Although linear codes which have been designed for correcting random error patterns and burst error patterns can be used, we would like to find codes which will correct a specified set of error patterns with the fewest possible redundant bits. Here, to reduce the complexity involved in finding the code with the smallest redundancy which can correct a specified set of error patterns, algebraic codes whose parity check matrix exhibits a particular structure are considered. If the number of redundant bits is T, the columns of the parity check matrix must be increasing powers of a field element in GF(2/sup T/). Given a set of error patterns to be corrected, computations to determine the code rates possible for these type of codes and hence the redundancy for different codeword lengths are presented. Results for various sets of error patterns suggest that the redundancy of these algebraic codes is close to the minimum redundancy possible for the set of error patterns specified and for any codeword length.>

The optimal design of a precorrelation filtering system for use in cross-spectrum symbol-rate detectors in the presence of additive Gaussian noise is described. This approach generalizes practical cross-spectrum symbol-rate detectors, and derives a necessary condition which achieves the maximum processed signal-to-noise ratio at an integer multiple of the symbol rate. The resultant optimum condition depends on the transfer functions of precorrelation filters and fixed signal model parameters. As a by-product, a performance measure applicable to any quadrature amplitude modulation format and including the effects of self-noise and intersymbol interference is derived. An algorithm for constructing physically realizable precorrelation filters that satisfy the optimum condition is given to complete the design process.>

Evidence is presented to support the conclusion that there exists only one equivalence class of binary two-dimensional arrays (both dimensions greater than 1) of +1's and -1's with all out-of-phase aperiodic autocorrelation values bounded in magnitude by unity. It is proved that no such array exists when either dimension is an odd prime or when one dimension is an odd integer and the other is twice an odd integer. Further constraints on the potentially possible dimensions of these structures are explored by developing their relationship to group difference sets, complementary sequences, and quaternary Barker sequences. The results of a computer search for binary arrays which have the smallest maximum out-of-phase autocorrelation magnitude are presented, and the utility of these arrays in waveform design problems is discussed.>

An investigation is reported of an acquisition system for digital communication over fading dispersive channels that is optimum in the maximum-likelihood sense. A performance measure for the synchronizer in the acquisition mode is defined. Upper and lower bounds on the performance measure are derived. The effective bounds on parameters, such as signal-to-noise ratio, pulse width and modulation, number of pulses, spread of the channel, and the size of the resolution cell, on the performance of the synchronizer is investigated.>

A generalized spread ambiguity function is defined, and its relationship to P.M. Woodward's (1953) ambiguity function for different models is developed. A derivation and discussion of the properties of the spread ambiguity function are presented. It is shown that smoothing the ambiguity function by the scattering function of the channel does not alter the properties of the ambiguity function. Measures of RMS correlation time and RMS correlation bandwidth of nonstationary processes are defined. An example is given to demonstrate how spread ambiguity functions can be used to help in signal design when dealing with doubly spread targets.>

The performance of sum/difference and reference/difference code tracking loops in direct-sequence spread-spectrum communication systems are fully analyzed and compared for nonwhite interference situations. In particular, symmetric dual-tone interference is considered and the worst case tone spacing and relative tone energies are determined. Parameterized curves of tracking-error variance and mean-time to lose lock are presented as a function of signal-to-interference ratio, dual tone spacing, and early-late gate delay difference.

Optimal design of a precorrelation filtering system for use in noncoberent direct-sequence code-tracking loops in the presence of colored noise is described, utilizing a linearized theory of loop operation. The design produces a bias-free loop with an odd S-curve, for which the rms tracking error is minimized. As a byproduct, one arm of the tracking loop provides an optimized signal for data-detection purposes. Widely applicable performance calculations, including rms tracking jitter, mean time to lose lock, and average detection signal-to-noise ratio, are given and illustrated, based on nonlinear models of loop operation.

Practical communication systems must cope with many uncertainties in addition to determining the transmitted data, e.g., the direction, timing, and distortion of the desired signal, and the spectral and spatial distribution of the interference, all of which may change with time. This paper describes exact least-squares (LS) recursive lattice algorithms which resolve these uncertainties in a direct-sequence spread-spectrum digital communication system. The adaptive LS algorithm is recursive beth in order and time, and converges rapidly to the uncertain parameters. Time-discrete algorithms may be mechanized by a receiver containing integrate-and-dump circuits operating at the chip rate of the pseudonoise (PN) sequence, one in each in-phase and each quadrature channel of each sensor array element's output. Different configurations of optimal time-discrete receivers are presented and transformed into adaptive receivers by taking advantage of the spectral properties of the different kinds of LS filters. Simulation results are presented and some guide lines are given for the architecture of an adaptive direct-sequence spread-spectrum system.

This paper presents additional historical information relating to the spread-spectrum history described in [1]. Included here are ties with speech scrambling technology, wide-band matched filter design, stimulus of the WHYN system design by British research, ITT's efforts to protect vital information during World War II, and other miscellaneous notes and references.

Recently, Olsen, Scholtz, and Welch presented families of binary sequences called bent-function sequences which can be generated through nonlinear operations onm-sequences. These families of sequences possess asymptotically optimum correlation properties and large equivalent linear span (ELS). Upper and lower bounds to the ELS of bent-function sequences are derived. The upper bound improves upon Key's upper bound and the lower bound, obtained through construction, and exceeds\left(\stackrel{n/2}{n/4}\right)\cdot 2^{n/4}, wherenis the length of the shift register generating them-sequence. An interesting general result contained in the derivation is the exhibition of a class of nonlinear sequences whose ELS is guaranteed to be large.

This monograph reviews events, circa 1920-1960, leading to the development of spread-spectrum communication systems. The WHYN, Hush-Up, BLADES, F9C-A/Rake, CODORAC, and ARC-50 systems are featured, along with a description of the prior art in secure communications, and introductions to other early spread-spectrum communication efforts. References to the available literature from this period are included.

In this paper we construct a new family of nonlinear binary signal sets which achieve Welch's lower bound on simultaneous cross correlation and autocorrelation magnitudes. Given a parameternwithn=0 \pmod{4}, the period of the sequences is2^{n}-1, the number of sequences in the set is2^{n/2}, and the cross/auto correlation function has three values with magnitudes\leq 2^{n/2}+1. The equivalent linear span of the codes is bound above by\sum_{i=1}^{n/4}\left(\stackrel{n}{i} \right). These new signal sets have the same size and correlation properties as the small set of Kasami codes, but they have important advantages for use in spread spectrum multiple access communications systems. First, the sequences are "balances," which represents only a slight advantage. Second, the sequence generators are easy to randomly initialize into any assigned code and hence can be rapidly "hopped" from sequence to sequence for code division multiple access operation. Most importantly, the codes are nonlinear in that the order of the linear difference equation satisfied by the sequence can be orders of magnitude larger than the number of memory elements in the generator that produced it. This high equivalent linear span assures that the code sequence cannot be readily analyzed by a sophisticated enemy and then used to neutralize the advantages of the spread spectrum processing.

A basic theory of frame synchronization for a singlechannel digital communication system is presented, along with extensive references to the literature. The design of frame markers is discussed and comparisons are drawn with more exotic techniques such as comma-free coding.

The class of all fixed-length statistically synchronizable codes may be completely characterized in several ways. A simple condition for determining statistical syncaronizability is demonstrated.

Theorems are presented concerning the optimality of rational approximations using non-Archimedean norms. The algorithm for developing the rational approximations is based on continued fraction techniques and is virtually equivalent to an algorithm employed by Berlekamp for decoding BCH codes. Several variations of the continued fraction technique and Berlekamp's algorithm are illustrated on a common example.

It is shown that Reed-Solomon (RS) codes can be decoded by using a fast Fourier transform (FFT) algorithm over finite fieldsGF(F_{n}), whereF_{n}is a Fermat prime, and continued fractions. This new transform decoding method is simpler than the standard method for RS codes. The computing time of this new decoding algorithm in software can be faster than the standard decoding method for RS codes.

The structure of the group of integers relatively prime tonunder multiplication modulonis reviewed, and the basic properties of characters defined on that group is developed. Appropriately chosen subcollections of the characters when viewed as periodic sequences are then shown to have relatively ideal autocorrelation and cross correlation properties. The results of a computer study indicate that the same subcollections when viewed as finite length sequences also have very good aperiodic autocorrelation and cross correlation properties.

This paper describes an idealized spread-spectrum communication system. The processing gain concept is developed as a measure of a well-designed system's robust performance against independent wide-sense stationary interference. Multipath and repeater jammer rejection, partial correlation problems, and security requirements are related to spread-spectrum code properties.

A set ofMequally-likely equal-energy transmittable signals is considered, each of which consists of a linear combination of tones fromDfree running oscillators(D \leq M). The oscillator tones are assumed sufficiently disjoint to be orthogonal. The design problem consists of finding the optimal receiver and signal set for variousMandD. For the additive white Gaussian noise channel, the optimal receiver first forms the sufficient statistic which consists of noncoherently detecting the energy in each of theDtones. Unlike previous designs of digital transmitters based on minimization of the probability of error, when noncoherent oscillations are employed, the optimal receiver and signal set are dependent on the signal-to-noise ratio. The imposed constraints restrict the signal vectors to the all-positive subspace of the surface of aD-dimen sional sphere. The optimal receiver, signal set, and resulting prob ability of error and channel capacity are determined forM \geq D = 2for low and high signal-to-noise ratios. Severe performance constraints imposed by using a suboptimal square-law receiver are discussed. Preliminary results have been obtained for the general caseM \geq D > 2.

The performance of a class of block codes with unbounded synchronization delay, though finite average synchronization delay, is analyzed. Basically the synchronizer inspects the code symbol stream for the first occurrence of one of a set of sequences that appear in only one timing position relative to true sync. The receiver can be implemented easily with shift registers and associated logic. The probability that the sync process will exceed any given number of code symbols is investigated and bounds on this probability are established. The average sync delay to the first occurrence of a synchronizing sequence is determined and the optimal encoding procedure for a memoryless message source is presented. If sync is established by observing ann-tuple,nbeing the codeword length, the optimal structure of the synchronizingn-tuple is found and the associated dictionary size is specified.

Bounded synchronization delay codes have the property that no proper cyclic rearrangement of the letters of a codeword is another codeword. Because of this property research in code design has centered on criteria for selecting one word from each nonperiodic cyclic equivalence class to satisfy various additional constraints. This is all that is necessary when it is feasible for the encoder and decoder to use table look-up procedures. However, even for moderate word length, the dictionary size can be quite large and prove a major obstacle in practical applications. This paper describes a systematic procedure for mapping data sequences into nonperiodic cyclic equivalence classes and for performing the inverse mapping. The scheme is arithmetic in nature and does not require large tables.

This paper explores the relationship between variable word-length synchronizable codes and comma-free codes. A simple construction procedure for comma-free codes of maximum dictionary size is presented. The concept of comma freedom is then reformulated to include the possibility of variable word length and two construction procedures for variable word-length comma-free codes are given. The resultant codes allow transmission of information at a higher rate than fixed word-length comma-free codes, for the same maximum synchronization delay.

The reviewer feels the author has succeeded, where many have failed, in writing a textbook for a course in detection and estimation theory. Derived from course notes, this text includes many of the peripheral structures which make a book suitable for classroom. Among them are numerous examples, over 120 pages of problems and a l2-page glossary of notation. The text is well referenced and is indexed by both subject and author.

In this paper biorthogonal codes are generalized in a natural way to a class of codes, calledN-orthogonal codes.N-orthogonal codes consist ofN^{M}signals divided intoN^{M-1}disjoint sets ofNsignals where signals in different sets are uncorrelated or orthogonal. One instance of theN-orthogonal codes is realized as a class of polyphase, constant-power modulated signals, the admissible phase set being denoted byN^{th}roots of unity. Matched filter receiver criteria for the Gaussian channel are developed and simplified integral expressions for the probability of error are derived.

A synchronizable(SC_{s})code has the property that the punctuation (comma or no comma, comma indicating that the next symbol is the beginning of a new code word) at a given position in a code symbol stream can always be determined by observing at mostscode symbols in the neighborhood of the position in question. The construction ofSC_{s}dictionaries and the mechanization of synchronizers using nonlinear shift registers are explained in detail. Necessary and sufficient conditions for the existence ofSC_{s}codes with specified word lengths are derived. By allowing unequal word lengths in the code, it is demonstrated that a substantial saving in average word length and information rate can be accomplished over other recently proposed codes having synchronization capability.

The problem of determining optimal signal waveforms for transmission through a phase-incoherent channel is examined under the following conditions: 1) the channel adds white Gaussian noise to the signal, 2) the receiver is synchronized, 3) the receiver is designed to minimize probability of error, 4) all signals have equal energy, 5) all messages are, a priori, equiprobable, and 6) there is no bandwidth restriction on the signal set. This signal design problem is expressed as a variational problem involving a search for the optimal matrix in a specific class of non-negative-definite matrices, or, equivalently, involving a search for the optimal signal correlation set in a collection of admissible signal correlation sets. For all signal-to-noise ratios, the probability of error is shown to have a local extremum in the class of all admissible signal sets at the orthogonal signal set. This extremum is then classified as a local minimum by proving that the second-order variations are, indeed, always positive. The probability of error is then evaluated numerically for the orthogonal signal structure.

A generalized Barker sequence is a finite sequence\{a_{r}\}of complex numbers having absolute value1, and possessing a correlation functionC(\tau)satisfying the constraint|C(\tau)| \leq 1, \tau \neq 0. Classes of transformations leaving|C(\tau)|invariant are exhibited. Constructions for generalized Barker sequences of various lengths and alphabet sizes are given. Sextic Barker sequences are investigated and examples are given for all lengths through thirteen. No theoretical limit to the length of sextic sequences has been found.