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] and N -dwell [5] systems are shown to be special cases of this unified approach.

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

We analyze in depth the MAX/TC criterion for code acquisition in spread-spectrum transmissions. The uncertainty region is divided into sectors: inside each sector, the cell with associated maximum test variable is selected (MAX criterion), and sectors are serially tested according to the threshold crossing (TC) criterion. The most commonly used analysis tools for code acquisition, namely the direct and the flow-graph approaches, are extended to the MAX/TC criterion. An accurate but simple approximation to the acquisition time probability density function is found in terms of a gamma distribution, which is shown to yield much better accuracy than the Gaussian distribution. The general formulation is applied to the particular case of direct-sequence spread-spectrum multiple-access (DS-SSMA) systems, showing that sector size is a fundamental parameter to be optimized in the minimization of acquisition time, and that in some cases MAX/TC with parallel architecture performs marginally better than MAX/TC with serial architecture.

On the MAX/TC criterion for code acquisition and its application to DS-SSMA systems

In this paper, we propose a search technique that takes advantage of multipath, which has long been considered deleterious for efficient communication, to aid the sequence acquisition in dense multipath channels. We consider a class of serial-search strategies and use optimization and convexity theories to determine fundamental limits of achievable mean acquisition times (MATs). In particular, we derive closed-form expressions for both the minimum and maximum MATs and the conditions for achieving these limits. We prove that a fixed-step serial search, a form of nonconsecutive serial search, achieves a near-optimal MAT. We also prove that the conventional serial search, in which consecutive cells are tested serially, should be avoided as it results in the maximum MAT. Our results are valid for all signal-to-noise ratio (SNR) values, regardless of the specifics of the detection layer and the fading distributions

Multipath Aided Rapid Acquisition: Optimal Search Strategies

The performance of four algorithms using pseudonoise matched filters (PNMFs), for direct-sequence spread-spectrum systems, is analyzed. They are: parallel search with fix dwell detector (PL-FDD), parallel search with sequential detector (PL-SD), parallel-serial search with fix dwell detector (PS-FDD), and parallel-serial search with sequential detector (PS-SD). The operation characteristic for each detector and the mean acquisition time for each algorithm are derived. All the algorithms are studied in conjunction with the noncoherent integration technique, which enables the system to operate in the presence of data modulation. Several previous proposal using PNMF are seen as special cases of the present algorithms. >

Rapid code acquisition algorithm employing PN matched filters

A 'direct' approach to obtain statistics of the code acquisition time for serial-search spread-spectrum receivers is presented, which combines the idea of algebraic characterization of the search with transform domain methods. This is a very general unified technique, yielding many other known results as special cases. One of the major advantages of the direct approach is that the effect of the search strategy on moments of the acquisition times can be isolated from the effect of the detection/verification logic. This fact will permit one both to analyze all known search strategies-confirming several conclusions regarding their comparative performance-and to propose two novel strategies (alternate search) which outperform the conventional ones when the code rewinding time is small in comparison to the dwell times. Optimum search strategy based on the maximum a posteriori criterion (MAP) is analyzed, thus ensuring an absolute and uniform basis of comparison. The two new strategies perform well by this measure. >

Analysis of strategies for serial-search spread-spectrum code acquisition-direct approach

Pseudonoise (PN) coding may be incorporated into the signal structure of a communication system for a variety of reasons. Once present, the PN code must be appropriately acquired before it can be tracked by the receiver. Toward this end various acquisition schemes have been proposed. These schemes include combinations of predetection/postdetection processing and code search strategies. With regard to the latter, a uniform search over the entire code uncertainty region would be undertaken in the absence of a priori epoch information. In the presence of such information a more sophisticated scheme, which may generally be termed an "expanding window search," would tend to reduce acquisition time. The present paper focuses on uniform and expanding window search strategies with the goal of analytically developing the PN acquisition time statistics as functions of salient system parameters such as predetection SNR, detection and false alarm probabilities, false alarm penalty time, and a priori information on epoch location. The significance of this analysis is its general applicability to arbitrary postdetection processing schemes-e.g., fixed dwell and sequential detection. Computed performance results account for the above salient parameters, wherein sequential detection is employed in conjunction with uniform and selected expanding window search strategies. Performance curves demonstrate the utility of the analysis and provide intuitive insight into performance sensitivity to search strategy.

Generalized Analysis for the Evaluation of Search Strategy Effects on PN Acquisition Performance

Under examination in this paper is the uncoded bit error rate (BER) performance of a satellite communications system in which the modulation scheme is binary PSK, the transponder contains an arbitrary amplitude nonlinearity, and high-level pulsed radio frequency interference (RFI) is present. The RFI may be characterized as either pulsed Gaussian noise or pulsed CW, with the burst duration shorter than that of the information bit and arrivals assumed to follow a Poisson law. Of special significance is the fact that a general approach is presented for direct BER evaluations; this is in contrast to other approaches which may, for example, employ signal-to-noise ratio suppression factors. Computed results are based on arbitrarily specified RFI scenarios and the presence of one of three amplitude nonlinearities-hard limiter, clipper, or blanker. In the context of these three specific nonlinearities, performance curves demonstrate the superiority of an appropriately chosen blanker when the RFI environment is particularly severe. Comparisons between hard limiting and clipping are also made. Additional results examine performance sensitivity to information bit rate, variations in signal power, and the ratio of CW to noise content. With respect to the latter, CW effects are found to be most severe.

On the Passage of High-Level Pulsed Radio Frequency Interference Through a Nonlinear Satellite Transponder

The bit error rate (BER) performance analysis of a data communication system is generally based on the assumption that signal waveforms are ideal and hardware-induced distortion is absent. In a satellite communication system, such distortion arises in the satellite repeater, as well as in the transmitter and receiver portions. NASA, which is in the process of developing its Tracking and Data Relay Satellite System (TDRSS), is very much interested in understanding the impact of numerous hardware constraints, that have been identified, on BER performance. The present paper, which treats one segment of this broad problem area, examines the cumulative impact of nine forms of distortion induced by the repeater on BPSK and QPSK signals. These include frequency offset, filter amplitude and phase ripple, phase noise, spurious phase modulation (PM), AM/AM and AM/PM conversion, incidental AM, and spurious outputs. For the present analysis, the transmitter and receiver are assumed to operate in essentially ideal fashions and thermal noise is introduced at the receiver front end only. Computed results indicate that BPSK and QPSK performances are impacted in substantially different manners, with QPSK generally more sensitive to a given form of distortion. One noteworthy example is the combined impact of the phase noise and spurious PM parameters which affect BPSK only slightly, but lead to very rapid QPSK performance degradation as the parameter values increase. This and the other distortion effects are illustrated via computed parametric performance curves. Results also demonstrate the need to account for interactions among distortion parameters.

The Effects of Transponder Imperfections on the Error Probability Performance of a Satellite Communication System

Employment of a repeater in a communication system may lead to the introduction of several sources of potential performance degradation. They are hard-limiting, IF filter group delay distrotion and center frequency offset, and additional noise in the links from transmitter-to-repeater and repeater-to-receiver. Specifically, the hardlimiter and IF filter may introduce signal waveform distortion while the former may also introduce signal-to-noise ratio suppression. In this paper the impact of the above on a pseudo-noise (PN) time-of-arrival (TOA) estimation system is considered. The assumed modulation scheme is differential phase shift keying (DPSK) and realistic nonconstant envelope signals are considered; the performance criterion is TOA estimate standard deviation. One surprising result is that the presence ot the limiter tends to degrade performance; this is contrary to corresponding results that have been derived for data detection. It was also found that performance degrades quite gradually with increasing IF filter differential group delay over the signal bandwidth. Finally, although analytical results presented here pertain specifically to the hard-limiter, they may be straightforwardly extended to determine the effects of repeater n th law devices.

A. Weinberg

Papers

Generalized Analysis for the Evaluation of Search Strategy Effects on PN Acquisition Performance

On the Passage of High-Level Pulsed Radio Frequency Interference Through a Nonlinear Satellite Transponder

The Effects of Transponder Imperfections on the Error Probability Performance of a Satellite Communication System

The Effects of Repeater Hard-Limiting, Filter Distortion, and Noise on a Pseudo-Noise, Time-Of-Arrival Estimation System