16-QASK Modulation with Eye Diagram Analysis for Optimal Decision Timing

In this document, we present a comprehensive implementation of 16-QASK modulation for random digital signals. The process involves generating random binary data, mapping it to 16-QASK constellation points, and applying raised-cosine filtering to simulate real-world channel conditions with additive noise. The implementation includes calculating the in-phase and quadrature components using mathematical mapping functions that convert 4-bit symbols to specific amplitude levels in both dimensions. We demonstrate how to create an eye diagram by overlapping multiple symbol periods, which provides visual insights into signal quality and timing synchronization. The eye diagram analysis involves sampling the received signal at different time instants and plotting the trajectories to observe the eye opening. Through code implementation, we show how to measure the eye opening width and height to determine the optimal sampling instant that maximizes the decision margin and minimizes bit error rate. The document explains the principles of raised-cosine filters, including their roll-off factor parameter that controls the bandwidth-symbol rate trade-off, and how to implement these filters using convolution operations with properly designed filter coefficients. We discuss the advantages of 16-QASK modulation, such as higher spectral efficiency compared to lower-order modulations, and its disadvantages, including increased susceptibility to noise and phase noise. Additionally, we provide code examples for adding Gaussian noise to simulate channel impairments and demonstrate how to calculate signal-to-noise ratio (SNR) metrics. The implementation includes timing recovery algorithms that use the eye diagram characteristics to automatically find the best decision points, typically where the eye opening is maximum. Through this documentation, you will gain practical understanding of implementing 16-QASK modulation in noisy channels and learn how raised-cosine filters and eye diagrams contribute to robust digital communication system design.