Q1Wireless Communication

DSSS with BPSK, and Comparison with FHSS

Direct Sequence Spread Spectrum (DSSS) with Binary Phase Shift Keying works by first BPSK-modulating the narrowband message data d(t) (each data bit represented as a phase of 0 or 180 degrees on the carrier), and then multiplying (spreading) this modulated signal by a much higher-rate pseudo-noise (PN) code sequence c(t), whose chip rate Rc is typically hundreds or thousands of times the data bit rate Rb. Since multiplying by the PN code sequence (which itself takes values of plus or minus 1) is equivalent to a second BPSK modulation of the data signal by the chip sequence, the composite baseband signal occupies a bandwidth approximately equal to the chip rate Rc rather than the original data bandwidth Rb, spreading the transmitted energy across a much wider bandwidth than the original message would require - this is the origin of the 'spread spectrum' name.

At the receiver, the incoming spread signal is multiplied (correlated) with a locally generated, precisely synchronized replica of the same PN code sequence used at the transmitter. Because the PN code is binary (plus/minus 1), multiplying the received signal by the same PN sequence again exactly de-spreads it back to the original narrowband BPSK signal (since c(t)*c(t) = 1 for a properly synchronized PN sequence), which can then be coherently demodulated using a standard BPSK detector to recover the original data bits. Crucially, any interfering signal or narrowband jammer that does not carry the same PN code, when multiplied by the receiver's PN reference, gets spread out over the wide chip-rate bandwidth rather than concentrated in the narrow data bandwidth, so after despreading and lowpass/matched-filtering only a small fraction of the jammer's power falls within the recovered narrowband signal bandwidth - this despreading gain against interference is precisely the processing gain of the system, and is the central benefit that spread-spectrum techniques provide over conventional narrowband modulation.

Comparing DSSS with FHSS (Frequency Hopping Spread Spectrum): DSSS spreads the signal continuously across the entire spread bandwidth simultaneously by multiplying with a high-chip-rate PN code, whereas FHSS instead divides the available spread bandwidth into many narrower frequency channels and rapidly hops the carrier frequency among these channels according to a pseudo-random hopping sequence, transmitting the (comparatively narrowband) modulated signal on only one channel at any instant. DSSS generally provides better performance against multipath fading (since the wideband signal experiences frequency-selective fading that a rake receiver, discussed elsewhere in this examination, can exploit for diversity combining) and against continuous-wave jamming, but requires tight chip-level synchronization between transmitter and receiver and is more vulnerable to the near-far problem in multi-user CDMA systems. FHSS, by contrast, is comparatively more robust against narrowband jamming concentrated at specific frequencies (since the signal simply avoids a jammed channel most of the time) and requires less stringent synchronization precision (only frequency-hop-level, not chip-level, synchronization is needed), but does not benefit as directly from rake-receiver-style multipath diversity combining, and its instantaneous bandwidth at any moment remains narrow, making it comparatively easier to detect and follow with agile jammers than a continuously wideband DSSS signal.

Properties of PN Sequences and Processing Gain Calculation

• Balance property: in each period of the PN sequence, the number of binary 1s and 0s (or +1s and -1s) differs by at most one, giving the sequence a near-equal balance of both logic levels.
• Run property: among the runs of consecutive identical symbols in one period, about half the runs have length 1, about a quarter have length 2, about an eighth have length 3, and so on, following a geometric distribution characteristic of genuinely random-like binary sequences.
• Correlation property (autocorrelation): the autocorrelation function of a PN sequence is highly peaked at zero shift and very close to a small constant value (ideally -1/N for an m-sequence of length N) at all nonzero shifts, closely approximating the impulsive autocorrelation of true white noise, which is essential for reliable code acquisition/synchronization at the receiver.
• Long period and deterministic generation: PN sequences are generated deterministically (typically via linear feedback shift registers, LFSRs), giving them a very long, precisely repeatable period while still exhibiting statistical randomness properties similar to genuine noise, allowing the same sequence to be reproduced exactly and synchronously at both transmitter and receiver.

Given a DSSS transmitter with chip rate Rc = 20 Mbps and message bit rate Rb = 10 kbps, the processing gain is calculated as the ratio of chip rate to bit rate:

Therefore the processing gain achieved with BPSK modulation is Gp = 2000, or equivalently 33 dB. This processing gain directly represents the factor by which the despreading operation at the receiver improves the effective signal-to-interference ratio relative to any narrowband interferer, and is the single most important figure of merit characterizing the interference-rejection and anti-jamming capability of any spread-spectrum communication link.

It is also worth noting that the choice of BPSK specifically (rather than a higher-order modulation such as QPSK or higher-order QAM) for the underlying data modulation stage of a DSSS system reflects a deliberate trade-off: BPSK provides the most robust bit-error-rate performance for a given energy-per-bit-to-noise-density ratio among common linear modulations, which is valuable in spread-spectrum applications where the system is often required to operate reliably even under significant residual interference after despreading, at the cost of a lower raw bit rate per unit bandwidth compared to higher-order modulation schemes. In practice, many modern DSSS-based systems (such as WCDMA/UMTS) do employ higher-order modulation combined with spreading specifically to balance the competing demands of interference robustness and spectral efficiency depending on the specific radio channel conditions experienced by each user.

Finally, it is useful to note that the processing gain figure calculated for a given DSSS system represents only the theoretical maximum interference-suppression capability available from the spreading and despreading operation alone; the actual jamming margin realized in a complete system (as calculated explicitly for a related DS-CDMA example elsewhere in this examination) is somewhat lower than the raw processing gain, since practical implementation losses (imperfect code synchronization, filter non-idealities, and quantization effects in a digital implementation) and the inherent signal-to-noise ratio required by the specific demodulation and channel-coding scheme in use both reduce the net jamming margin available below the theoretical processing-gain ceiling.