This paper discussed four open-loop frequency acquisition techniques for suppressed-carrier BPSK signals. The techniques, which do not require accurate symbol timing nor a data preamble sequence, employ fast Fourier transforms (FFT's) on the Costas loop phase detector output to detect the Doppler frequency offset. Performance of the full-, half-, and staggered-symbol integration techniques as well as the low-pass filter technique are compared in terms of the error signal output SNR's. Then, the probability of detecting the frequency offset is computed for the special case when the frequency of the tone to be detected coincides with one of the FFT-bin center frequencies. It is shown that the performance of the integration techniques depends strongly on the symbol timing offset. On the other hand, the detection probability for the one-pole arm filter technique depends directly on the filter bandwidth. The staggered integration technique is shown to have comparable performance to the low-pass filter technique for low-to-medium symbol SNR's but the latter is superior at high symbol SNR's.>

An expression is derived which shows that when the bandpass filter preceding a Costas loop is not symmetric and the arm filters are not balanced, a static phase error, which becomes larger as the SNR decreases, can occur due to noise. Conversely, if either condition does not apply, then no noise-induced phase error bias will exist. It is shown, for a modified Costas loop in which one arm filter is removed, that the static phase error may be significant.

This paper determines the tracking performance of a filter and square bit synchronizer loop (FSTL) for the case of NRZ symbols and a probability of data transition of 0.5. Results are compared to the early late gate tracking loop (ELGTL) and the digital transition tracking loop (DTTL). The FSTL is much easier to implement and, in addition, has a standard deviation of tracking error only about 14 percent larger than the DDTL loop.

The spread spectrum acquisition and tracking performance for the ShuttleS-band andKu-band communication links are analyzed and compared to test results. TheS-band link requirements are more severe than those of theKu-band links, hence, different despreader designs were developed for the two systems. TheS-band despreader acquires pseudonoise code lock by examining all possible code phases in half chip steps while theKu-band despreader acquires pseudonoise code lock by continuously sweeping a tau-jitter loop. Both despreaders employ a tau-jitter loop for code tracking. The code tracking performance is computed for the tau-jitter loop and compared to that of the more complex delay lock loop.

This paper is concerned with new results on data related false lock of Costas loops caused by arm filter distortion of the data. The false lock phenomena is demonstrated to occur for random as well as periodic data and the relative levels of lock are predicted. It is shown that, for the case of random data with Manchester symbols, strong lock points exist when the incoming carrier frequency and the loop VCO frequency differ bynR_{s}/2 (n = 1, 2, 3, ...)Hz where Rsis the data symbol rate. In addition to the loop error signal the lock detection signal(I^{2}Q^{2})is also analyzed for false lock effects. The theory also applies to the case of NRZ data symbols with the main result being strong false lock points also occur at VCO frequency offsets ofnR_{s}/2 (n = l, 2, 3, \ldot)but at different levels than the Manchester data. The results of these analyses lead to schemes capable of detecting false lock.

A solution to the mean time to lose lock for a first order, pseudo-noise, code tracking loop is derived for both the fulltime delay-lock loop and the time-shared delay lock loop, with both utilizing an early-late gate size of 1/2 chip, and assuming ideal bandpass filters. The result allows a spread spectrum system designer to assess the slip time performance of his code tracking loop by a simple calculation and then a reading of a curve presented in this paper. The results presented here are actually very general and apply to other code loop spacings and types. It also applies to carrier tracking loops and agrees with the carrier loop result of Viterbi [3].

The false (sideband) lock problem in Shuttle Costas loop receivers, in the presencse of noise, is assessed in this paper. False lock margin is defined depending on symbol signal-to-noise ratio rather than in the absence of noise as reported earlier in [4], [5]. Closed form results are given when the arm filters of the Costas loop are one-pole Butterworth filters as used in the Shuttle receivers. However, the approach taken is also general enough to cover filters of arbitrary characteristics. As part of the development of the false lock margin, it is shown that the false lock phenomenon of the squaring loop is identical to that of the Costas loop.

This paper develops the mean and variance of the time to acquire for single dwell time PN-type spread-spectrum systems. A model is specified, and then exact results are obtained by use of the generating function for the acquisition process. The paper is somewhat tutorial in that the analysis technique is developed in a logical step-to-step manner for the Markov chain model and can be readily used on other models. The effects of Doppler and other imperfections of the original model are discussed. Finally the results of the double dwell time system are presented and the appropriate modifications for Doppler effect are given.

A simple second-order digital phase-locked loop has been designed to synchronize itself to a square-wave subcarrier. Analysis and experimental performance are given for both acquisition behavior and steady-state phase error performance. In addition, the damping factor and the noise bandwidth are derived analytically. Although all the data are given for the square-wave subcarrier case, the results are applicable to arbitrary subcarriers that are odd symmetric about their transition region.

A new mechanization of a first-order all digital phaselocked loop (ADPLL) is discussed and analyzed. The purpose of the loop is to provide continuous tracking of the incoming waveform corrupted by the presence of white Gaussian noise (WGN). Based on a random-walk model, solutions are obtained for the steady-state timing-error variance and mean time to slip a cycle. As a result of the mean first-time-to-slip analysis, a difference equation and its solution are obtained that generalize a result of Feller [1]. Using a procedure that appears new, an upper bound on the timing-error bias due to a Doppler shift of the synchronized waveform is also derived. An example, for which the results presented here are applicable, is considered in some detail.

The maximum-likelihood estimate based on order statistics for both a single-sample and anM-sample estimate are derived for the first-order Reed-Muller code sent over a zero-mean white Gaussian noise channel. The estimation method is subject to an equipment-complexity constraint. The constraint imposed requires that the estimates be obtained from successive comparisons of the correlations in a serial system, without the use of arithmetic operations. The maximum-likelihood estimates obtained here are compared to that of Posner [1], Posner et aL [2], and also the unrestricted maximum-likelihood estimate.