Diffusion approximation for a heavily loaded multi-user wireless communication system with cooperation |
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Authors: | S Bhardwaj R J Williams |
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Institution: | 1.Department of Electrical and Computer Engineering,University of California at San Diego,La Jolla,USA;2.Department of Mathematics,University of California at San Diego,La Jolla,USA |
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Abstract: | A cellular wireless communication system in which data is transmitted to multiple users over a common channel is considered.
When the base stations in this system can cooperate with each other, the link from the base stations to the users can be considered
a multi-user multiple-input multiple-output (MIMO) downlink system. For such a system, it is known from information theory
that the total rate of transmission can be enhanced by cooperation. The channel is assumed to be fixed for all transmissions
over the period of interest and the ratio of anticipated average arrival rates for the users, also known as the relative traffic
rate, is fixed. A packet-based model is considered where data for each user is queued at the transmit end. We consider a simple
policy which, under Markovian assumptions, is known to be throughput-optimal for this coupled queueing system. Since an exact
expression for the performance of this policy is not available, as a measure of performance, we establish a heavy traffic
diffusion approximation. To arrive at this diffusion approximation, we use two key properties of the policy; we posit the
first property as a reasonable manifestation of cooperation, and the second property follows from coordinate convexity of
the capacity region. The diffusion process is a semimartingale reflecting Brownian motion (SRBM) living in the positive orthant
of N-dimensional space (where N is the number of users). This SRBM has one direction of reflection associated with each of the 2
N
−1 boundary faces, but show that, in fact, only those directions associated with the (N−1)-dimensional boundary faces matter for the heavy traffic limit. The latter is likely of independent theoretical interest. |
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Keywords: | |
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