  In this paper, we propose an input-output space clustering criterion (IOCC)
to optimize the locations of the remote antenna units (RAUs) of generalized
Distributed Antenna Systems (DASs) under sum power constraint. In IOCC, the
input space refers to RAU location space and output space refers to location
specific ergodic capacity space for noise-limited environments. Given a
location-specific arbitrary desired ergodic capacity function over a
geographical area, we define the error as the difference between actual and
desired ergodic capacity. Our investigations show that i) the IOCC provides an
upper bound to the cell averaged ergodic capacity error; and ii) the derived
upper bound is equal to a weighted quantization error function in
location-capacity space (input-output space) and iii) the upper bound can be
made arbitrarily small by a clustering process increasing the number of RAUs
for a feasible DAS. IOCC converts the RAU location problem into a codebook
design problem in vector quantization in input-output space, and thus includes
the Squared Distance Criterion (SDC) for DAS in [15] (and other related papers)
as a special case, which takes only the input space into account. Computer
simulations confirm the theoretical findings and show that the IOCC outperforms
the SDC for DAS in terms of the defined cell averaged "effective" ergodic
capacity.
