MIMO III: diversity multiplexing tradeoff and universal space-time codes in .NET Printing barcode 3/9 in .NET MIMO III: diversity multiplexing tradeoff and universal space-time codes

MIMO III: diversity multiplexing tradeoff and universal space-time codes generate, create code 3 of 9 none with .net projects Microsoft SQL Server the distribut visual .net USS Code 39 ion of the fading channel gains. The drawback of the approach is that the performance of the designed codes may be sensitive to the supposed fading distribution.

This is problematic, since, as we mentioned in 2, accurate statistical modeling of wireless channels is difficult. The outage formulation, however, suggests a different approach. The operational interpretation of the outage performance is based on the existence of universal codes: codes that simultaneously achieve reliable communication over every MIMO channel that is not in outage.

Such codes are robust from an engineering point of view: they achieve the best possible outage performance for every fading distribution. This result motivates a universal code design criterion: instead of using the pairwise error probability averaged over the fading distribution of the channel, we consider the worst-case pairwise error probability over all channels that are not in outage. Somewhat surprisingly, the universal code-design criterion is closely related to the product distance, which is obtained by averaging over the Rayleigh distribution.

Thus, the product distance criterion, while seemingly tailored for the Rayleigh distribution, is actually more fundamental. Using universal code design ideas, we construct codes that achieve the optimal diversity multiplexing tradeoff. Throughout this chapter, the receiver is assumed to have perfect knowledge of the channel matrix while the transmitter has none.

. 9.1 Diversity multiplexing tradeoff In this secti bar code 39 for .NET on, we use the outage formulation to characterize the performance capability of slow fading MIMO channels in terms of a tradeoff between diversity and multiplexing gains. This tradeoff is then used as a unified framework to compare the various space-time coding schemes described in this book.

. 9.1.1 Formulation When we analy barcode 39 for .NET zed the performance of communication schemes in the slow fading scenario in s 3 and 5, the emphasis was on the diversity gain. In this light, a key measure of the performance capability of a slow fading channel is the maximum diversity gain that can be extracted from it.

For example, a slow i.i.d.

Rayleigh faded MIMO channel with nt transmit and nr receive antennas has a maximum diversity gain of nt nr : i.e., for a fixed target rate R, the outage probability pout R decays like 1/SNRnt nr at high SNR.

On the other hand, we know from 7 that the key performance benefit of a fast fading MIMO channel is the spatial multiplexing capability it provides through the additional degrees of freedom. For example, the. 9.1 Diversity multiplexing tradeoff capacity of a Visual Studio .NET ANSI/AIM Code 39 n i.i.

d. Rayleigh fading channel scales like nmin log SNR, where nmin = min nt nr is the number of spatial degrees of freedom in the channel. This fast fading (ergodic) capacity is achieved by averaging over the variation of the channel over time.

In the slow fading scenario, no such averaging is possible and one cannot communicate at this rate reliably. Instead, the information rate allowed through the channel is a random variable fluctuating around the fast fading capacity. Nevertheless, one would still expect to be able to benefit from the increased degrees of freedom even in the slow fading scenario.

Yet the maximum diversity gain provides no such indication; for example, both an nt nr channel and an nt nr 1 channel have the same maximum diversity gain and yet one would expect the former to allow better spatial multiplexing than the latter. One needs something more than the maximum diversity gain to capture the spatial multiplexing benefit. Observe that to achieve the maximum diversity gain, one needs to communicate at a fixed rate R, which becomes vanishingly small compared to the fast fading capacity at high SNR (which grows like nmin log SNR).

Thus, one is actually sacrificing all the spatial multiplexing benefit of the MIMO channel to maximize the reliability. To reclaim some of that benefit, one would instead want to communicate at a rate R = r log SNR, which is a fraction of the fast fading capacity. Thus, it makes sense to formulate the following diversity multiplexing tradeoff for a slow fading channel.

A diversity gain d r is achieved at multiplexing gain r if R = r log SNR and pout R SNR d or more precisely, lim log pout r log SNR = d r log SNR (9.3). (9.1). (9.2).
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