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.>

The design of digital phase locked loops (DPLL) using estimation theory concepts in the selection of a loop filter is presented. The key concept, that the DPLL closed-loop transfer function is decomposed into an estimator and a predictor, is discussed. The estimator provides recursive estimates of phase, frequency, and higher-order derivatives, and the predictor compensates for the transport lag inherent in the loop.>

The effect of filtering on the signal-to-noise ratio (SNR) of a coherently demodulated band-limited signal is determined in the presence of worst-case amplitude ripple. The problem is formulated as an optimization in the Hilbert space L/sub 2/. The form of the worst-case amplitude ripple is specified, and the degradation in the SNR is derived in closed form. It is shown that, when the maximum passband amplitude ripple is 2 delta (peak-to-peak), the SNR is degraded by at most (1- delta /sup 2/), even when the ripple is unknown or uncompensated. For example, an SNR loss of less than 0.01 dB due to amplitude ripple can be assured by keeping the amplitude ripple under 0.42 dB.>

A method is presented for achieving a considerable improvement in phase tracking of square-wave subcarriers or other square waves. The amplitude of the phase quadrature reference signal is set to zero, except near the zero crossings of the input signal. Without changing the loop bandwidth, the variance of the phase error can be reduced by approximately W sigma /sub 0//sup 2/ where sigma /sub 0//sup 2/ is the phase error variance without windowing and W is the fraction of cycle in which the reference signal has a nonzero value. Simulation results confirm the results of the analysis and establish minimum W versus SNR (signal-to-noise ratio). Typically, the window can be made so narrow as to achieve a phase error variance of 1.5 sigma /sub 0//sup 4/.>

Some new algorithms are presented for efficiently generating pseudorandom noise both in hardware and software. In software, a new word of pseudorandom bits can be generated about every 12 machine cycles, and hardware implementations can generate pseudo Gaussian noise with bandwith of 20 MHz or more. The algorithms generate binary maximal-length linear recursive sequencies of high degree and with many nonzero terms. The ability to efficiently implement high-degree recursions is important because the number of consecutive bits which can be guaranteed to be both linearly and statistically independent is equal to the degree of the recursion. The implementations are by interconnection of several short shift registers in a linear manner in such a way that different widely spaced phase shifts of the same p-n sequence appear in the stages of the several registers. Some specific algorithms have been subjected to extensive statistical evaluation, with no evidence found to distinguish the sequences from purely random binary sequences.

The performance of a sequential decoder on data transmitted on a spacecraft link was demonstrated on February 26, 1968, culminating a series of experiments utilizing Lunar Orbiter V and the Deep Space Net (DSN) Echo station. It was demonstrated that sequential decoding can perform on a spacecraftlink as well as was predicted by theoretical results and laboratory experiments. Performance is significantly better than that of practical block codes. For example, an erasure probability of10^{-4}can be attained using sequential decoding with2dB less signal-to-noise ratio than required to attain an error probability of10^{-4}using a(32,6)biorthogonal code and maximum-likelihood decoding.

The output correlation function is derived for anN-step, symmetric amplitude quantizer when the input is the sum of a sine wave and stationary, zero mean, Gaussian noise. The derivation, which follows the transform method of Rice, Bennett, and Middleton, is perfectly general in that there are no restrictions on the quantizer characteristic or the signal or noise powers. Results of previous studies are restricted to quantizers with uniform steps or to cases in which the rms amplitude of the input is small compared to the amplitude range covered by the quantizer. For low signal-to-noise ratios, approximations can be made which greatly simplify the calculations. These approximations are described, and graphical results are presented for two, three, and four bit linear quantizers when the input noise spectrum is rectangular narrow-band and the SNR is small.