Delay analysis for Fair Power Allocation Strategy in multi antenna broadcast channels

Abstract

This paper concerns delay analysis for Fair Power Allocation Strategy (FPAS) in multi antenna Broadcast Channel (BC). It is assumed the transmitter aims at sending individual information to a large number of single-antenna users (n) through a common wireless channel. Assuming there is a total transmit power constraint, the FPAS attempts to select the maximum number of active users in which each can receive the minimum rate constraint of R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">min</sub> . Noting this and assuming the system delay is defined as the minimum number of channel uses such that each user with probability approaching one is selected at least once, we show that for the case of single-antenna BC, the expected delay of FPAS scales as R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">min</sub> ((n logn)/(loglogn)) + ω(n/(loglogn)). Then, using our earlier proposed FPAS for multi-antenna BC, it is shown the expected delay of this strategy behaves like R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">min</sub> ((n logn)/(M loglogn-θ(1))) + ω(n/(loglogn)), where M denotes the number of transmit antennas. Moreover, it is shown for sufficiently large (k) number of channel uses, the average number of services received by a randomly selected user for single-antenna and multi-antenna BC scale as (k loglogn)/(nR <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">min)</sub> (1+O(√(logk)/k)) and (kM loglogn)/(nR <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">min</sub> ) (1+O(√(logk)/k)), respectively.