3 research outputs found
The Necessity of Relay Selection
We determine necessary conditions on the structure of symbol error rate (SER)
optimal quantizers for limited feedback beamforming in wireless networks with
one transmitter-receiver pair and R parallel amplify-and-forward relays. We
call a quantizer codebook "small" if its cardinality is less than R, and
"large" otherwise. A "d-codebook" depends on the power constraints and can be
optimized accordingly, while an "i-codebook" remains fixed. It was previously
shown that any i-codebook that contains the single-relay selection (SRS)
codebook achieves the full-diversity order, R. We prove the following:
Every full-diversity i-codebook contains the SRS codebook, and thus is
necessarily large. In general, as the power constraints grow to infinity, the
limit of an optimal large d-codebook contains an SRS codebook, provided that it
exists. For small codebooks, the maximal diversity is equal to the codebook
cardinality. Every diversity-optimal small i-codebook is an orthogonal
multiple-relay selection (OMRS) codebook. Moreover, the limit of an optimal
small d-codebook is an OMRS codebook.
We observe that SRS is nothing but a special case of OMRS for codebooks with
cardinality equal to R. As a result, we call OMRS as "the universal necessary
condition" for codebook optimality. Finally, we confirm our analytical findings
through simulations.Comment: 29 pages, 4 figure
Distributed Beamforming in Wireless Multiuser Relay-Interference Networks with Quantized Feedback
We study quantized beamforming in wireless amplify-and-forward
relay-interference networks with any number of transmitters, relays, and
receivers. We design the quantizer of the channel state information to minimize
the probability that at least one receiver incorrectly decodes its desired
symbol(s). Correspondingly, we introduce a generalized diversity measure that
encapsulates the conventional one as the first-order diversity. Additionally,
it incorporates the second-order diversity, which is concerned with the
transmitter power dependent logarithmic terms that appear in the error rate
expression. First, we show that, regardless of the quantizer and the amount of
feedback that is used, the relay-interference network suffers a second-order
diversity loss compared to interference-free networks. Then, two different
quantization schemes are studied: First, using a global quantizer, we show that
a simple relay selection scheme can achieve maximal diversity. Then, using the
localization method, we construct both fixed-length and variable-length local
(distributed) quantizers (fLQs and vLQs). Our fLQs achieve maximal first-order
diversity, whereas our vLQs achieve maximal diversity. Moreover, we show that
all the promised diversity and array gains can be obtained with arbitrarily low
feedback rates when the transmitter powers are sufficiently large. Finally, we
confirm our analytical findings through simulations.Comment: 41 pages, 14 figures, submitted to IEEE Transactions on Information
Theory, July 2010. This work was presented in part at IEEE Global
Communications Conference (GLOBECOM), Nov. 200