## MIMO channel model based on information theoretic tools

A general framework for deriving a channel model which is consistent with one's state of knowledge has been provided based on Information Theoretic tools. This has led to the proposal of a new time variant frequency selective double directional MIMO model. For this model, an asymptotic analysis (in the number of antennas) of the achievable transmission limit was conducted using tools of random matrix theory. A central limit was provided on the asymptotic behaviour of the mutual information and validated in the finite case by simulations and measurements performed at 2.1 GHz (using results of the FLOWS D10 deliverable). The results are both useful in terms of designing a system based on criteria such as quality of service and in optimising transmissions in multi-user networks.

The problem of modelling channels is crucial for the efficient design of wireless systems. Unlike the Gaussian channel, the wireless channel suffers from constructive/destructive interference signalling. This yields a randomised channel with certain statistics to be discovered. Recently, the need to increase spectral efficiency has motivated the use of multiple antennas at both the transmitter and the receiver side.

Hence, in the case of the i.i.d Gaussian model and perfect channel knowledge at the receiver, it has been proved that the ergodic capacity increase is min(r,t) bits per second per hertz for every 3dB increase ( is the number of receiving antennas and is the number of transmitting antennas) at high Signal to Noise Ratio (SNR). However, for realistic channel models, results are still unknown and may seriously put into doubt the MIMO hype. As a matter of fact, the actual design of efficient codes is tributary of the channel model available: the transmitter has to know in what environment it is transmitting in order to provide the codes with the adequate properties: as a typical example, in Rayleigh fading channels, when coding is performed, the hamming distance (also known as the number of distinct components of the multi-dimensional constellation) plays a central role whereas maximizing the Euclidean distance is the commonly approved design criteria for Gaussian channels.

As a consequence, channel modelling is the key in better understanding the limits of transmissions in wireless and noisy environments. In particular, questions of the form:

what is the highest transmission rate on a propagation environment where I only know the mean of each path, the variance of each path and the directions of arrival? are crucially important. It will justify the use (or not) of MIMO technologies for a given state of knowledge.

The problem of modelling channels is crucial for the efficient design of wireless systems. Unlike the Gaussian channel, the wireless channel suffers from constructive/destructive interference signalling. This yields a randomised channel with certain statistics to be discovered. Recently, the need to increase spectral efficiency has motivated the use of multiple antennas at both the transmitter and the receiver side.

Hence, in the case of the i.i.d Gaussian model and perfect channel knowledge at the receiver, it has been proved that the ergodic capacity increase is min(r,t) bits per second per hertz for every 3dB increase ( is the number of receiving antennas and is the number of transmitting antennas) at high Signal to Noise Ratio (SNR). However, for realistic channel models, results are still unknown and may seriously put into doubt the MIMO hype. As a matter of fact, the actual design of efficient codes is tributary of the channel model available: the transmitter has to know in what environment it is transmitting in order to provide the codes with the adequate properties: as a typical example, in Rayleigh fading channels, when coding is performed, the hamming distance (also known as the number of distinct components of the multi-dimensional constellation) plays a central role whereas maximizing the Euclidean distance is the commonly approved design criteria for Gaussian channels.

As a consequence, channel modelling is the key in better understanding the limits of transmissions in wireless and noisy environments. In particular, questions of the form:

what is the highest transmission rate on a propagation environment where I only know the mean of each path, the variance of each path and the directions of arrival? are crucially important. It will justify the use (or not) of MIMO technologies for a given state of knowledge.