2015/06/04 by Martin Haenggi, Haenggi, Martin · 4 citations
Business, Management and Accounting · Computer Science · Engineering · #Advanced MIMO Systems Optimization #Advanced Queuing Theory Analysis #Advanced Wireless Network Optimization #Cooperative Communication and Network Coding #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Networking and Internet Architecture (cs.NI) #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.1506.01644
openalex publication_date 2015/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The calculation of the SIR distribution at the typical receiver (or,\nequivalently, the success probability of transmissions over the typical link)\nin Poisson bipolar and cellular networks with Rayleigh fading is relatively\nstraightforward, but it only provides limited information on the success\nprobabilities of the individual links. This paper introduces the notion of the\nmeta distribution of the SIR, which is the distribution of the conditional\nsuccess probability P given the point process, and provides bounds, an exact\nanalytical expression, and a simple approximation for it. The meta distribution\nprovides fine-grained information on the SIR and answers questions such as\n"What fraction of users in a Poisson cellular network achieve 90% link\nreliability if the required SIR is 5 dB?". Interestingly, in the bipolar model,\nif the transmit probability p is reduced while increasing the network density\n\λ such that the density of concurrent transmitters \λ p stays\nconstant as p\→ 0, P degenerates to a constant, i.e., all links have\nexactly the same success probability in the limit, which is the one of the\ntypical link. In contrast, in the cellular case, if the interfering base\nstations are active independently with probability p, the variance of P\napproaches a non-zero constant when p is reduced to 0 while keeping the\nmean success probability constant.\n