The low-error-rate requirement of ultra-reliable communication poses a significant challenge to simulation-based performance evaluation of such systems, as conventional Monte Carlo (MC) simulation becomes extremely time-consuming at very low error rates. This work considers fast simulation of multi-input multi-output (MIMO) orthogonal frequency division multiplexing (OFDM) transmission over multipath fading channels via importance sampling (IS). The efficiency of an IS simulator hinges on several key factors: 1) how sharply it can differentiate error-causing and non-error-causing subsets in the sample space, 2) how readily it can profile the probability distribution regarding these subsets, and 3) how proficiently it can generate and distribute samples over particular subsets of interest. In this perspective, we develop a novel IS method in the vein known as histogram-shaping Monte Carlo (HSMC). First, an error gauging function that is generally applicable to channel-coded MIMO-OFDM systems is proposed to highlight potentially error-causing samples in multipath fading channels. Second, we develop a sampler that not only generates random samples effectively from error-causing subsets but also facilitates fast estimation of subset-associated probabilities. New Radio (NR) link-level simulation is conducted to showcase the advantages of the proposed method, revealing approximately 10- to$10^{7}$-fold speedup compared to conventional MC simulation.

To estimate the probability Peof an error event to an accuracy in variance not exceeding ${ \in ^2}P_e^2$, conventional Monte Carlo (MC) requires approximately 1/(ε2Pe) simulation runs. Hence the low error probabilities demanded for ultra-reliable communication pose a significant issue in simulation-based evaluation of transmission performance. Advanced fast simulation techniques are therefore coveted. Conceptually, we may view a sequence of symbols transmitted by a communication system as a point in a multidimensional space. Channel distortion and noise may cause displacement of the point. The receiver commits an error if it fails to recover the transmitted point location from the received. The efficiency of a simulator depends on how sharply it can differentiate error-causing and non-error-causing displacements and how simply it can determine the probability of encountering an error-causing displacement. We consider convolutionally coded communication in which the receiver employs Viterbi decoding. We propose a corresponding noise gauging function (NGF) which can make relatively sharp differentiation between error-causing and non-error-causing noise vectors. We also propose a way to estimate the distribution of the NGF values to support error rate evaluation. The result is employed in an MC-type technique that adaptively shapes the histogram of the NGF values of the generated noise vector samples towards one that minimizes the variance in Peestimation under given number of simulation runs. Simulation considering the additive white Gaussian noise channel shows an approximately one to two orders of magnitude in speed-up compared to conventional MC.

To estimate the probability of an event, conventional Monte Carlo (MC) needs 100/Pesimulation runs to attain a 10% precision, where Peis the probability of the event. It therefore encounters difficulty in simulation-based evaluation of packet error rates for ultra-reliable communication under its stringent requirement. Many fast simulation techniques for evaluating the probability of rare events have been proposed. However, a more efficient method for coded communication systems that can adaptively exploit the code structure and concentrate the generated noise vectors to the error-prone regions is desirable. We propose a method which seeks to adaptively learn a certain optimal histogram of the noise vectors and generate the noise vectors accordingly. The said histogram is a one-dimensional function and hence is easy to work with. The adaptation mechanism is code-agnostic. Simulation with cyclic redundancy check-aided polar coding in additive white Gaussian noise shows an approximately 10-100 times speed-up compared to conventional MC.