How to Couple from the Past Using a Read-Once Source of Randomness

We give a new method for generating perfectly random samples from the stationary distribution of a Markov chain. The method is related to coupling from the past (CFTP), but only runs the Markov chain forwards in time, and never restarts it at previous times in the past. The method is also related to an idea known as PASTA (Poisson arrivals see time averages) in the operations research literature. Because the new algorithm can be run using a read-once stream of randomness, we call it read-once CFTP. The memory and time requirements of read-once CFTP are on par with the requirements of the usual form of CFTP, and for a variety of applications the requirements may be noticeably less. Some perfect sampling algorithms for point processes are based on an extension of CFTP known as coupling into and from the past; for completeness, we give a read-once version of coupling into and from the past, but it remains unpractical. For these point process applications, we give an alternative coupling method with which read-once CFTP may be efficiently used.Comment: 28 pages, 2 figure

Maximal Ratio Transmission in Wireless Poisson Networks under Spatially Correlated Fading Channels

The downlink of a wireless network where multi-antenna base stations (BSs) communicate with single-antenna mobile stations (MSs) using maximal ratio transmission (MRT) is considered here. The locations of BSs are modeled by a homogeneous Poisson point process (PPP) and the channel gains between the multiple antennas of each BS and the single antenna of each MS are modeled as spatially arbitrarily correlated Rayleigh random variables. We first present novel closed-form expressions for the distribution of the power of the interference resulting from the coexistence of one intended and one unintended MRT over the considered correlated fading channels. The derived expressions are then used to obtain closed-form expressions for the success probability and area spectral efficiency of the wireless communication network under investigation. Simulation results corroborate the validity of the presented expressions. A key result of this work is that the effect of spatial correlation on the network throughput may be contrasting depending on the density of BSs, the signal-to-interference-plus-noise ratio (SINR) level, and the background noise power.Comment: 6 pages, 6 figures, IEEE GLOBECOM 201