William J. Hurd

High Dynamic GPS Receiver Using Maximum Likelihood Estimationand Frequency Tracking

A new high dynamic global positioning system (GPS) receiver ispresented and its performance characterized by analysis,simulation, and demonstration. The demonstration receiver is abreadboard model capable of tracking a single simulated satellitesignal in pseudorange and range rate. Pseudorange and range rateestimates are made once every 20 ms, using a maximum likelihoodestimator, and are tracked by means of a third-order fadingmemory filter in a feedback configuration. The receiver trackspseudorange with rms errors of under 1 m when subjected tosimulated 50 g, 40 g/s circular trajectories. The tracking thresholdis approximately 28 dB·Hz, which provides 12 dB margin relativethe the minimum specified signal strength, assuming 3.5 dB systemnoise figure and 0 dB antenna gain.

Digital Transition Tracking Symbol Synchronizer for LOW SNR Coded Systems

In coded telemetry systems symbol synchronization must be performed at low symbol signal-to-noise ratios ( ST/N_{0} ) with negligible degradation from the perfect synchronization case. A digital transition tracking synchronizer which operates with less than 0.03-dB degradation at ST/N_{0} = -3 dB and at rates of 5.6 bit/s to 250 kbit/s is described.

Correlation function of quantized sine wave plus Gaussian noise

The output correlation function is derived for an N -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.

A method to dramatically improve subcarrier tracking

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/. >

Improved Carrier Tracking by Smoothing Estimators

Smoothing as a way to improve the carrier phase estimation is proposed and analyzed. The performance of first-and second-order Kalman optimum smoothers are investigated. This perfomance is evaluated in terms of steady-state covariance error computation, dynamic tracking, and noise response. It is shown that with practical amounts of memory, a second-order smoother can have a position error due to an acceleration or jerk step input less than any prescribed maximum. As an example of importance to the NASA deep space network (DSN), a second-order smoother can be used to track the Voyager spacecraft at Uranus and Neptune encounters with significantly better performance than a second-order phaselocked loop.

Carrier Tracking by Smoothing Filter Improves Symbol SNR

The potential benefit of using a smoothing filter to estimate a carrier phase over use of phase-locked loops (PLL) is determined. Numerical results are presented for the performance of three possible configurations of an all-digital coherent demodulation receiver. These are residual carrier PLL, sideband-aided residual carrier PLL, and finally sideband aided with Kalman smoother. The average symbol SNR after losses due to carrier phase estimation is computed for different total power SNRs, symbol rates, and symbol SNRs. It is found that smoothing is most beneficial for low symbol SNRs and low symbol rates. Smoothing gains up to 0.7 dB over sideband-aided residual carrier PLL, and the combined benefit of smoothing and sideband aiding relative to residual carrier loop is often in excess of 1 dB.

Degradation of signal-to-noise ratio due to amplitude distortion

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. >

Spacecraft demonstration of sequential decoding using Lunar Orbiter V (Corresp.)

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 of 10^{-4} can be attained using sequential decoding with 2 dB less signal-to-noise ratio than required to attain an error probability of 10^{-4} using a (32,6) biorthogonal code and maximum-likelihood decoding.