Semi-Analytic Techniques for Fast MATLAB Simulations

Advances in electronics and telecommunications are leading to complex systems able to efficiently use the available resources. Fast electronics, complex modulation schemes and correction codes enable transmissions on channels with unfavorable characteristics, coexistence between different services in the same frequency bands and high transmission rates. However, the complexity of such communications systems often prevents analytical characterizations. For example, figures of merit such as the Bit Error Rate (BER) are difficult to determine analytically for transmission schemes involving correction codes and communication channels with Inter-Symbol Interference (ISI) and fading. In such cases, the system is characterized through Monte Carlo simulations [1, 2]. The Monte Carlo framework involves simulations of the whole system under analysis. For example, when considering a communications system, the whole transmission-reception chain is simulated. A large number of sequences are sent through the simulated system and the message recovered by the simulated receiver is compared to the original transmitted sequence. This comparison allows one to determine the average number of transmission errors and compute the BER.