How do I calculate the processing gain of a correlation receiver in a spread spectrum system?
Spread Spectrum Processing Gain
Processing gain is the fundamental advantage of spread spectrum: it enables operation at SNR levels well below 0 dB (the signal can be below the noise floor and still be recovered), which is essential for GPS, CDMA, and military communications.
| Parameter | Superheterodyne | Direct Conversion | Digital IF |
|---|---|---|---|
| Image Rejection | 60-90 dB (filter) | 30-50 dB (mismatch) | N/A (digital) |
| DC Offset | No issue | Major issue | No issue |
| LO Leakage | Low | High | Low |
| Integration | Difficult | Easy (single chip) | Moderate |
| Dynamic Range | 80-120 dB | 60-90 dB | 70-100 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
Frequently Asked Questions
How does the correlator work?
The correlation receiver (despreader): multiplies the received spread spectrum signal by a locally generated copy of the spreading code. If the local code is time-aligned with the received signal's code: the multiplication despreads the desired signal (concentrating its energy into the data bandwidth, effectively boosting the SNR by the processing gain). If the local code is not aligned (different code or different timing): the multiplication does not despread (the signal remains spread, and the energy is distributed across the bandwidth, appearing as low-level wideband noise). After multiplication: a low-pass filter or integrate-and-dump circuit extracts the narrowband data signal from the wideband noise+interference. The output SNR is: SNR_out = SNR_in + PG.
What about frequency hopping?
Frequency-hopping spread spectrum (FHSS): the carrier frequency hops rapidly across a set of frequencies according to a pseudo-random sequence. The processing gain for FHSS is different from DSSS: PG_FHSS = 10×log10(number of hop frequencies) = 10×log10(total_hopping_bandwidth / instantaneous_bandwidth). For example: 100 hop frequencies, each 200 kHz wide: total hopping BW = 20 MHz. PG = 10×log10(100) = 20 dB. FHSS processing gain represents the ability to avoid narrowband jammers (the jammer must jam all hop frequencies simultaneously, requiring N× more power; or: the jammer can jam only 1/N of the hops, losing PG dB of effectiveness).
What limits the processing gain?
Processing gain limits: practical code length (longer codes provide more PG but: require more time to acquire (the receiver must search through all possible code phases to find the correct alignment), require faster chip clocking (higher bandwidth), and are more complex to generate and correlate). Bandwidth availability (the spread bandwidth is limited by the available spectrum allocation). Near-far problem (in CDMA: a strong nearby transmitter can overwhelm a weak distant transmitter despite the processing gain; this limits the effective PG in multi-user environments; mitigated by: power control and successive interference cancellation).