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.

Given. A qualitative comparison between spread-spectrum multiple access and the channelised alternatives, with the illustrative figures quoted below taken from the IS-95 and Bluetooth air interfaces.

Find. The mechanisms that let every user occupy the whole band, the operation and detection of the two spreading techniques, the way capacity degrades with load compared with a slotted system, and the penalties spread spectrum pays for its advantages.

Part (a) — what makes full-band sharing feasible. Four properties do the work, and they are best read as one mechanism seen from four sides. First, every user's data is multiplied by a distinct pseudonoise sequence whose members are nearly orthogonal to one another, so the receiver's correlator responds strongly to the one sequence it holds a replica of and only weakly to all the others; separation is achieved in code space rather than in time or frequency. Second, the chip rate $R_{c}$ vastly exceeds the data rate $R_{b}$, and the ratio $$G_{p} = \frac{R_{c}}{R_{b}} = \frac{B_{ss}}{R_{b}}$$ is the processing gain: on despreading, the wanted signal collapses back into a bandwidth $R_{b}$ while every interferer stays spread, so only the fraction $1/G_{p}$ of each interferer's power lands inside the decision bandwidth. In IS-95, 1.2288 Mchip/s carrying a 9.6 kbit/s vocoder gives $G_{p} = 128$, or 21.07 dB of suppression. Third, spreading the same power over a hundred times the bandwidth drops the power spectral density to or below the noise floor, so a transmission does not need an exclusive channel to coexist with others. Fourth — and this is an engineering requirement rather than a gift — closed-loop power control equalises the received powers so that a nearby terminal does not swamp a distant one, and accurate code and carrier synchronisation makes the correlation gain real rather than nominal.

Part (b) — direct sequence spread spectrum. The binary data waveform $d(t)\in\{\pm 1\}$ at rate $R_{b}$ is multiplied by a pseudonoise chip waveform $c(t)\in\{\pm 1\}$ at a much higher rate $R_{c}$, and the product modulates a carrier, normally by BPSK or QPSK: $$s(t) = \sqrt{2P}\,d(t)\,c(t)\cos(2\pi f_{c}t).$$ Because the multiplication is by a fast, nearly random sign sequence, the transmitted spectrum is that of the chip waveform — roughly $R_{c}$ wide instead of $R_{b}$ wide — with the total power unchanged and the density therefore reduced by the processing gain. Detection is coherent. After carrier recovery the receiver multiplies by a locally generated replica of the same sequence, time-aligned to the incoming chips; since $c^{2}(t)=1$ the wanted term is restored to $d(t)$ exactly, while an interferer multiplied by an uncorrelated sequence remains spread. The result is integrated over one bit period and compared with a threshold, which is the matched-filter receiver for the composite waveform. Synchronisation is acquired by sliding correlation over the code phase until the correlator output exceeds a threshold, then held by a delay-lock loop; in multipath a rake receiver combines several resolvable delays, turning delay spread from an impairment into diversity gain. Examples: the IS-95 and cdma2000 cellular air interfaces, the GPS C/A signal at 1.023 Mchip/s, and the original 802.11b DSSS physical layer.

Part (c) — frequency hopping spread spectrum, and the sense in which it spreads. The total band is divided into $N$ channels and the carrier is switched among them according to a pseudorandom hop pattern generated from a key known to both ends. Data modulation is usually non-coherent $M$-ary FSK, because carrier phase cannot be maintained across a hop, so the receiver has nothing to track phase against. Detection mirrors the transmitter: after acquiring hop timing from a preamble or a network beacon, the receiver's synthesiser steps through the identical pattern, dehopping the signal to a fixed intermediate frequency where an ordinary bank of matched filters or envelope detectors demodulates it. In slow hopping several bits are sent per dwell and coding plus interleaving repairs the occasional hit channel; in fast hopping the carrier moves several times per bit and the receiver combines the pieces, which buys frequency diversity within each bit. The technique is spread spectrum in the time-averaged sense: the instantaneous bandwidth is only that of a single hop channel, which is why a spectrum analyser with a short sweep sees a narrowband signal, but averaged over many hops the occupied band is $N$ times wider and the mean power spectral density is $N$ times lower. The spreading is achieved by diversity in frequency over time rather than instantaneously, and the processing gain is correspondingly $G_{p}\approx N$. Bluetooth is the standard example, hopping over 79 channels of 1 MHz at 1600 hops per second, a dwell of 625 µs.

Part (d) — how performance changes with the number of users, against fixed-slot TDMA. A spread-spectrum system is interference limited, not slot limited. Each additional user adds a noise-like contribution to every other user's correlator output, so with $K$ equal-power users the ratio available to each is approximately $$\frac{E_{b}}{N_{0}} \approx \frac{G_{p}}{K-1}$$ when thermal noise is negligible. There is no hard admission limit — one more user does not get blocked, everyone simply gets slightly worse, which is the property known as graceful degradation or soft capacity. The practical limit is where the ratio falls below what the required error rate demands: rearranging, $$K_{\max} \approx 1 + \frac{G_{p}}{(E_{b}/N_{0})_{req}},$$ and with $G_{p}=128$ and a 7 dB requirement (a factor of 5.01) this gives about 26 users per cell, a figure that real systems then improve on by exploiting voice activity of roughly 40 % and by sectorising the antenna. TDMA with a fixed slot count behaves in the opposite way. Every admitted user occupies one exclusive slot and receives the full, constant quality of that slot regardless of how many others are active; the $(N+1)$-th user is refused outright. So TDMA converts load into a hard blocking probability while holding quality constant, whereas spread spectrum converts load into a gradual quality loss while never blocking. The choice is therefore an engineering trade between deterministic quality of service and statistical capacity, and it is why CDMA systems can carry a brief overload that would simply be turned away by a slotted system.

Part (e) — disadvantages against TDMA and FDMA. The first and most serious is the near–far problem: because all users share the band, a terminal 100 m from the receiver can bury one at 1 km under its sidelobes, so fast closed-loop power control is mandatory rather than optional, and a single mispowered or non-compliant transmitter degrades the whole cell. Second, capacity is soft, which is an operational disadvantage as much as a technical one: it cannot be guaranteed in a service-level agreement, and planning has to be statistical. Third, the receiver is substantially more complex — code acquisition and tracking, rake combining for multipath, wideband front ends and faster converters — where an FDMA receiver needs only a filter and a local oscillator. Fourth, the technique needs a wide contiguous and reasonably clean allocation, so it is inflexible where spectrum is licensed in narrow blocks or fragmented, and it is vulnerable to a strong narrowband interferer that exceeds the jamming margin. Fifth, the wide front end admits proportionally more thermal noise, which costs sensitivity and power. For frequency hopping specifically there is the overhead of hop synchronisation and the roughly 3 dB penalty for non-coherent FSK relative to coherent PSK. Against all this, channelised systems are simple, their interference is easy to coordinate and bill for, and legacy interoperability is straightforward — which is why FDMA and TDMA remain the sensible choice for narrowband telemetry, land mobile radio and point-to-point microwave links. In Canada, licence-exempt digital modulation and frequency-hopping equipment in the 902–928 MHz, 2.4 GHz and 5 GHz bands operates under ISED RSS-247, which sets the permitted hop counts, dwell times and power limits.