Charles L. Weber

A Unified Approach to Serial Search Spread-Spectrum Code Acquisition--Part I: General Theory

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.

A Mathematical Model

The mathematical model presented in this chapter is intended to be sufficiently general to include the examples of Chapter 1 as well as many others, and yet sufficiently specific to enable us to apply the concepts of statistical-decision theory as well. We shall examine the general reception problem as a statistical-decision problem and hence shall assume certain statistics of the messages and channel disturbances depending on the criterion for system evaluation prescribed and the set of decisions permitted by the receiver. We shall also have to make certain assumptions concerning the nature of the available data, such as whether it resulted from discrete or continuous sampling of the observed waveform. Finally, we must specify the performance criterion by which we are seeking the optimal system.

A Unified Approach to Serial Search Spread-Spectrum Code Acquisition--Part II: A Matched-Filter Receiver

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.

Performance considerations of code division multiple-access systems

The performance of code division multiple-access (CDMA) systems is determined using direct-sequence spectral spreading. Asynchronous users are assumed so that there is no network control. Under relatively ideal conditions, the degradation in system performance as a function of the number of users is shown to have a threshold effect. This basic limitation in the number of users of the system is further limited if the powers are unequal. For two users, system performance as a function of their power ratios also has a threshold effect. System performance as a function of the amount of spectral spreading is determined. The performance of both coded and uncoded systems is predicted.

Multiple Dwell Serial Search: Performance and Application to Direct Sequence Code Acquisition

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.

Higher-order correlation-based approach to modulation classification of digitally frequency-modulated signals

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. >

Statistical Performance of Single Dwell Serial Synchronization Systems

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.

Maximum-likelihood blind equalization

A new approach to blind equalization is investigated in which the receiver performs joint data and channel estimation in an iterative manner. Instead of estimating the channel inverse, the receiver computes the maximum-likelihood estimate of the channel itself. The iterative algorithm that is developed involves maximum-likelihood sequence estimation (Viterbi decoding) for the data estimation part, and least-squares estimation for the channel estimation part. A suboptimal algorithm is also proposed that uses a reduced-state trellis instead of the Viterbi algorithm. Simulation results show that the performance obtained by these algorithms is comparable to that of a receiver operating with complete knowledge of the channel.

Asynchronous classification of MFSK signals using the higher order correlation domain

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.

Detection Performance Considerations for Direct-Sequence and Time-Hopping LPI Waveforms

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).