Structural Properties of Optimal Power Allocation for DAS-OFDM Under Joint Total and Individual Power Constraints

Abstract

We study the structural properties of the optimal power allocation for a distributed antenna system with orthogonal frequency division multiplexing (DAS-OFDM), in which <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${K}$ </tex-math></inline-formula> remote radio heads (RRHs) allocate power over <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${N} &gt; {K}$ </tex-math></inline-formula> subchannels under joint total and individual power constraints. The constraints allow the system to limit the overall energy consumption for cost and/or environmental factors, while also preventing individual RRHs to overdrive their high-powered amplifiers due to hardware limitations. In order to obtain some fundamental insights on the optimal power allocation that maximizes the achievable transmission rate, we start by analyzing the two-RRH case. In this simpler case, the optimal power allocation has a novel solution structure that at most one subchannel is used for joint transmission, which can be identified by an efficient subchannel rearrangement scheme. We then extend this property into the general <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${K}$ </tex-math></inline-formula> -RRH case and show that the optimal power allocation solution has an interesting sparse feature: Among <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${N}$ </tex-math></inline-formula> subchannels, at most <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${K} -1$ </tex-math></inline-formula> subchannels can be allocated power for joint transmission by multiple RRHs, and the rest of the subchannels must be served by a single RRH. Based on this property, we show that within the total <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">NK</i> power allocation links, at least ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${N} -1$ </tex-math></inline-formula> )( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${K} -1$ </tex-math></inline-formula> ) links must have zero power allocation, which may provide useful insight for practical CSI feedback design. Finally, numerical results are presented to verify our theoretical results.