Generation of Random Binary Bit Sequences and Digital Modulation Analysis with MATLAB Implementation

In this technical problem, we need to perform the following tasks: First, implement code to generate a random sequence of binary bits (0s and 1s) using programming languages like MATLAB or Python. This can be achieved using random number generators such as rand() or randi() functions with appropriate thresholding to produce binary values. Next, we need to apply four different modulation techniques - 2ASK (Amplitude Shift Keying), 2FSK (Frequency Shift Keying), 2PSK (Phase Shift Keying), and 2DPSK (Differential Phase Shift Keying) - to modulate these sequences onto a higher carrier frequency. The modulation parameters (carrier frequency, amplitude, phase shifts) can be customized as needed. In code implementation, this involves generating carrier signals and multiplying them with the binary data according to each modulation scheme's specifications. We then need to plot the time-domain waveforms corresponding to the first 8 bits. This requires implementing waveform generation code that calculates the modulated signal samples over time and using plotting functions like plot() in MATLAB to visualize the results. Additionally, we must create schematic block diagrams for coherent and non-coherent demodulators after these signals pass through an Additive White Gaussian Noise (AWGN) channel. We need to derive the mathematical expressions for observation values before decision-making. For modulation schemes that cannot support non-coherent demodulation (such as 2PSK), we must explain the reasons, typically due to phase ambiguity issues in carrier recovery without phase reference. Based on the given mathematical expressions for observation values, we should implement the decision process in code. This involves programming threshold detection algorithms and comparing the decision results with original data to calculate Bit Error Rate (BER) at different Signal-to-Noise Ratio (SNR) values. For comprehensive analysis, it's recommended to set the SNR range from 0dB to 10dB with 1dB increments, implementing noise addition using AWGN functions and BER calculation through statistical comparison. After completing the simulations, we obtain BER simulation curves. We should compare these with theoretical BER curves and discuss the discrepancies. Additionally, we need to analyze and discuss the error performance differences among various modulation and demodulation schemes, implementing comparative analysis code to evaluate their relative performance under different channel conditions. The provided modifications aim to meet all technical requirements while incorporating practical code implementation details for each step of the digital communication system simulation.