TY - GEN

T1 - On the capacity of vector Gaussian channels with bounded inputs

AU - Rassouli, Borzoo

AU - Clerckx, Bruno

N1 - Publisher Copyright:
© 2015 IEEE.

PY - 2015/9/9

Y1 - 2015/9/9

N2 - The capacity of a multiple-input multiple-output (MIMO) identity channel under the peak and average power constraints is investigated. The approach of Shamai et al. is generalized to the higher dimension settings to derive the necessary and sufficient conditions for the optimal input probability density function. This approach prevents the usage of the identity theorem of the holomorphic functions of several complex variables which seems to fail in the multi-dimensional scenarios. It is proved that in the spherical coordinates, the magnitude and phases of the capacity-achieving distribution are mutually independent and its support is a finite set of hyper-spheres where the points are uniformly distributed on them. Subsequently, it is shown that when the average power constraint is relaxed, if the number of antennas is large enough (e.g. massive MIMO), the capacity has a closed form solution and constant amplitude signaling at the peak power achieves it. Finally, it will be observed that in a discrete-time memoryless Gaussian channel, the average power constrained capacity, which results from a Gaussian input distribution, can be closely obtained by an input where the support of its magnitude is a discrete finite set.

AB - The capacity of a multiple-input multiple-output (MIMO) identity channel under the peak and average power constraints is investigated. The approach of Shamai et al. is generalized to the higher dimension settings to derive the necessary and sufficient conditions for the optimal input probability density function. This approach prevents the usage of the identity theorem of the holomorphic functions of several complex variables which seems to fail in the multi-dimensional scenarios. It is proved that in the spherical coordinates, the magnitude and phases of the capacity-achieving distribution are mutually independent and its support is a finite set of hyper-spheres where the points are uniformly distributed on them. Subsequently, it is shown that when the average power constraint is relaxed, if the number of antennas is large enough (e.g. massive MIMO), the capacity has a closed form solution and constant amplitude signaling at the peak power achieves it. Finally, it will be observed that in a discrete-time memoryless Gaussian channel, the average power constrained capacity, which results from a Gaussian input distribution, can be closely obtained by an input where the support of its magnitude is a discrete finite set.

UR - http://www.scopus.com/inward/record.url?scp=84953708896&partnerID=8YFLogxK

U2 - 10.1109/ICC.2015.7248954

DO - 10.1109/ICC.2015.7248954

M3 - Conference contribution

AN - SCOPUS:84953708896

T3 - IEEE International Conference on Communications

SP - 4030

EP - 4035

BT - 2015 IEEE International Conference on Communications, ICC 2015

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - IEEE International Conference on Communications, ICC 2015

Y2 - 8 June 2015 through 12 June 2015

ER -