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.

This question is entirely qualitative: five five-mark parts, each expecting a short paragraph of correct mechanism rather than a calculation. The unifying idea is that both spreading techniques deliberately occupy far more bandwidth than the data rate requires, and buy interference immunity, multiple access and low probability of interception with that surplus bandwidth.

(a) Direct sequence spread spectrum (5 marks)

Modulation. The data stream, of bit rate $R_b$ and bit duration $T_b$, is multiplied bit by bit with a much faster pseudo-noise (PN) sequence of chip rate $R_c$ and chip duration $T_c \ll T_b$; each data bit is therefore represented by $N = T_b/T_c = R_c/R_b$ chips, and the composite $\pm 1$ chip stream is then applied to a conventional modulator, typically BPSK or QPSK. Because multiplication in the time domain is convolution in the frequency domain, the transmitted spectrum takes the shape of the chip waveform rather than the data waveform, and so occupies roughly $R_c$ hertz instead of $R_b$ hertz.

Detection. The receiver generates the identical PN sequence, aligns it with the incoming signal (acquisition, then tracking by an early–late or delay-locked loop), and multiplies again. Since the PN chips take values $\pm 1$, multiplying twice by the same sequence returns the original data, so the wanted signal collapses back to its narrow data bandwidth and can be recovered by an ordinary matched filter or integrate-and-dump correlator. Any signal not carrying that PN sequence — a narrowband jammer, or another user with a different code — is multiplied by the PN sequence only once, and is therefore spread across the wide band, so the post-correlation filter admits only a small fraction $1/N$ of its power.

The sense in which it is ‘spread spectrum’. The occupied bandwidth is deliberately made $N = R_c/R_b$ times larger than the data rate requires, with $N$ the processing gain. The transmitted power is unchanged, so the power spectral density is reduced in the same proportion — often below the receiver's own noise floor, which is what makes the transmission hard to detect or intercept. The spectrum is spread at every instant, which distinguishes direct sequence from hopping.

(b) Frequency hopping spread spectrum (5 marks)

Modulation. The data are modulated onto a conventional narrowband carrier — most often non-coherent M-ary FSK, because maintaining carrier phase across a hop is impractical — and the carrier frequency itself is retuned at each hop instant to a channel selected by a PN generator driving a frequency synthesiser. In slow hopping several symbols are sent per hop; in fast hopping the carrier moves several times within one symbol, and the receiver combines the per-hop decisions.

Detection. The receiver runs the same PN generator and the same hop table, synchronised to the transmitter, so its local oscillator tracks the transmitted carrier from channel to channel. After dehopping, the signal appears at a fixed intermediate frequency and is demodulated by an ordinary narrowband FSK detector. A receiver without the hop sequence sees only brief unrelated bursts scattered across the band.

The sense in which it is ‘spread spectrum’. The instantaneous bandwidth is not spread at all — it is that of the underlying narrowband modulation. What is spread is the bandwidth occupied on average, over many hops: the signal visits the whole hop set, so its long-term spectrum covers $N_h$ channels and the processing gain is the number of hop channels. This is the essential contrast with direct sequence, and the reason a frequency-hopping system survives a narrowband jammer by avoiding it most of the time rather than by suppressing it in the correlator.

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

Yes — spread spectrum is the better fit for bursty traffic. TDMA and FDMA are fixed-assignment schemes: each user is granted a time slot or a frequency channel, and that resource is reserved whether or not the user has anything to send. When traffic is highly irregular the reserved slot sits idle for most of its life, so the utilisation of the medium collapses, while a user with a sudden burst is throttled to the capacity of a single slot and must either wait or negotiate more — and any dynamic reassignment adds signalling delay and complexity.

A spread-spectrum (CDMA) system has no slot structure to allocate. Every user occupies the entire band all of the time, separated by code rather than by time or frequency, so a user transmits the instant it has data and simply stops when it does not. A silent user contributes no interference and therefore consumes no capacity, which is precisely the property bursty traffic needs: the system's capacity is shared statistically among whoever happens to be active, rather than partitioned in advance among whoever might be. This gives graceful, load-dependent behaviour — the mechanism part (e) quantifies — and avoids the acquisition and slot-synchronisation delays that make TDMA inefficient for short packets. The price is that the receiver's interference environment now depends on the instantaneous number of active users, so power control becomes essential.

(d) Why spread spectrum in the ISM band (5 marks)

The industrial, scientific and medical bands (notably 2.4 GHz) are unlicensed: any compliant device may transmit, so a receiver must expect uncoordinated interference from Wi-Fi, Bluetooth, cordless telephones, and microwave ovens, none of which cooperate with it. Spread spectrum answers this in three ways. First, processing gain: a narrowband interferer that survives despreading is attenuated by the spreading factor, and a hopping system spends only a fraction of its time in any one occupied channel, so both techniques ride through interference that would destroy a narrowband link. Second, low power spectral density: because a direct-sequence transmitter's power is smeared across tens of megahertz, the interference it inflicts on other ISM users is correspondingly small, which is the co-existence property regulators want. Third — and decisively — the regulators require it: the spectrum rules governing the ISM bands (in Canada, ISED's RSS-247, historically RSS-210, and in the United States the equivalent FCC Part 15.247) have long permitted higher transmit power for digitally modulated or frequency-hopping systems than for narrowband ones, and impose hopping and dwell-time requirements on FHSS devices. Bluetooth's adoption of frequency hopping with adaptive channel avoidance is a direct response both to the regulatory framework and to the crowded 2.4 GHz environment it must survive.

(e) Trading users against interference (5 marks)

In a code-division system all $K$ active users transmit in the same band at the same time, distinguished only by codes that are not perfectly orthogonal in an asynchronous channel. Each user's despreader therefore sees the other $K-1$ signals as residual multiple-access interference, suppressed by the processing gain $N$ but not eliminated. With ideal power control the effective signal-to-interference ratio is approximately $$\mathrm{SIR} \approx \frac{N}{K-1},$$ so admitting more users raises the interference floor and lowers every user's SIR in direct proportion. Capacity is therefore not a hard count of channels, as it is in TDMA or FDMA, but the point at which the SIR falls to the minimum the modulation and coding can tolerate: $K_{\max} \approx 1 + N/\mathrm{SIR}_{\min}$.

The practical consequences are worth stating. The degradation is graceful — one extra user beyond the nominal limit slightly degrades everyone rather than being refused outright — which is exactly the opposite of the hard blocking of a fixed-assignment scheme. Anything that reduces the interference each user contributes buys capacity directly: voice activity detection (a talker is silent about 60 % of the time), sectored antennas, and stronger forward error correction all lower the required SIR or the average interference and so raise $K_{\max}$. Conversely, poor power control is catastrophic, because a single strong nearby transmitter raises the interference floor for every other user — the near–far problem, which is why closed-loop power control is a defining feature of practical CDMA systems.