A pseudo-maximum-likelihood data estimation (PML) algorithm for discrete channels with finite memory in additive white Gaussian noise environment is developed. Unlike the traditional methods that utilize the Viterbi algorithm (VA) for data sequence estimation, the PML algorithm offers an alternative solution to the problem. The simplified PML algorithm is introduced to reduce the computational complexity of the PML algorithm for channels with long impulse response. The adaptive version of the PML algorithm suitable for time-varying channels such as frequency-selective Rayleigh fading channels is also introduced. Computer simulation results demonstrate the performance of these algorithms and compare them to the VA-based techniques for different types of channels. The performance design criterion for the PML algorithm is derived in the Appendix.

The problem of asynchronous classification of M-ary frequency-shift keying (MFSK) signals when contaminated by additive white Gaussian noise (AWGN) is addressed. Two approaches are adopted. The first is based on the classical likelihood-ratio theory, which provides performance that is optimal, but sensitive to unknown frequency offsets. The second completely eliminates the fixed-frequency structure and instead utilizes measurements made strictly in the higher order correlation (HOC) domain. Assessed are the sensitivity gaps in performance incurred by the synchronous rules when the unknown signal time of arrival or epoch offsets are introduced. This sensitivity is ameliorated by averaging over a reduced-uncertainty epoch model. Fairly satisfactory results are reported with a small number of the discretized epoch uncertainty levels.

A new approach to the problem of data detection for communications over band-limited channels with unknown parameters is introduced. We propose a new way to implement the Viterbi algorithm (VA) for maximum-likelihood data sequence estimation (MLSE) in a known channel environment and utilize it to derive block adaptive techniques for joint channel and data estimation, when the channel-impulse response (CIR) is unknown. We show, via simulations, that we can achieve a probability of error very close to that of the known channel environment and nearly reach a mean-square error in the channel estimate as predicted by analytical bounds, operating on static channels, which exhibit deep nulls in their magnitude response and nonlinear phase. The proposed schemes accomplish channel acquisition after processing a few hundred symbols while operating without a training sequence, whereas linear blind equalizers, such as Sato's (1975) algorithm, fail to converge at all. The application of block processing to adaptive MLSE is also investigated for time-varying frequency-selective Rayleigh-fading channels, which are used for modeling mobile communication systems. In such environments it is shown that the proposed scheme exhibits improved performance compared to the conventional adaptive MLSE receiver using tentative delayed decisions.

This paper considers a maximum-likelihood (ML) noncoherent detection scheme for multiple full response continuous-phase frequency shift keying (CPFSK) waveforms and introduces a trellis-coded modulation (TCM) scheme for this noncoherent modulation. By utilizing a Gaussian approximation for Rician random variables, we express the pairwise error probability as a function of the equivalent normalized squared distance (ENSD). ENSD plays the same role as normalized squared Euclidean distance when evaluating error probability performance for coherent detection. We derive an analytical approximation on the bit-error probability by employing ENSD for both the coded system and the uncoded system. For the uncoded system we show that the bit-error probability of noncoherent detection approaches that of coherent symbol-by-symbol detection in the limit as the multiplicity of the symbol goes to infinity for large signal-to-noise ratio (SNR), We determine specific optimal trellis encoders for binary and 4-ary CPFSK with modulation index 1/2 and 1/4, respectively, by application of Ungerboeck's (1982) set partitioning approach.

This paper describes a technique related to the design of a trellis encoder, combined with the full response M-ary continuous phase frequency shift keying (CPFSK) with modulation index 1/M. A new representation of CPFSK waveforms in N signaling intervals, is proposed as a function of an (N+1)-D vector. We also decompose the generation of the proposed CPFSK waveform into two stages, an N-consecutive continuous phase encoder (NCPE) and a memoryless modulator (MM). This decomposition makes it possible to design binary convolutional encoders with various code rates, cascaded to the NCPE. Specific optimal outer convolutional encoders of two and three-consecutive full response four-ary CPFSK with modulation index 1/4 are designed following Ungerboeck's (1982) set partitioning approach. These codes achieve asymptotic coding gains up to 4.77 dB for the two consecutive case with code rate 3/4, and asymptotic coding gains up to 5.45 dB for the three-consecutive case with code rate 5/6.

A general framework that theoretically links the higher-order correlation (HOC) domain with statistical decision theory is explored. It is then applied to the problem of classification of M-ary frequency shift keying (MFSK) signals when contaminated by additive white Gaussian noise (AWGN). In particular, we propose a novel class of classifiers that utilizes time-domain HOC operations while completely avoiding the explicit determination of the spectrum of the observed signal. It is shown that this method delivers a performance that tightly lower-bounds that of the optimal likelihood-ratio test. In addition, this intrinsically wideband HOC-based method possesses an immunity to imperfect knowledge of exact frequency locations. Substantial performance improvement is also reported over the energy-based rule whenever it is applicable.>

Two iterated algorithms for evaluating the performance of a class of sequential tests are proposed. The goal is equivalent to computing the distribution function of the first passage time for a random walk to cross a one-sided barrier. Limitations on both algorithms are studied, and associated methods for eliminating those limitations when possible are derived. These algorithms are applied to a pseudonoise code acquisition system and a range-sampled radar searching problem. Related computational problems are discussed, and numerical results are given.>

The effects of data modulation and/or narrow-band interference on the acquisition time of direct sequence (DS) systems are assessed when particular acquisition schemes are selected. Finally, the results of these analyses are used to propose receivers which mitigate the deleterious effects of the data or jamming. The analyses demonstrate that the I-Q detector, modified for a data modulated carrier, is superior to the correlator/square-law detector despite the latter's robustness to data. When the average pulsed jammer power is constrained, the analyses illustrate that the jammer's duty factor does not impact acquisition time when the pulse repetition frequency (PRF) is high; a duty factor of unity maximally degrades acquistion performance when the PRF is low. A proposed adaptive receiver provides considerable jamming protection; the acquistion performance of such a receiver bounds the performance of all adaptive acquistion receivers.

The implementation and performance of wide-band detectors for direct-sequence and time-hopping spread-spectrum waveforms in the presence of additive white Gaussian noise are considered in this paper. Of interest here is the performance penalty incurred when going from optimal to suboptimal detector structures. In both cases, performance is quantified by appropriately defined distance measures and is ultimately compared to that of the simplest hypothesis-discriminating device, namely, the energy detector (radiometer).

The purpose of this paper is to apply the renewal theory approach for analyzing aperiodic finiteS-curve code-tracking loops developed by Meyr [9] to the case of a noncoherent, arbitrary offset, early-late, delay-locked loop ("noncoherent δ-DLL"). The exact (renewal) approach is compared to the approximate (periodic-extension) approach of using the periodicS-curve or phase-locked loop theory, as well as to the linear theory developed herein for the aforementioned codetracking loop. Finally, loop optimization with respect to the offset δ is carried out according to certain performance criteria. The results indicate that, for low SNR, the exact and approximate theories could deviate significantly while, for high SNR, all three theories yield identical performance, as expected. Furthermore, it is shown that the optimal δ for both low and high SNR could differ from the commonly accepted choice\delta = 1/2.

The purpose of this two-part paper is threefold: 1) Part I discusses the code-acquistion problem in some depth and 2) also provides a general extension to the approach of analyzing serial-search acquisition techniques via transform-domain flow graphs; 3) Part II illustrates the applicability of the proposed theoretical framework by evaluating a matchedfilter (fast-decision rate) noncoherent acquisition receiver as an example. The theory is formulated in a general manner which allows for significant freedom in the receiver modeling. The statistics of the acquisition time for the single-dwell [2], [3] andN-dwell [5] systems are shown to be special cases of this unified approach.

The unified theory developed in Part I [1] is employed here in the analysis of a noncoherent, matched-filter (fast-decision-rate) code acquisition receiver in a direct-sequence spread-spectrum system. The results illustrate the dynamic dependence of the mean acquisition time on system parameters, such as the predetection signal-to-noise ratio (SNR), the decision threshold settings, and the ratio of the decision rate to the code rate.

The technique of multiple dwell serial search is described and analyzed. The advantage of the multiple dwell procedure is that the examination interval need not be fixed, allowing incorrect cells to be quickly discarded, which in turn results in a shorter search time than is possible with a fixed dwell time procedure. This type of search scheme is particularly useful for direct sequence code acquisition in a spread-spectrum communication system. An expression for the generating function is obtained from a flow graph representation of the multiple dwell technique. The generating function is used to develop expressions for the mean and variance of the search time in terms of the following parameters: the dwell times, the detection probability, the false alarm probability, and the false alarm penalty time. Coherent detector characteristics are then used to investigate the performance of the multiple dwell technique for direct sequence code acquisition. It is shown that the multiple dwell procedure can significantly reduce the expected acquisition time from that obtained with a single dwell system. The most significant improvement is obtained by using a two-dwell system. Additional but nominal improvement is gained when more than two dwells are employed.

Single dwell serial search techniques are common and useful for coarse time and frequency synchronization of spreadspectrum systems. A valuable system performance criterion, namely, the probability of successful synchronization for a single dwell serial synchronization system is derived. This probability is a function of the number of cells searched and is expressed in terms of the following four parameters: the dwell per cell, the detection probability, false alarm probability and the penalty time for a false alarm. Numerical results are presented to show the relationship between these parameters and system performance.

A demod-remod coherent tracking loop for QPSK and SQPSK is described and analyzed. This type of receiver is attractive since all of the available signal power is despread and used to generate the tracking error signal when the pulses reaching the nonlinearities are rectangular. The same demod-remod circuit is widely used for bandlimited pulses, for which less than full power is converted to the carrier phase error signal. All system parameters pertinent to system performance are enumerated. The effects of the IF and arm filters on the statistics of the noise are determined. With respect to the signal, the filters are considered only insofar as they reduce the delivered signal power. It is demonstrated how a tracking phase error converts some of the signal power into additional noise power. The results of performance computation are presented.

A demod-remod coherent tracking loop for QPSK and SQPSK is described and analyzed in [1]. Those results are used to obtain the power spectral density of the equivalent noise of the tracking loop and the probability density function of the steady-state phase error, The effects of the IF and arm filters on the statistics of the noise and QPSK signal are developed. The results of performance computations are presented.

The performance of a class of pulse Doppler radars with a digitally implemented signal processing unit is investigated. TheKuband rendezvous radar onboard the Shuttle Orbiter is a pulse Doppler radar which is in this class. The detection capability is first presented. A unified analysis of digital radar tracking loops is presented which employs logarithmic discriminants. The results are applied to angle, range, and range rate tracking loops. Numerical results of the amplitude monopulse angle tracking loop are presented for theKu-band rendezvous radar of the Space Shuttle.

For convolutional codes, thc variation of the minimum distance between nonmerging codewords with the lengths of those codewords is considered for all finite lengths. This is carried out in terms of a new distance parameter for convolutional codes do, the minimum average weight per branch over all cycles. Upper and lower bounds on do for binary convolutional codes of rate1/nare presented. The tradeoff betweend_{o}and the free distanced_{free}is obtained for small memory length codes.

The choice ofMequiprobable equipowered narrow-band waveforms of equal duration for the noncoherent communication system is considered. With the bandwidth constrained, the problem of finding optimal signal sets of given dimension is formulated as a variational one. For dimensionalityD \leq 2M - K,K \leq 2[M/3], where [ ] denotes "integer part of," andM \geq 6, signal inner-product matrices consisting ofKregular simplices placed mutually orthogonal to one another, are local extremals of the probability of error, thereby establishing a marked similarity between the coherent and noncoherent signal-design problems.

In a previous study, a general expression for the detection probability was given for the transmission of an arbitraryM-ary signaling alphabet through the incoherent-phase channel which adds white Gaussian noise. Necessary and sufficient conditions were obtained demonstrating that with no dimensionality or bandwidth restrictions, the incoherent orthogonal signal structure locally minimizes the error probability for all signal-to-noise ratios. The previous expression is improved herein, from which it is verified that, when the signal dimensionality and bandwidth are restricted to be less than that necessary for the previous optimum, necessary conditions to locally extremize the probability of error are satisfied by the signal-waveform inner product matrix whose dimensionality is as large as possible. The form of the solution obtained is a2 \times 2block diagonal matrix with each block the regular simplex inner-product matrix.

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 fundamental problem of statistical communication theory is that of selecting the optimal set ofMequipowered finite duration waveforms to minimize the error rate for a coherent channel perturbed by white Gaussian noise, the signals being restricted toDdegrees of freedom, whereD < M. It is demonstrated that the concept of placing lower-dimensional regular simplicities mutually orthogonal to one another (the technique of known solutions) can be extended. In fact, such signal structures are solutions to the signal design problem for the cases where the dimensionality is restricted to be at mostM-K, whereKis any fixed integer between2andM/2. Of the several solutions for eachK, the most preferred of these is determined at large signal-to-noise ratio, and in certain cases numerical computation has shown this preference to agree with that at small signal-to-noise ratio. Finally, the effect on probability of error due to successive reductions in the allowed dimensionality of the signal set is analyzed for the optimal solutions known to date.