Until quite recently spread spectrum techniques were almost exclusively in the military domain. Their use in GPS and the latest cellular phones will be followed by many other civil applications. This article, the first of [two] parts, examines the technology by describing an experimental direct sequence voice transmission system as a worked example.
However the rationale of using the very wide bandwidths required by Spread Spectrum systems needs explanation. Claude Shannon produced a ground breaking paper on the mathematical theory of communication in 1949. Shannon's resulting theorem can be expressed as:
where C = data rate in bits per second, W = bandwidth (Hz), S = average signal power (W), N = mean white gaussian noise power (W). It can be seen from the equation that the only options available to increase a channel's capacity are to increase either the bandwidth (W) or the signal to noise ratio (S/N).
An increase in the signal to noise ratio requires an increase in transmitter power as the noise within the channel is beyond our control! Thus we can either trade power or bandwidth to achieve a specified channel data rate. Because of the logarithmic relationship, increasing the power output is often unrealistic. However if frequency allocation constraints permit, the bandwidth can be increased. An appreciable increase in data capacity or signal to noise ratio (for a fixed data rate) can then be achieved.
Spread spectrum systems utilise very wide bandwidths and low signal to noise ratios. From Shannon's theorem:
changing bases
By logarithmic expansion
In a spread spectrum system the signal to noise ratio (S/N) is typically small, much less than 0.1
From the derived relationship it can be clearly seen that a desired signal to noise ratio for a fixed data rate C, can be achieved by increasing the transmission bandwidth.
For example, assume a data rate of 32 Kbits-1 and a signal to noise ratio of 0.001 (-30 dB)
So for a data rate of 32 Kbits-1, operation at the very low S/N ratio of -30db is achievable by spreading the signal over a bandwidth of 22 MHz. By using a very much wider bandwidth than that of the original data it is possible to maintain data capacity without increasing the transmitter output power. It is an extreme example of a power-bandwidth trade off.
Two criteria (see Dixon) for a spread spectrum system are:
However should the receiver not be synchronised to the transmitter or a conventional receiver be used, nothing will be heard unless the transmitter hops onto the receiver's tuned frequency. As a frequency hopping transmitter typically hops over tens to thousands of frequencies per second (the hop rate), the time it stays on a particular channel (the dwell time) is very short and as a result the signal would appear as a burst of interference.
The other major spread spectrum technique is known as direct sequence or pseudo-noise. In this technique a pseudo-random code directly phase shift keys the carrier increasing its bandwidth (see Figure 2). In a typical direct sequence system a double-balanced mixer (DBM) is driven by the PN code to switch a carrier's phase between 0 degrees and 180 degrees. This is known as biphase shift keying (BPSK) or sometimes phase reversal keying (PRK). Unlike a frequency hopping transmitter where the pseudo-random sequence commands a synthesiser to change frequency, the direct sequence signal is directly generated by the pseudo-random sequence.
The receiver despreads this wideband signal by using an identical synchronised pseudo-random code to that in the transmitter. As with the frequency hopper, the receiver must use a circuit to adjust its clock rate so that the receiver's pseudo-random code is at the same point in the code as the transmitter. A tracking circuit is necessary to maintain synchronism once it has been attained.
Obviously some modulation formats are less suitable than others. Amplitude modulation and its derivatives are the least desirable as their use will destroy the signal's uniform power spectral density. This constant carrier envelope is very desirable for spread spectrum systems designed for covert usage.
Frequency modulation (frequency shift keying for data) is often used in frequency hopping systems, but is infrequently used in direct sequence systems. This is because when a direct sequence signal passes through a squaring or frequency doubling circuit, a carrier at twice the signal's centre frequency is produced. This twice frequency narrowband carrier will contain any modulation impressed on the direct sequence signal. Thus with analogue modulation it is possible for the signal to be demodulated without any prior knowledge of the pseudo-random spreading code.
One of the commonest modulation techniques used in conjunction with direct sequence is known as code inversion or modification. The digitised voice or digital data is exclusive ORed with the PN spreading code. This will invert the PN code sequence if the data is a "1" or pass the PN code unmodified if it is a "0". Provided that the data stream is synchronised with the PN code, the correlation properties of the code are unaffected.
Assuming synchronisation at the receiver, the unmodified code despreads the direct sequence signal. This produces a narrowband signal which is still biphase shift modulated, but this time with the data or digitised speech. This signal can then be demodulated by a conventional biphase shift demodulator such as a squaring or Costas loop demodulator.
This code modification modulation is simple to implement in the transmitter and relatively easy to demodulate in the receiver. It also has the advantage of providing message privacy which the analogue modulated direct sequence signal does not have. It should be noted that it is possible to directly demodulate uncorrelated spectral components of an analogue modulated direct sequence signal should the demodulating receiver be very close to the transmitter. In addition the code modification technique preserves the constant power envelope of the direct sequence signal.
One disadvantage of code modification is that voice or other analogue signals require digitisation. As in any system design, the selection of the digitisation technique is very important. The technique selected must use the lowest possible data rate as data rate is inversely proportional to the process gain of the system. The technique selected for the system described uses a enhanced form of delta modulation to digitally encode the voice into a serial data stream.
At the receiver, the transmitted pulses are integrated and passed through a low-pass filter to remove unwanted high frequency components. The output consists of the original analogue signal together with some additional noise somewhat similar to quantisation noise.
Continuously Variable Slope Delta Modulation (CVSD) takes advantage of the fact that voice signals do not change abruptly and that there is only a small change from one sample to the next. A reasonably good reproduction can be obtained by transmitting in a given interval whether the output signal should increase or decrease. A linear delta modulated system has the undesirable feature that there is one input level which maximises the signal to noise ratio. In CVSD this is overcome by compressing the large amplitude in the signals relative to the smaller ones prior to encoding using a compressor circuit. In this way the input level to the encoder can be maintained close to the value which gives the maximum signal to noise ratio.
The receiver decodes the delta modulated binary stream and passes the analogue signal through an expander to counteract the effects of the transmitter compressor. Companding is optimised for the human voice. CVSD is considerably more effective than standard delta modulation and also exhibits less serious sound degradation in the presence of digital noise interference than PCM.
The system is described in functional blocks. First, the transmitter direct sequence modulator. The exciter's clock frequencies are provided by a master 4 MHz crystal oscillator and a divider. Power-up reset (with manual override) is configured around a Schmidt-trigger.
A shift register and exclusive OR gates are configured as a 4 MHz 127 chip (code bit) long maximal pseudo-random code generator (see section pseudo-random codes and generation).
Microphone audio is amplified by the VOGAD (Voice Operated Gain Adjusting Device) to the optimum level for the input of the delta modulator. The delta modulator converts the audio into a 32 Kbits-1 serial data stream (see column sending data with spread spectrum). This serial binary data stream must be coded into a format which is polarity insensitive because the receiver demodulator cannot recover the de-spread data's absolute phase. Only data transitions are recovered at the receiver, hence there is no way of determining whether the output data stream is inverted or not.
The digitised audio is converted from a non return to zero (NRZ) format into a polarity insensitive diphase (biphase-mark) data stream. This sub-circuit produces a diphase signal (Figure 4), where a logic 1 has start, mid-bit and end transitions and a logic 0 has only start and finish transitions.
In addition to providing phase insensitive data transmission the format also makes clock recovery at the receiver relatively easy, as unlike NRZ even a continuous stream of diphase encoded 0's results in many start and finish data cell transitions. The diphase encoded delta modulated digital voice signal is ex-ORed with the pseudo-random code producing a code modified PN spreading code.
The data modified PN code from the output of the exclusive-OR gate provides a balanced drive (plus or minus 24 mA as an AC logic family device has equal sink and source currents) via a coupling capacitor and 50 ohm matching pad, to a double balanced mixer (DBM) configured as a biphase shift keyer.
The PN code output alternately sinks and sources current, causing the diodes in the DBM to alternately switch on and off producing 180 degree phase reversals in the 435 MHz carrier signal (see Figure 5). The output spectrum consists of a series of symmetrical sidebands which have a Sinc2x distribution due to the many frequency components of the pseudo-random code.
As the spreading code has a pseudo-random character, the occurrence of a particular frequency is pseudo-random in time and the direct sequence output appears as noise on a spectrum analyser. The spread spectrum signal has a main lobe bandwidth of 8 MHz (twice the PN code clock rate for BPSK). This is amplified by a MAR8 MMIC (monolithic microwave integrated circuit) and further amplified to around 100 mW by a Motorola CA4812 Class A Amplifier module. Helical band pass filtering is used to ensure that the output signal is within the permitted bandwidth before free-space transmission.
where,
BWRF = 3dB bandwidth of the transmitted spread spectrum signal (Hz). Rinfo = data rate of the information transmitted (bits per second).
For a direct sequence signal, BWRF is assumed to be equal to the 3 dB bandwidth of the spectrum (which is 0.88 times the pseudo-random code clock rate for a biphase shift keyed direct sequence system). For a frequency hopping system BWRF is equal to m times the channel bandwidth where m is the number of frequency channels available.
Jamming Margin. Although the process gain is directly related to the interference rejection properties a more indicative measure of how a spread spectrum system will perform in the face of interference is the jamming margin (Mj). The process gain of a system will always be greater than its jamming margin.
where,
Lsystem = system implementation losses (dB); Gp = process gain (dB); (S/N)out = signal to noise ratio at the information output. (dB)
A spread spectrum system with a 30 dB process gain, a minimum required output signal to noise of 10 dB and system implementation loss of 3 dB would have a jamming margin of 30-(10+3) dB which is 17 dB. The spread spectrum system in this example could not be expected to work in an environment with interference more than 17 dB above the desired signal.
Power Spectral Density. By nature of the spreading process, the output power of the spread spectrum transmitter is spread over typically many megahertz of bandwidth. The spectral density is the number of Watts of radio frequency power present per Hertz of bandwidth. Thus for a direct sequence transmitter of 1W output and a spread bandwidth of 8MHz the power spectral density is:
For a conventional AM transmitter, power spectral density is around
some 31dB greater.
The advantage to the military user is that the signal strength apparent to a conventional narrowband receiver is very, very low and would probably not be recognised as a communications signal, hence the expression "Low Probability of Intercept" and "Low Probability of Recognition".
Auto-correlation: This is a measure of similarity between a signal and a time shifted replica of itself. Auto-correlation is a special case of cross-correlation. The auto-correlation function is the fundamental theoretical basis of spread spectrum communications.
Biphase Shift Keying (BPSK): A phase shift keying technique where the carrier phase changes between 0 degrees and 180 degrees (0 and pi radians) under the control of a binary code. BPSK is frequently used to generate direct sequence spread spectrum signals, where the binary code is a pseudo-random sequence.
Chip: A single element of the spreading code. This may be one or more of the PN code bits, depending on the modulation technique used. For BPSK one chip represents one code bit, whereas for quadrature phase shift keying (QPSK) one chip represents two code bits.
This is because there are four states for QPSK (0, 90, 180 and 270 degrees) and only two states for BPSK (0 and 90 degrees). Obviously two binary bits are required to represent four states and only one bit for two states.
Code: The term code usually refers to the pseudo-random code used to control the modulation technique used to spread the carrier.
Code Division Multiple Access (CDMA): A multiplexing technique where each user is given a different pseudo-random spreading code. To communicate with a particular user, the sender must select the code assigned to that user.
If the CDMA codes are carefully selected to ensure good correlation properties, then unwanted CDMA transmissions will not be correlated and hence rejected as wideband interference (up to the limit of the jamming margin Mj of the system). This technique can permit many users to operate simultaneously on the same frequency.
Correlator: A device to measure the similarity of two signals. Sometimes referred to as a de-spreader in direct sequence systems.
Costas Loop: A compound phase locked loop sometimes called an I-Q (In-phase/Quadrature phase) loop. It is used for demodulating double-sideband suppressed carriers (DSBSC) which is the modulation format of a biphase phase-shift keyed signal.
Cross-correlation: This is a measure of the similarity of two signals.
Delay Locked Loop: A tracking circuit which ensures the direct sequence receiver PN clock tracks (follows) any variation in the transmitter's PN clock rate once synchronisation has been achieved. (See column The Delay Locked Loop).
Delta Modulation: A analogue to digital conversion technique (see column Sending Data with Spread Spectrum).
Diphase (biphase-mark): A polarity-insensitive waveform, where a transition occurs at the beginning of every data period. A logic 1 is represented by a transition one half period later. There is no second transition for a logic 0.
Direct Sequence (ds): A spread spectrum modulation technique where a pseudo-random code directly phase modulates a carrier, increasing the bandwidth of the transmission. The resulting signal has a noise-like spectrum. The signal is despread by correlating with a pseudo-random code identical to and in synchronism with the code used to spread the carrier at the transmitter.
Frequency Hopping (fh): A spread spectrum modulation technique where the transmitter frequency hops from channel to channel in a predetermined but pseudo-random manner. The signal is de-hopped at the receiver by a frequency synthesiser controlled by a pseudo-random sequence generator synchronised to the transmitter's pseudo-random generator.
Jamming Margin (Mj): A measure of a spread spectrum system's resistance to jamming or un-intentional interference, (see column Spread Spectrum Terminology).
Linear Codes: Pseudo-random codes generated using only modulo-2 addition or subtraction,(see column Pseudo-random Codes and their Generation).
Maximal Code: A maximal code is the longest that can be generated with a feedback type pseudo-random generator (see column Pseudo-random Codes and Generation).
Process Gain (Gp): The measure of the gain or signal-to-noise improvement exhibited by a spread spectrum system by nature of the spreading and de-spreading process.
Pseudo-noise: Code sequences which have noise-like properties. The term pseudonoise (pn) is often used for direct sequence systems which use such codes to spread the carrier.
Sinc x: Sinc x is the mathematical term for the following expression:
A BPSK spread spectrum has a Sinc2x power spectrum.
Squaring Loop: A BPSK (or DSBSC) demodulator which regenerates the suppressed carrier through a frequency squaring (or doubling) process. This doubling process produces a twice frequency unmodulated carrier, which when divided by two can be multiplied with the input BPSK signal to recover the data.
In next month's issue: detailed transmitter circuitry