How do I calculate the processing gain of a spread spectrum communication system?
Spread Spectrum Processing Gain
Processing gain is the fundamental performance multiplier of spread spectrum systems, enabling operation below the noise floor, resistance to interference, and multiple access without frequency coordination.
| Parameter | Free Space | Urban | Indoor |
|---|---|---|---|
| Path Loss Model | Friis (1/r²) | Okumura-Hata | IEEE 802.11 |
| Fading Margin | 0 dB | 10-30 dB | 5-15 dB |
| Multipath | None | Severe | Moderate-severe |
| Typical Range | Line of sight | 1-30 km | 10-100 m |
| Shadow Fading (σ) | 0 dB | 6-12 dB | 3-8 dB |
Margin Allocation
In DSSS: the data signal is multiplied by a high-rate pseudo-random code (PN code) before transmission. The transmitted signal occupies a bandwidth = chip rate × (1 + roll-off). At the receiver: the same PN code is used to despread the signal, collapsing the wideband signal back to the data bandwidth. The despreading process: (1) The desired signal is correlated with the correct PN code (code-matched). The correlation gain = N_chips_per_bit = PG. The signal power is concentrated into the data bandwidth. (2) Interference (noise, jammers, other CDMA users) is not correlated with the PN code. The despreader spreads the interference across the chip bandwidth, reducing its power density by PG. (3) After despreading: the effective SNR is improved by PG compared to the pre-despreading SNR. SNR_out = SNR_in + PG(dB). If SNR_in = -10 dB (signal is 10 dB below the noise/interference) and PG = 21 dB: SNR_out = 11 dB (signal is 11 dB above the noise after despreading, well above the 7 dB Eb/No threshold for BPSK).
Propagation Modeling
In FHSS: the carrier frequency hops across a set of N_hop channels according to a pseudo-random hopping pattern. The instantaneous bandwidth is the channel bandwidth (narrowband), but the time-averaged bandwidth equals N_hop × channel_BW. Processing gain of FHSS: PG = N_hop (the number of hop channels). For a system hopping across 100 channels: PG = 20 dB. The interference rejection mechanism differs from DSSS: a narrowband jammer can only affect 1 out of N_hop hops. With FEC coding: the receiver can tolerate a fraction of jammed hops. For a rate 1/2 code with 100 hops: the system can tolerate 30-40% of hops being jammed (jamming margin = PG + coding gain). Military anti-jam systems use fast-hopping (multiple hops per data symbol) with very high PG: N_hop = 1000-10000 channels, hop rate = 1000-100000 hops/sec. PG = 30-40 dB.
- Performance verification: confirm specifications against the application requirements before finalizing the design
- Environmental factors: temperature range, humidity, and vibration affect long-term reliability and parameter drift
- Cost vs. performance: evaluate whether the application demands premium components or standard commercial grades
- Interface compatibility: verify impedance, connector type, and mechanical form factor match the system architecture
Fade Mitigation
The jamming margin (M_j) is the maximum jammer-to-signal ratio the system can tolerate: M_j = PG - Eb/No_required - L_implementation (dB). For WCDMA with PG = 25 dB, Eb/No = 5 dB, L_impl = 2 dB: M_j = 25 - 5 - 2 = 18 dB. A jammer must be 18 dB stronger than the desired signal to prevent communication. For GPS C/A code: PG = 43.1 dB, Eb/No = 6 dB, L = 2 dB. M_j = 35.1 dB. A jammer at the GPS antenna must exceed the GPS signal by 35 dB. Since the GPS signal at the surface is -130 dBm: the jammer needs -130 + 35 = -95 dBm at the GPS antenna. A 1 W (30 dBm) jammer at 10 km range: received power ≈ 30 - 130 = -100 dBm (close to the jamming threshold). GPS military P(Y) code: PG = 53 dB, providing 10 dB more jamming margin. The direct acquisition of P(Y) code requires 10 dB more correlator processing but provides much better anti-jam capability.
Frequently Asked Questions
Can I increase processing gain indefinitely?
In principle, PG = R_chip / R_data can be increased by either raising the chip rate or lowering the data rate. In practice, limits include: (1) Bandwidth availability: higher chip rate requires wider bandwidth. The spreading bandwidth must be within a single allocated band. GPS uses 2 MHz (C/A) or 20 MHz (P code). Military systems: 50-100 MHz spreading bandwidth. (2) Code synchronization: higher chip rates require faster and more precise code tracking loops. At 100 Mcps: timing resolution must be < 5 ns (chip period = 10 ns, tracking to ±0.5 chip). (3) Multipath resolution: higher chip rate provides finer multipath resolution (each chip = c/R_chip meters of range resolution), which is beneficial. But: the receiver must process wider bandwidth, requiring faster ADCs and more FPGA processing. (4) Data rate floor: reducing the data rate below the application minimum is not acceptable. For voice: minimum 2.4-4.8 kbps. For command/control: can go very low (100-1000 bps).
How does processing gain relate to GPS accuracy?
Processing gain directly affects GPS receiver sensitivity (ability to acquire and track weak signals in urban canyons or indoors). GPS accuracy is primarily determined by: (1) Timing precision: proportional to 1/BW. C/A code (1.023 MHz BW): timing resolution ≈ 300 m (one chip). With correlation peak tracking: 3-10 m accuracy. P(Y) code (10.23 MHz BW): timing resolution ≈ 30 m (one chip). With tracking: 0.3-1 m accuracy. L5 signal (10.23 MHz): civilian signal with P-code-like performance. (2) Processing gain affects acquisition sensitivity: C/A code PG = 43 dB allows acquisition at very low SNR. Higher PG → longer integration time → weaker signals can be acquired (assisted GPS uses 20 ms to 100+ ms integration). (3) Processing gain does NOT directly improve timing accuracy; it improves the SNR of the correlation peak, which indirectly improves the precision of the peak location estimate.
What is the near-far problem in CDMA?
In CDMA, all users share the same frequency. A nearby user with a strong signal (e.g., -50 dBm) and a distant user with a weak signal (e.g., -100 dBm) are both present at the base station receiver. After despreading: the strong user interference on the weak user code = P_strong - PG = -50 - 21 = -71 dBm. The weak desired signal = -100 dBm. Effective SIR = -100 - (-71) = -29 dB (the strong user overwhelms the weak user despite despreading). Solution: precise power control. The base station commands each user to adjust transmit power so that all users arrive at the base station at approximately the same power level (±1 dB). IS-95 uses open-loop power control (based on received signal strength) and closed-loop power control (800 Hz update rate). WCDMA: 1500 Hz power control update rate, ±1 dB step size. Without power control: CDMA capacity drops by 50-80%.