On the Capacity of MIMO Optical Wireless Channels

Abstract

This paper studies the capacity of a general multiple-input multiple-output (MIMO) free-space optical intensity channel under a per-input-antenna peak-power constraint and a total average-power constraint over all input antennas. The main focus is on the scenario with more transmit than receive antennas. In this scenario, different input vectors can yield identical distributions at the output, when they result in the same image vector under multiplication by the channel matrix. We first determine the most energy-efficient input vectors that attain each of these image vectors. Based on this, we derive an equivalent capacity expression in terms of the image vector, and establish new lower and upper bounds on the capacity of this channel. The bounds match when the signal-to-noise ratio (SNR) tends to infinity, establishing the high-SNR asymptotic capacity. We also characterize the low-SNR slope of the capacity of this channel.

Bounds on the Capacity Region of the Optical Intensity Multiple Access Channel

“…It is shown that the bound from Lemma 4 due to [17], [18] is extremely tight, while the one from [9], [11] performs slightly better only when the PNR is below about 3 dB. Recently, the upper bounds (51) and (52) have been utilized in the studies on the capacity of optical intensity channels with multiple transmit apertures [27]- [29].…”

“…Finally, it is worthwhile to note that in recent years there has been a lot of research activity in communications over multiple-input and multiple-output (MIMO) optical intensity channels where the user may employ multiple transmit apertures and/or multiple detectors [1], [2], [36], [37]. Several works have investigated the channel capacity of MIMO optical intensity channels [27]- [29], [38], [39]. Similar to the OIMAC, in a MIMO optical intensity channel a detector observes a superposition of signals from multiple transmit apertures.…”

“…By(26) we can show that when user i achieves C i in (26a), userĩ can achieve C sum − C i , which exceeds Rĩ in(29). However, the rate pair(R i , Rĩ) = (I E (SNR i ), C sum − C i ) is not necessarily achievable because C sum − C i may exceed I E (SNR 1 + SNR 2 ) − I E (SNR i ).…”

Capacity of optical wireless communication channels

“…according to a distribution that maximizes I (X; Y), with respect to f X , subject to peak and average constraints. This problem has been investigated in [31][32][33][34][35].…”

“…In this case, transmission schemes can use a pre-coding matrix G ∈ R n r ×n t + to reduce the effective MIMO channel to an n r × n r channel, over which the above results can be applied. This case was studied more extensively in [35], which develops minimum-energy signalling schemes, capacity lower bounds, upper bounds and asymptotic capacity expressions.…”