Exact and approximate statistical models (analytical and simulation), based on average- and maximum-likelihood ratio tests, are studied and compared for the purpose of establishing an accurate assessment of the performance of noncoherent SFH M-FSK intercept receivers. Both continuous and discontinuous phase M-FSK cases are considered with important differences between the two.>

The optimum hop timing estimator, based on classical likelihood-ratio (LR) theory, is derived for noncoherent slow and fast frequency-hopped M-FSK intercept receivers. Such receivers have no a priori knowledge of the hopping code and thus the solution to this estimation problem differs considerably from the more commonly considered case of the friendly receiver. The implementation and performance of the LR hop timing structures are presented and compared with that of other previously documented suboptimum schemes. In particular, when compared to the multiple-hop autocorrelation (MHAC) approach and the "ping-pong" approach, the average-likelihood ratio (ALR) and maximum-likelihood ratio (MLR) optimum estimators offer an improvement in performance of several dB in input SNR. Robustness issues for the optimal estimator are examined and alternative configurations are proposed that offer enhanced insensitivity to unknown frequency offsets.>

Exact and approximate statistical models (analytical and simulation), based on average-and maximum-likelihood ratio tests, are studies and compared for the purpose of establishing an accurate assessment of the performance of coherent SFH M-FSK intercept receivers.>

Optimum detectors have previously been derived for fast frequency-hopped (FFH) signals with M-ary frequency-shift-keyed (MFSK) data modulation received in additive white Gaussian noise (FFH here implies that a single MFSK tone is transmitted per hop), The present paper extends that work to the more analytically complex category of slow frequency-hopped (SFH) signals with multiple MFSK tones per hop. A special subset of the SFH/MFSK format that receives particular attention in the paper is the case of continuous-phase modulation (CPM) for which the carrier phase is assumed to be constant over the entire hop. A fundamental conclusion is that SFW/CPM modulation is advantageous not only to the communicator but also to a sophisticated noncoherent detector. By applying techniques developed in the paper to exploit the continuous-phase characteristic, an intercept receiver of reasonable complexity will perform appreciably better than traditional channelized detectors.>

A spread-spectrum code acquisition technique for a direct-sequence (DS) system in the presence of Doppler effect and data modulation is investigated. Both the carrier-frequency offset and code-frequency offset due to severe Doppler effect are considered. The code-chip slipping during the correlation process caused by code-frequency offset can degrade the acquisition performance significantly. However, this issue can be alleviated by compensating code-frequency offset in an appropriate manner. Results are presented for the cases with and without data modulation. Coherent detection is considered when there is no data modulation. If data modulation is present, the authors partition the correlation time into subintervals and the integration results in these subintervals are square-law noncoherently combined for detection. The implementation of this code acquisition technique using the fast Fourier transform (FFT) algorithm is described. The use of theoretical results to estimate the hardware complexity of an actual system is illustrated step by step, showing that implementation is feasible with existing technology. The tradeoff between hardware complexity and acquisition performance is discussed.>

An acquisition procedure for data-modulated direct-sequence spread-spectrum systems is investigated. The correlation time is partitioned into subintervals, and the integration results in these subintervals are noncoherently combined for detection. The tradeoff between noncoherent combining loss and data modulation degradation guides the optimum choice of the number of subintervals. Two forms of data modulation are considered, namely, the alternate-data and random-data cases. The parallel acquisition schemes discussed allow multiple code-phase offsets to be examined at each test. The circular state diagram approach is used to analyze the performances of these schemes. The theory presented is valid for a class of such parallel schemes.>

An upper bound on the bit-error probability (BEP) of a linear cyclic code over GF(2/sup l/) with hard-decision (HD) maximum-likelihood (ML) decoding on memoryless symmetric channels is derived. Performance results are presented for Reed-Solomon codes on GF(32), GF(64), and GF

Continued fraction techniques are equivalent to Berlekamp's algorithm. The sequenceD(k), k \geq 0, in Berlekamp's algorithm provides the information about when Berlekamp's algorithm completes one iterative step of the continued fraction. In fact, this happens whenD(K) < k + 1/2; and whenD(k) \neq D(k + 1), it implies that Berlekamp's algorithm begins the next iterative step of the continued fraction.

Balanced binary sequences of period2^{n}-1with the run property and the two-level autocorrelation property are not necessarily PN sequences.