Question 5 of 5: Spread spectrum modulation

Question 5: Spread spectrum modulation (25 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Part (a) — direct sequence spread spectrum. In direct sequence spread spectrum (DSSS) the data waveform is multiplied, before modulation onto the carrier, by a pseudo-noise (PN) sequence running at a chip rate $R_c$ far higher than the bit rate $R_b$. Each data bit of duration $T_b$ is thus replaced by a fixed pattern of $N = T_b/T_c = R_c/R_b$ chips, and since the polarity of that pattern carries the bit, the transmitted waveform is a $\pm 1$ chip stream whose envelope is indistinguishable from noise to anyone without the code. The composite signal is then modulated conventionally, almost always with BPSK or QPSK, and radiated at the same total power the unspread signal would have used.

Detection reverses the operation exactly. The receiver generates a local replica of the same PN sequence and, once it has acquired and tracked chip and code timing, multiplies the incoming waveform by that replica. Because the sequence takes values $\pm 1$, multiplying twice returns $c(t)^2 = 1$ and the wanted signal collapses back to its original narrow bandwidth, whereupon an ordinary matched filter and BPSK detector recover the bit. Anything not carrying the same code is multiplied by an essentially random $\pm 1$ stream and is therefore spread by the despreading operation instead of being collapsed; the narrowband detection filter that follows then admits only a fraction $R_b/R_c$ of that interference power. The improvement is the processing gain, $G_p = R_c/R_b$, typically 10 to 30 dB, and it is the reason DSSS tolerates narrowband jammers and multiple simultaneous users on the same carrier. Acquisition of code phase is the practical price paid, and in a multipath channel the same code correlation properties allow a RAKE receiver to resolve and constructively combine echoes separated by more than one chip.

The technique is "spread spectrum" in the literal and most direct sense: the occupied radio-frequency bandwidth, roughly $2R_c$, is many times the minimum bandwidth the data rate would require, and it is spread continuously and instantaneously — at every moment the signal genuinely occupies the whole band, at a power spectral density reduced by the same factor $N$, often below the ambient noise floor.

Part (b) — frequency hopping spread spectrum. Frequency hopping spread spectrum (FHSS) achieves the same end by a different mechanism. The available band is divided into $N_{ch}$ channels, and a PN generator drives a frequency synthesiser so that the carrier moves from channel to channel according to a code-determined pseudo-random pattern, dwelling on each for a hop period $T_h$. Data are modulated onto whichever carrier is currently active. Because phase coherence is generally not maintained across a hop, the modulation of choice is non-coherent M-ary FSK rather than PSK. The system is described as slow hopping when one hop carries several symbols and fast hopping when several hops carry one symbol, the latter giving each symbol built-in frequency diversity at the cost of a much faster synthesiser.

Detection mirrors the transmitter: the receiver runs the identical PN generator, and once hop timing is acquired, its synthesiser dehops the incoming signal by mixing with the same sequence of local-oscillator frequencies, presenting a fixed intermediate frequency to a conventional non-coherent demodulator. An interferer or another user occupying one channel corrupts only the hops that happen to land there, so with error-control coding and interleaving across hops the damage is spread thin and correctable; an unsynchronised eavesdropper sees only brief unrelated bursts scattered across the band.

The sense in which FHSS is "spread spectrum" differs from DSSS and the distinction is exactly what the question is probing. At any instant the transmitted signal is narrowband, occupying only one channel. It is the time-averaged occupancy that is wide: over many hop periods the signal visits the entire hopping band, so the average power spectral density is that of a signal spread over $N_{ch}$ channels, and the processing gain is $G_p = N_{ch}$, the ratio of total hopping bandwidth to instantaneous channel bandwidth. DSSS spreads in frequency at every instant; FHSS spreads in frequency only when averaged over time, and both achieve the defining property of a spread-spectrum system, namely a transmission bandwidth set by a code rather than by the data.

Part (c) — where each is the right choice. Spread spectrum is the better answer when many uncoordinated users must share one band, when the interference environment is hostile or unknown, or when the channel is severely multipath. The clearest example is a licence-exempt 2.4 GHz industrial installation — Wi-Fi and Bluetooth devices operating under ISED RSS-247 in a plant or hospital, alongside microwave ovens and cordless equipment. No central authority can assign slots or channels to devices from a dozen vendors that come and go without notice, so an orthogonal scheme cannot be maintained; DSSS and FHSS degrade gracefully instead, since an extra user or a narrowband interferer raises the noise floor a little rather than colliding outright. Cellular CDMA, GPS and military anti-jam links belong to the same family, adding soft capacity, RAKE multipath combining and a low probability of intercept to the argument.

TDMA or FDMA is the better answer when the users are few, coordinated, and persistent, and when spectral efficiency is what the operator is paying for. A point-to-point licensed microwave backhaul, or a satellite transponder carrying a handful of high-rate carriers, is the natural example: the link budget is known, the users are assigned by a network operator rather than arriving at random, and there is no reason to give away a factor of $G_p$ in bandwidth. Orthogonal separation means one user's transmission contributes essentially nothing to another's noise, whereas in a CDMA system every additional user raises the multiple-access interference seen by all the others, so capacity is soft and power control becomes mandatory to solve the near-far problem — a strong nearby transmitter would otherwise swamp a distant weak one whose code offers only $G_p$ of protection. Where that discipline can be imposed cheaply by a frequency plan or a slot map, it should be, and the spread-spectrum machinery is unnecessary complexity.