Detecting Pseudo-Noise
(PN) Spread Spectrum
Signals

Maurice L. Schiff, Ph.D.
Vice President, Adv. Systems
ELANIX Inc.,
Westlake Village, CA 91632

Introduction

There have been several articles in this magazine describing the applications of PN spread spectrum systems, and how they are generated. Figure 1 shows the basic elements of a spread spectrum signal as generated by our System View simulation software. The information source is multiplied by a spreading code having a much higher data rate. This signal is usually PSK modulated and filtered before transmission. The channel adds white noise. At the receiver, the PSK demodulator reproduces the baseband spread signal. The spreading code is available at the receiver. After a synchronizing operation the local code is multiplied with the received signal. This last action removes the spreading code leaving the original data behind.

A major area of use is communications, where the anti-jam and covert nature of these signals is of value. From a generals monitoring standpoint, detecting and characterizing these signals is also important. In this article we will describe one such detection technique, the chip rate detector.

Direct Sequence PN Spread Spectrum

In its simplest form, a PN system takes the digital data and multiplies it with a spreading code having a much higher data rate. This action, among other things reduces the power spectral density, (PSD), of the signal as seen on a spectrum analyzer. The area under the PSD curve is the power associated with the signal. The multiplication process does not change the power, but does widen the bandwidth. To accommodate this wider bandwidth, the height of the PSD is reduced correspondingly. Eventually the signal PSD will fall below the ambient noise level of the intercept receiver, and become invisible to a spectrum analyzer. No matter how small the analyzer resolution bandwidth is, the signal will never 're-appear'.

Figure 2 shows this effect in the frequency domain. For illustration purposes, the PN spreading code has a rate 10 times (10 dB processing gain) higher than the basic signal. Note the nulls in the PSD spectra differ by a factor of 10, and the peak of the wideband PN, PSD is 10 dB lower, In a real spread spectrum application the spread rate would be at least 100, and commonly up to 1000. Once the spread signal is generated, the most common from of RF modulation is binary phase shift keying (BPSK).

Chip Rate Detector

The chip rate detector, shown in Figure 3, is simple in concept. The operation consists of multiplying the signal with a delayed version of itself followed by some form of spectral analysis. The basics of this operation are shown in Figure 4.

The top trace is a basic PN signal. The middle trace is this signal delayed by one half of the chip rate. The bottom trace is the product signal. We have represented the 1's, and the product detector is a straight multiplier. His is equivalent to representing the signal as logic 1, or 0, and using an exclusive or as the multiplier.

The fundamental point of Figure 4 is that the product signal is al ways a+1 where the original and delayed version over lap in time. This is true whether the data was a +1 or a -1. The product signal then contains two parts; (1) a series of +1 coherent pulses one half chip wide and one half chip apart, and (2) a random pulse train known as the self noise which fills the gaps between coherent pulses. When viewed on a spectrum analyzer, this composite signal appears as shown in figure 5. The PSD of the coherent pulse train contains only discrete lines at frequencies which are multiples of the PN chip rate, hence the name of the detector. The self noise PSD is a continuous spectra with the familiar sin(x)/x form.

It is easy to show that when the delay is one half the chip time , the power contained in the fundamental chip rate line is at a maximum. Further, the spectra then only contains odd harmonics of the basic rate, and there harmonics to warrant the hardware resources to process them.

If the chip rate of the signal is not known apriori, a search procedure is required. The search parameter is the delay. If the delay is greater than the actual chip rate, no rate line will be produced. If the delay is much shorter, then the rate line power will be too small to detect. Fourier analysis of a pulse train shows that as long as the delay is within the range .25 t < t < .75t , then the power in the rate line will not fall below 3 dB of its maximum value when t=t /2.A general search procedure can then be set up by stepping the delay line over values that are compatible with the range of chip rates of interest.

The discrete chip rate lines have (theoretically zero bandwidth. This means that the spectrum analyzer or equivalent FFT operation bandwidth can be reduced to any arbitrary limit without losing any signal power. By contrast, the noise spectra is continuous in nature. Thus, as the detection bandwidth is reduced, the noise power is reduced accordingly. No matter how weak the PN signal is, it is always possible to filter the chip rate line to the point where it becomes detectable.

Conclusion

This article presented the basic concept of a chip rate detector which is capable of detecting PN spread spectrum signals. It is a practical algorithm that can recover all of the external data associated with the signal namely; (1) the chip rate, (2) the carrier frequency, and (3) the relative time of arrival of the chip transitions. In addition, the detector works equally well on higher order modulations such as QPSK.

For more information about System View (available at $985), its features and other applications please call or FAX us.

ELANIX, Incorporated
Tel: 818597-1414
FAX 818-597-1427
5655 Lindero Canyon Road
Suite 304
Westlake Village, CA 91362

Enhanced SS Analysis
Capabilities for ACOLADE

The ICUCOM Corporation has released Version 3.2 of ACOLADE, the graphics-based CAE software package for the design, simulation and analysis of communication systems. This new version has features that further enhance ACOLADE'S already powerful spread spectrum utility.

"ACOLADE now contains the most advanced and comprehensive spread spectrum simulation capabilities of any package of the market", said DR. Kurt Matis, President of ICUCOM. "Included are Direct Sequence and Frequency Hopped modulations, as well as a wide variety of spreading codes including Gold codes, Kasami sequences, bent sequences and others. ACOLADE has been successfully used to evaluate a wide variety of spread spectrum applications, including jammer rejection, code division multiple access, multi-path reduction, and low probability of intercept applications utilizing PC hardware and ACOLADE user designs the communication system of choice by placing, connecting and parameterizing blocks -- chosen from the hundreds of selections from the ACOLADE Model Library -- on the screen. Custom code is also easily integrated. Being a free topology system, ACOLADE supports full multi-layer hierarchical design. After initial design, the system can be tested, explored and r efined using a comprehensive variety of simulation and analysis tool. These include "quick-look"analysis, full Monte Carlo Simulation, sophisticated waveform analysis and bit error rate plots. The user interface is a modern "point and click"Windowslike GUI design.

The system is priced at $8,000, and a UNIX version will soon be released. Contact:

Mr. Indy Pommers
Amber Technologies, Inc.
508-369-0515

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