Phase digitizing: a new method for capturing and analyzing spread-spectrum signals - includes related article on a method of reading a counter on the fly - technical

Hewlett-Packard Journal, Feb, 1989 by David C. Chu

Phase Digitizing: A New Method for Capturing and Analyzing Spread-Spectrum Signals

PRECISE AMPLITUDE MEASUREMENT has been the basis of many traditional instruments. Oscilloscopes, spectrum analyzers, power meters, and voltmeters all focus on precise analog voltage as their basic measurement. Even a vector analyzer, which measures both amplitude and phase, does so by measuring two analog voltages: the I and Q modulation components.

This preoccupation with precise analog amplitude in instrumentation is at variance with modern modulation methods, which tend to deemphasize analog amplitude modulation in favor of frequency, phase, and time modulation for more reliable communication. Not only ordinary FM, PM, and pulse width modulation, but also modern FSK, PSK, and QPR in communications in Barker (binary phase), polyphase, and chirp modulation in radar, all deemphasize amplitude in favor of time-based parameters. Even QAM signals contain more information in the phase than in the amplitude. For these signals, fidelity is characterized by precision in frequency, phase, and time. Interest in amplitude is often connected with studying dropouts only.

The frequency agile signal, which is active over a wide frequency range in a short period of time, poses another challenge to many established practices in instrument design. Techniques such as quasistatic range switching to cover different frequency bands, searching for a signal with a sweeping narrowband receiver, or taking time to phaselock to a signal are no longer appropriate with the agile signal. Another difficulty is that some signals are not repeatable, at least not well enough to be measured by equivalent-time techniques. The output of a pulsed VCO and the waveform of on oscillator acquiring lock with another are examples of signals that are different on each occurrence. Often, it is statistical variations, such as jitter, and not just an average value, that are of interest. These can only be measured with repeated single-pass measurements, even though the signal is nominally repetitive. Measurement methods that require multiple passes for one measurement are not applicable.

In short, traditional narrowband, amplitude-based instruments requiring repetitive signals are suddenly found wanting when confronted with frequency agile, time-encoded or phase-encoded signals that do not repeat.

Amplitude Digitizing

The waveform recorder (or high-sampling-rate digitizing oscilloscope) is wideband and can capture a transcient spread-spectrum signal by digitizing its voltage, taking samples regularly spaced over time. While this is a good way to view the waveform, it is a difficult and inefficient method of characterizing the signal's modulation fidelity.

Consider a modulated signal with an agile frequency carrier randomly hopping about. To capture the waveform without aliasing requires sampling above the Nyquist rate. For such a signal, the sampling rate must be more than twice (closer to four times in practice) the highest carrier frequency plus modulation. Since the modulation (information) bandwidth is always less, and often much less, than the waveform bandwidth, sampling for full waveform recovery is grossly inefficient, resulting in unnecessary data bulk, if only the information is of interest. Apart from this, processing the data to uncover the modulation is a complex and difficult process since the data is in the form of voltage, that is, v(t.sub.i.), where v(t) may take on the form v(t) = [V.sub.o + V.sub.a.(t)]sin[2[pi]f(t)t + [theta](t)] and any of the three--the amplitude V.sub.o at V.sub.a.(t), the frequency f(t), and the phase [theta](t), may change with time depending on the modulation type. Selecting the optimum band-limited functions V.sub.a.(t), f(t), and [theta](t) to fit a set of v(t.sub.i.) means iterative curve fitting to trigonometric functions with complicated and possibly discontinuous arguments, an incredibly messy operation "prone to undersirable convergence behavior because of the nonlinear behavior relationship between parameters." This is true when V.sub.a., f, and [theta] are constants. The complexity of fitting to variable parameters is simply staggering.

A less sophisticated but more effective approach is to find the locations of peaks and zero crossings. For a properly band-limited signal, interpolation between samples using digital signal processing allows computation of a voltage given a time. Computing a zero crossing time is the reverse; one computes a time given a voltage (zero). For slow-slewing signals, a combination of (sin x)/x interpolation and linear approximation may enhance the resolution of zero-crossing time measurements below one sampling period. Using this technique and counting the crossings in software, Nichols simulated a frequency counter with a variable gate for frequency profiling. Unfortunately, for binary-voltage fast-switching signals, there is no timing resolution enhancement, the precision voltage measuring capability of the waveform recorder is not really being used, and the resulting counter performance is poor.