Question 4 of 5: Spread Spectrum Modulation

Question 4: 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 a direct-sequence system the binary data stream, running at a bit rate $R_b$, is multiplied bit by bit with a pseudo-noise (PN) sequence running at a much higher chip rate $R_c$. The PN sequence is a deterministic but noise-like binary waveform — typically generated by a maximal-length shift register — whose values are $\pm 1$, so the multiplication simply inverts the polarity of the carrier at the chip rate. Each data bit is thereby replaced by a fixed block of $N = R_c/R_b$ chips, and this ratio is the processing gain. The composite signal is then applied to a conventional modulator, almost always BPSK or QPSK, and transmitted.

Because the chip waveform changes $N$ times faster than the data, the null-to-null bandwidth of the transmitted signal is set by the chip rate rather than the bit rate, so the occupied bandwidth grows by the factor $N$. The total transmitted power does not change, which means the power spectral density — watts per hertz — falls by the same factor $N$. This is precisely the sense in which the technique is “spread spectrum”: the information occupies a bandwidth far greater than the minimum needed to carry it, and the spreading is driven by a code that is independent of the data. With enough processing gain the transmitted spectrum can sit below the receiver's own thermal noise floor, as sketched in Figure 4.1, which is why direct-sequence signals are described as having a low probability of intercept.

Detection reverses the process. The receiver downconverts coherently and multiplies the result by a locally generated replica of the same PN sequence, aligned in time with the incoming one; acquiring and then tracking that alignment is the hardest practical problem in a direct-sequence receiver and is usually handled by a sliding correlator followed by a delay-locked loop. For the wanted signal, multiplying by the PN sequence twice returns the original data because $c(t)\cdot c(t) = +1$ everywhere, so the wanted signal collapses back to its original narrow bandwidth. Any interferer, however, is being multiplied by the PN sequence for the first time, so it is spread out to the chip bandwidth. The integrate-and-dump filter that follows then accepts only the narrow data bandwidth and rejects the fraction of the spread interference that falls outside it, giving an effective improvement in signal-to-interference ratio equal to the processing gain. Narrowband jamming, partial-band interference and multipath echoes delayed by more than one chip are all suppressed by this mechanism, and the same correlation property allows several users with different, nearly orthogonal codes to share the band simultaneously — the basis of code-division multiple access.

Part (b) — Frequency-hopping spread spectrum.

A frequency-hopping system takes an entirely different route to the same end. The data are modulated onto a carrier in a conventional narrowband fashion — because the carrier phase is discontinuous across a hop, non-coherent schemes such as M-ary FSK are the natural choice — and the carrier frequency itself is then retuned at regular intervals under the control of a PN sequence. The PN generator drives a frequency synthesiser, and each output word selects one channel from a set of $N$ available hop channels spanning the whole allocated band. A hop that lasts longer than one symbol is called slow hopping; a hop faster than a symbol, so that one symbol is spread across several frequencies, is fast hopping and buys additional diversity against a fade or a jammer that happens to sit on one channel.

The sense in which this is “spread spectrum” differs from the direct-sequence case and is worth stating carefully, because it is what the question is asking. At any given instant the transmitted signal is not wideband: it occupies only the bandwidth of one hop channel. What is wide is the spectrum occupied over time, as the transmission visits all $N$ channels in pseudo-random order. Averaged over many hops the signal therefore looks like a wideband, noise-like emission covering the whole band, and the processing gain is the number of hop channels $N$ rather than a chip-to-bit ratio.

Detection requires the receiver to run an identical PN generator and synthesiser, synchronised to the transmitter so that it dehops by tuning to the same channel at the same moment. Once dehopped, the signal is a stationary narrowband carrier and an ordinary non-coherent FSK demodulator recovers the data. A narrowband jammer or an unrelated user can only corrupt those hops that land on its frequency; if that is a fraction $\rho$ of the band, only about $\rho$ of the symbols are hit, and an interleaver plus a forward-error-correction code across hops repairs them. This graceful behaviour under partial-band interference, together with the fact that hopping requires no wideband linear front end, is why frequency hopping is used for Bluetooth and for tactical military radio, whereas direct sequence dominates where the highest processing gain and multipath resolution are wanted. In Canada both approaches are operated licence-exempt in the industrial, scientific and medical bands under ISED Canada RSS-247, which sets the hopping and bandwidth conditions that a compliant design must meet.

Part (c) — Bursty traffic: spread spectrum against TDMA and FDMA.

Yes — for highly irregular traffic, spread-spectrum multiple access is generally the better fit, and the reason is the difference between reserved and shared capacity. Both FDMA and TDMA are fixed-assignment schemes: a user is granted a frequency slot or a time slot, and that resource is unavailable to anyone else for the duration of the assignment whether or not the user has anything to send. When traffic is bursty, the ratio of peak to average demand is large, so an allocation sized for the peak sits idle most of the time and an allocation sized for the average cannot carry the burst. Recovering that waste requires a demand-assignment protocol with a signalling channel, request and grant messages, and the associated latency and overhead — and for short bursts the reservation exchange can easily cost more than the data it schedules.

A spread-spectrum system has no such slots. Every user occupies the whole band all the time, separated only by code, so a station that has nothing to send simply stops transmitting and its share of the interference budget instantly becomes available to everyone else. Capacity in such a system is interference-limited rather than slot-limited: it degrades gradually as more users become active, instead of hard-blocking when the last slot is taken, and it benefits directly from the statistical multiplexing of many independent bursty sources whose peaks rarely coincide. The same voice-activity effect is what allows a code-division cellular system to carry more conversations than a slot-based one of equal bandwidth. Access is also immediate, since a station can begin transmitting on its code without waiting for a grant or for slot synchronisation, which matters most for exactly the short, unpredictable transmissions the question describes.

The qualification worth adding is that this advantage is statistical rather than absolute. If the number of simultaneously active users rises far enough, the accumulated multiple-access interference degrades everyone at once, and near–far effects mean that power control becomes essential; a fixed-assignment system, by contrast, protects the users it has admitted and simply refuses the rest. For steady, high-duty-cycle streams of known rate — a trunk carrying continuous traffic, for instance — TDMA or FDMA remains the more efficient and more predictable choice.