Abstract
This paper studies the characterization of the optimal input for impulsive ambient noise channels under average power constraint. Our focus is on the two-term Gaussian mixture complex noise model, which has been widely used to model impulsive noise arising in various communication channels. We first demonstrate that there exists a unique input distribution that achieves the channel capacity and the capacity-achieving input distribution has a uniformly distributed phase. By examining the Kuhn-Tucker conditions (KTC), we further show that if the optimal amplitude input distribution contains an infinite number of mass points on a bounded interval, the channel output must be Gaussian distributed. However, by using Bernstein's theorem to examine the completely monotonic condition, it is shown that the assumption of a Gaussian distributed output is not valid. As a result, there is always a finite number of mass points on any bounded interval in the optimal amplitude distribution. In addition, by applying a novel bounding technique on the KTC and using the Envelop Theorem, we demonstrate that the optimal amplitude distribution cannot have an infinite number of mass points. That gives us a unique solution of the optimal input having discrete amplitude with a finite number of mass points. Given such interesting results, we also develop an efficient way to compute the discrete optimal input and the corresponding capacity.
Original language | English (US) |
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Title of host publication | IEEE International Conference on Communications |
Publisher | Institute of Electrical and Electronics Engineers Inc. |
Pages | 4042-4047 |
Number of pages | 6 |
Volume | 2015-September |
ISBN (Print) | 9781467364324 |
DOIs | |
State | Published - Sep 9 2015 |
Event | IEEE International Conference on Communications, ICC 2015 - London, United Kingdom Duration: Jun 8 2015 → Jun 12 2015 |
Other
Other | IEEE International Conference on Communications, ICC 2015 |
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Country/Territory | United Kingdom |
City | London |
Period | 6/8/15 → 6/12/15 |
Keywords
- Capacity-achieving distribution
- discrete input
- impulsive noise
- Shannon capacity
ASJC Scopus subject areas
- Electrical and Electronic Engineering
- Computer Networks and Communications