tutorial on mimo channel modeling.pdf

Information Theory and Wireless Channel Modeling
M´erouaneDebbah1
Alcatel-Lucent Chair on Flexible Radio, SUPELEC, 3 rue Joliot-Curie 91192 GIF SUR YVETTE CEDEX, France
merouane.******@
1 Introduction
The problem of modelling channels is crucial for the efficient design of wireless systems [1, 2, 3]. The wireless
channel suffers from constructive/destructive interference signaling [4, 5]. This yields a randomized channel
with certain statistics to be discovered. Recently ([6, 7]), 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 Gaussian
entries of the MIMO link and perfect channel knowledge at the receiver, it has been proved [8] that the ergodic
capacity increase is min(nr,nt) bits per second per hertz for every 3dB increase (nr is the number of receiving
1
antennas and nt is the number of transmitting antennas) at high Signal to Noise Ratio (SNR) . However,
for realistic2 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 the transmission occurs 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 ponents of the multi-dimensional constellation)
plays a central role whereas maximizing the Euclidean distance is monly approved design criteria for
Gaussian channels (see Giraud and Belfiore [9] or Boutros and Viterbo [10]).
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 we only know the mean of each p