04-01-2013, 03:04 PM
on Quasi-static MIMO Channels and its Application
to Adaptive Modulation
Accurate Approximation of QAM Error Probability.pdf (Size: 252.36 KB / Downloads: 38)
Abstract
An accurate approximation for the conditional error probability on quasi-static multiple antenna (MIMO)
channels is proposed. For a fixed channel matrix, it is possible to accurately predict the performance of quadratureamplitude
modulations (QAM) transmitted over the MIMO channel in presence of additive white Gaussian noise.
The tight approximation is based on a simple Union bound for the point error probability in the n-dimensional real
space. Instead of making an exhaustive evaluation of all pairwise error probabilities (intractable in many cases), a
Pohst or a Schnorr-Euchner lattice enumeration is used to limit the local theta series inside a finite radius sphere.
The local theta series is derived from the original lattice theta series and the point position within the finite multidimensional
QAM constellation. In particular, we take into account the number of constellation facets (hyperplanes)
that are crossing the sphere center. As a direct application to the accurate approximation for the conditional error
probability, we describe a new adaptive QAM modulation for quasi-static multiple antenna channels.
I. INTRODUCTION
Since the achievable information rate of conventional systems using a single antenna at both transmitter
and receiver is limited by the constellation size, most recent wireless systems use multiple transmit and
multiple receive antennas (MIMO channel) to achieve higher data rates [22][9] with a high diversity
order [20]. Several techniques have been proposed to improve the performance of these multiple antenna
systems regarding the wireless channel conditions, e.g. adaptive modulation [17] and antenna selection
[12].
An adaptive modulation technique [10][11] selects the highest information rate (e.g. increase the modulation
alphabet size) subject to a double constraint on error rate and the average transmitted power. The
selection is conditioned on the instantaneous channel state information within the current frame. Hence,
analytical expressions and numerical evaluations for the conditional error probability can be employed to
establish an adaptive modulation scheme.
ACCURATE APPROXIMATION OF ERROR PROBABILITY
The lattice representation of a multiple antenna channel converts the MIMO model given in (1) into
a simple additive white Gaussian noise (AWGN) channel model r = x + . For a given random lattice
generated by a fixed channel matrix H, let Pe() denote the point error probability associated to the
infinite set and let Pe(CH) denote the average point error probability associated to the finite constellation
CH. Trivial geometrical properties leads to the inequality Pe(CH) ≤ Pe().