Signal Processing

CDMA signals have the property that when a received message is compared (convolved) with a replica stored in the receiver and they match, a correlation peak occurs. Otherwise, no peak occurs. This type of detector is commonly referred to as a Matched Filter. The figures show the auto- and cross-correlation for two unique 31-bit CDMA messages generated using Gold-code pseudo-random noise (PRN) encoding when processed through a Matched Filter.

I think it’s awesome how bandpass filters make modern communication possible by controlling the electromagnetic spectrum. Bandpass filters constrain signals to a specific frequency range, allowing users at different frequencies to share the same transmission medium (air, copper) without interfering. The image shows a communication signal before and after filtering. Without bandpass filters, modern communication would be unreliable or impossible.

I was curious about Gold codes, so I generated some from scratch to understand them better. Gold codes are a pseudorandom noise (PRN) sequence used in CDMA and GPS technologies. They function as unique "fingerprints" for different transmissions, allowing multiple users to share the same frequency without interfering with one another. Results: the figure shows two (of eight) optimal 31-bit Gold codes generated from two well-established maximum-length sequences (m-sequences).

In engineering, some of the most basic concepts are often the most powerful. Take BPSK (binary phase shift keying), for example. We can encode a binary message by simply changing the phase of a carrier signal from 0 degrees to 180 degrees. BPSK is used in GPS, satellite TV, and modern communication systems. The figure shows a BPSK message of 101110.

I found it interesting that CDMA signals have a rounded shape due to bandpass filtering. The rounded shape allows overlapping CDMA signals (orange and blue) to be detected because when one signal is low, the other has an opportunity to peak through and be detected, even in the presence of noise (green).

I was curious how the detection quality of CDMA signals at a receiver would change as the receiver moved away from one transmitter toward another (i.e., same frequency, same transmit power, different pseudo-random noise (PRN) codes). Logically, when the receiver is halfway between two transmitters, the received power levels would be the same. Would the signals then interfere with each other and cause both to drop out, or is CDMA robust enough to handle the interference and al