This study conducts a systematic comparative analysis of the Squared-Difference (SD) algorithm and the Costas loop algorithm for carrier synchronization in high-order Pulse Amplitude Modulation (PAM) systems, assessing their noise resilience and computational complexity to inform algorithm selection in high-speed communication systems. We tested both algorithms using the same simulation framework for 4/6/8-PAM modulation over additive white Gaussian noise (AWGN) channels. We looked at how well they did in terms of steady-state phase error variance, speed of convergence, and extra work needed to run the program. The most important results show that the Costas loop works better than the SD algorithm when there is a lot of noise (noise power >5) and when there is a lot of modulation (8-PAM). It has better phase tracking accuracy (with a variance of only 0.022 rad²) and is less likely to be affected by noise.The Costas loop works much better than the SD algorithm, but it costs almost twice as much to run, needing 1013 operations per symbol instead of 512. The SD algorithm matches Costas loop performance in low-noise or low-order modulation but suffers rapid degradation under high noise due to decision-directed error propagation (8-PAM variance peaks at 0.15 rad²).The Costas loop gives up speed for stability, while the SD algorithm is great at converging quickly. These insights make it clear where the application boundaries are. Satellite communications and other systems that need to be very reliable work best with the Costas loop. The SD algorithm works best for short-range links that don't use a lot of resources and have good channel conditions. This study creates a quantitative, multi-dimensional framework for choosing algorithms in high-order PAM systems.
Research Article
Open Access