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.

(a) Direct sequence spread spectrum (10 marks)

In direct sequence spread spectrum (DSSS) the data waveform is multiplied, before modulation, by a much faster pseudo-random binary waveform known as the spreading code or chipping sequence. If the data bits have duration $T_b$ and the code chips have duration $T_c$, the ratio $N = T_b/T_c$ is the number of chips per bit and is called the processing gain or spreading factor; a typical value is tens to hundreds. The product waveform is then applied to an ordinary carrier modulator, almost always BPSK or QPSK, so the transmitted signal is $s(t) = \sqrt{2P}\,b(t)\,c(t)\cos(2\pi f_c t)$, where $b(t) = \pm1$ carries the data and $c(t) = \pm1$ is the code.

Because $c(t)$ switches $N$ times faster than $b(t)$, the product $b(t)c(t)$ has the bandwidth of the code rather than of the data. The transmitted signal therefore occupies roughly $N$ times the bandwidth that plain BPSK of the same data rate would need, and since the total power is unchanged, the power spectral density is reduced by the same factor — often to the point where the signal sits below the receiver's thermal noise floor and is difficult even to detect without knowing the code. That bandwidth expansion, driven by a code independent of the data, is the precise sense in which the technique is “spread spectrum”: the occupied bandwidth is set by the spreading sequence and is far larger than the minimum required by the information rate.

Detection is the mirror image of the transmitter and is called despreading. The receiver generates a local replica of the same pseudo-random code, aligns it in time with the incoming chips — a two-stage process of coarse acquisition (typically a sliding correlator or a matched-filter search over code phase) followed by fine tracking (a delay-locked or tau-dither loop) — and multiplies the received signal by that replica. Since $c(t)^2 = 1$ for a $\pm1$ code, the wanted signal collapses back to its original narrow data bandwidth, and an ordinary coherent BPSK integrate-and-dump detector over each bit interval then recovers the data.

The benefit appears in what happens to everything the receiver did not want. Any interferer, jammer or other user's signal is uncorrelated with the local code, so multiplying it by that code spreads it across the wide bandwidth instead. The narrowband detector that follows then integrates only a fraction $1/N$ of the interferer's power while collecting all of the wanted signal, giving an SNR improvement equal to the processing gain, $G_p = T_b/T_c = B_{ss}/B_{data}$, commonly quoted as $10\log_{10}N$ dB. The same mechanism gives DSSS its other well-known properties: resistance to narrowband jamming, a low probability of intercept, resolvable multipath (echoes delayed by more than one chip decorrelate and can be combined constructively in a RAKE receiver), and code-division multiple access, in which many users share the same band simultaneously and are separated only by the low cross-correlation of their assigned codes.

(b) Frequency hopping spread spectrum (10 marks)

Frequency hopping spread spectrum (FHSS) achieves the same end by a different means: instead of widening the instantaneous bandwidth, it moves a narrowband signal rapidly and pseudo-randomly around a wide band. The available spectrum is divided into a set of $M$ hop channels, and a pseudo-random sequence — the hop pattern — drives a frequency synthesiser that selects one of those channels for each hop interval $T_h$. The data are modulated onto the resulting carrier, most commonly with a non-coherent scheme such as M-ary FSK, because the synthesiser cannot in general maintain carrier phase continuity across a hop.

The hop rate relative to the symbol rate defines the two regimes. In slow hopping several data symbols are sent per hop, which is simple to implement and is what Bluetooth uses (1600 hops/s over 79 or 40 channels in the 2.4 GHz ISM band). In fast hopping the carrier changes several times within a single symbol, so each symbol is spread over several channels and the receiver combines the pieces; this gives strong frequency diversity, at the cost of a much faster and more expensive synthesiser.

Detection requires the receiver to run the identical hop pattern in synchronism with the transmitter. After acquiring hop timing and phase, the receiver's synthesiser is stepped through the same channel sequence, and the incoming signal is mixed down to a fixed intermediate frequency where a conventional narrowband FSK demodulator recovers the symbols. From the demodulator's point of view the channel looks stationary; all of the hopping has been removed by the dehopping mixer.

The sense in which FHSS is “spread spectrum” differs subtly from DSSS and is worth stating explicitly. At any given instant the signal is narrowband — it occupies only one hop channel. It is the time-averaged spectrum, taken over many hops, that is spread across the full band, because the hop pattern visits every channel with roughly equal probability. The processing gain is correspondingly the number of hop channels, $G_p = M = B_{ss}/B_{channel}$. Interference rejection also works differently: rather than averaging a jammer down as DSSS does, FHSS simply avoids it most of the time. A narrowband jammer that occupies $J$ of the $M$ channels corrupts only the fraction $J/M$ of the hops, and those hits are then repaired by the error-control coding and interleaving that a practical FH system always carries. This makes FHSS particularly effective against partial-band jamming and against the near–far problem that troubles DSSS-CDMA, and it is why FHSS is preferred where the band is shared with strong, unco-operative narrowband emitters.

(c) Bursty traffic: spread spectrum versus TDMA/FDMA (5 marks)

Yes — for bursty, highly irregular traffic, spread spectrum is generally the more appropriate choice. TDMA and FDMA both work by reservation: a user is assigned a time slot or a frequency channel and holds it whether or not there is anything to send. When traffic is bursty, the assigned resource sits idle for most of its life, and the fixed capacity is wasted in exact proportion to the burstiness. Reassigning slots dynamically is possible but requires a signalling exchange for every burst, which adds latency and control overhead that can exceed the payload for short messages.

Spread spectrum with code-division multiple access instead lets every user transmit on the whole band at any time, separated only by code. There is no slot to reserve and no channel to request, so a station with a burst simply sends it. The cost of another simultaneous user is a small increase in the interference floor rather than the loss of a whole channel, so capacity is soft: the system degrades gracefully as load rises instead of blocking hard when the last slot is taken, and statistical multiplexing means the aggregate of many independent bursty sources loads the medium far more evenly than any one of them does. Random access without co-ordination also becomes practical, since two overlapping transmissions with different codes need not destroy each other the way two overlapping TDMA bursts would.

The qualification worth adding is that this advantage is a property of bursty, many-user traffic specifically. For a small number of users with steady, high-rate streams, TDMA/FDMA is the more spectrally efficient answer, because the reserved resource is never idle and none of the bandwidth is spent on spreading. It is precisely the mismatch between peak and average demand that spread spectrum exploits.