A Fresh Look at Multicanonical Monte Carlo from a Telecom Perspective

Abstract

Abstract-The Multicanonical Monte Carlo (MMC) techniqueis a new form of adaptive importance sampling (IS). Thanks to its blind adaptation algorithm, it does not require an in-depth system knowledge for exploitation as does traditional IS. Hence MMC is a practical, handy tool to estimate via simulation the probability of rare events in complex telecom systems, such as the symbol error rate or the outage probability. In this paper, we present the analytical connections between MMC and IS, and describe the recursive algorithm via which MMC seeks an optimal "flat-histogram" warping. We also provide practical guidelines on how MMC can be successfully applied in telecom to achieve accelerations of simulation time by many orders of magnitude with respect to standard Monte Carlo.

Minimum Codebook Size to Achieve Maximal Diversity Order for RVQ-Based MIMO Systems

“…From (20) and (23) we find that for codebook sizes higher or equal than M − K + 2 there is no loss due to quantization, as the achievable diversity is equal to M − K + 1.…”

“…The results presented are a function of the bit error rate over the energy per bit to noise power spectral density ratio per antenna (E b /N 0 ). To estimate the BER for different E b /N 0 values the Multicanonical Monte Carlo algorithm [20] has been used. The best element from codebook T is selected using the BER as a metric.…”

Transition Matrix Monte Carlo technique for outage probability estimation in MIMO channels

“…More information on the MMC technique and its application in a telecommunication context can be found in [12] and [15].…”

“…is the domain in the input space that maps into the mth bin [15]. The probability that a sample falls in the mth bin, P m , can be expressed as…”

Fast Simulation of Error Control Coded Systems Using Flat Histogram Monte Carlo Methods

“…DAIS uses the multicanonical Monte Carlo (MMC) method, which is a form of adaptive IS [7], to approximate the probability density function (pdf) of a control variable that is a suitable function of noise samples in an AWGN environment. The control variable of DAIS is not directly related to the bit error probability (BEP) of the system; hence, a second cycle of MMC simulation is required to determine the error performance of the system [6].…”