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MIMO Wireless Channels: Capacity and Performance Prediction
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Multiple-input multiple-output (MIMO) communication techniques make use of multi-element antenna arrays at both the TX and the RX side of a radio link and have been shown theoretically to drastically improve the capacity over more traditional single-input multiple output (SIMO) systems [2, 3, 5, 7]. SIMO channels in wireless networks can provide diversity gain, array gain, and interference canceling gain among other benets. In addition to these same advantages, MIMO links can offer a multiplexing gain by opening Nmin parallel spatial channels, where Nmin is the minimum of the number of TX and RX antennas. Under certain propagation conditions capacity gains proportional to Nmin can be achieved [8]. Space-time coding [14] and spatial multiplexing [1, 2, 7, 16] (a.k.a. \BLAST") are popular signal processing techniques making use of MIMO channels to improve the performance of wireless networks.

Previous work and open problems. The literature on realistic MIMO channel models is still scarce. For the line-of-sight (LOS) case, previous work includes [13]. In the fading case, previous studies have mostly been conned to i.i.d. Gaussian matrices, an idealistic assumptions in which the entries of channel matrix are independent complex Gaussian random variables [2, 6, 8]. The influence of spatial fading correlation on either the TX or the RX side of a wireless MIMO radio link has been addressed in [3, 15]. In practice, however, the realization of high MIMO capacity is sensitive not only to the fading correlation between individual antennas but also to the rank behavior of the channel. In the existing literature, high rank behavior has been loosely linked to the existence of a dense scattering environment. Recent successful demonstrations of MIMO technologies in indoor-to-indoor channels, where rich scattering is almost always guaranteed.

Here we suggest a simple classification of MIMO channel and devise a MIMO channel model whose generality encompasses some important practical cases. Unlike the channel model used in [3, 15], our model suggests that the impact of spatial fading correlation and channel rank are decoupled although not fully independent, which allows for example to describe MIMO channels with uncorrelated spatial fading at the transmitter and the receiver
but reduced channel rank (and hence low capacity). This situation typically occurs when the distance between transmitter and receiver is large. Furthermore,our model allows description of MIMO channels with scattering at both the transmitter and the receiver.

We use the new model to describe the capacity behavior as a function of the wavelength, the scattering radii at the transmitter and the receiver, the distance between TX and RX arrays, antenna beamwidths, and antenna spacing. Our model suggests that full MIMO capacity gain can be achieved for very realistic values of scattering radii, antenna spacing and range. It shows, in contrast to usual intuition, that large antenna spacing has only limited impact on capacity under fairly general conditions. Another case described by the model is the "pin-hole" channel where spatial fading is uncorrelated and yet the channel has low rank and hence low capacity.We show that this situation typically occurs for very large distances between transmitter and receiver. In the 1 * 1 case (i.e. one TX and one RX antenna), the pinhole channel yields capacities worse than the traditional Rayleigh fading channel. Our results are validated by comparing with a ray tracing-based channel simulation. We find a good match between the two models over a wide range of situations.

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