Outage performance of multi-antenna multicasting for wireless networks

Abstract

Wireless cellular networks often need to convey the same data to multiple users simultaneously. This kind of transmission is known as physical layer multicasting. Unfortunately, when any user fails to receive the data correctly, the information must be retransmitted to all the users, resulting in a waste of radio resources. Thus, it is important to investigate the outage probability of multicast channels, which is defined as the probability that the smallest maximum achievable rate among all of the users is smaller than a specified transmission rate. In this paper, we consider the use of multiple antenna multicast channels where the transmitter is equipped with M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> antennas and independent data is transmitted on each antenna to K users. Using extreme value theory, we derive a closed form limiting distribution that the exact distribution of the multicasting channel converges to when the number of users K is taken to infinity. From this result, we find upper and lower-bounds on the outage probability. It is shown that for a given outage probability the upper-bound becomes sufficiently tight to approximate the exact outage probability with K such that it converges to the exact one with a speed faster than Theta (K <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1/M</sup> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sup> ). Using this upper-bound, we identify conditions on the transmission rate and the transmit power necessary to maintain constant outage performance as K increases. Specifically, the transmission rate should be decreased as Theta (K <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1/M</sup> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sup> ) or the transmit power should be increased as Theta (K <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/M</sup> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sup> ). This means that the outage performance improves as the number of transmit antennas increases, because spatial diversity can be well exploited. However, this increase in the number of transmit antennas requires a significant cost. To improve the performance without requiring additional cost, we consider a multiple-slot multicasting that transmits the same data over multiple slots and an antenna subset selection scheme that transmits the data over some subset of the transmit antennas. It is shown that the transmission rate of multiple-slot scheme can be increased when the number of slots is carefully chosen and the diversity-multiplexing trade-off is the same as that of K = 1. Also, the gain in the transmission rate from selecting some subset of the transmit antennas is derived.