Filtering through AWGN Channel with BER and Constellation Diagram Analysis for 16QAM

16QAM modulation is an efficient modulation scheme that transmits 4-bit binary information by mapping 16 distinct complex points on a constellation diagram. In practical communication systems, baseband signals undergo pulse shaping before transmission through an AWGN (Additive White Gaussian Noise) channel. The receiver must demodulate the signal and analyze both Bit Error Rate (BER) and constellation diagrams to evaluate system performance.

16QAM Signal Generation The modulation process begins by converting input bit streams into corresponding complex symbols. The 16 constellation points are uniformly distributed along I (in-phase) and Q (quadrature) axes, typically employing Gray coding to minimize bit error probability between adjacent symbols. Code implementation would involve mapping 4-bit groups to predefined complex symbols using lookup tables or mathematical mapping functions.

Pulse Shaping Filter To reduce Inter-Symbol Interference (ISI), baseband signals require pulse shaping filters (such as raised-cosine filters) to limit signal bandwidth and optimize waveforms for distortion-free sampling points. Implementation typically involves convolution between symbol sequences and filter coefficients, with careful consideration of roll-off factors and filter length.

AWGN Channel Transmission Signals transmitted through AWGN channels experience additive white Gaussian noise, causing distortion at the receiver. Channel simulation requires setting specific Signal-to-Noise Ratio (SNR) values to emulate various noise environments. Code implementation involves generating complex Gaussian noise samples scaled according to the desired SNR and adding them to transmitted symbols.

Receiver Processing The receiver first applies matched filtering to maximize SNR, followed by symbol timing recovery and carrier synchronization operations. The demodulated constellation diagram visually represents noise and distortion effects on signals. Implementation requires correlation-based timing recovery algorithms and phase-locked loops for carrier synchronization.

BER Analysis Bit Error Rate serves as a crucial metric for communication system reliability. By comparing transmitted and received bit streams, BER values at different SNR levels can be calculated, with BER curves plotted to evaluate system performance. Code implementation involves error counting and statistical averaging across multiple simulation frames.

Constellation scatter plots provide visual insights into channel effects, while BER analysis quantitatively assesses system noise immunity. Both serve as fundamental references for digital communication system design and optimization.