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In this paper, we consider an intensity modulated direct detection MIMO optical wireless communication (OWC) system. For such a system, a novel super-rectangular cover theory is developed to characterize both the unique identifiability and full reliability. This theory states that a transmitted matrix signal can be uniquely identified if and only if the cover order is equal to the transmitter aperture number, i.e., full cover. In addition, we prove that full reliability is guaranteed for space-time block coded MIMO-OWC over commonly used log-normal fading channels with an ML detector if and only if the STBC enables full cover. In addition, the diversity gain can be geometrically interpreted as the cover order of the super-rectangle, which should be maximized, and the volume of this super-rectangle, as the diversity loss, should be minimized. Using this established error performance criterion, the optimal linear STBC for block fading channels is proved to be spatial repetition code with an optimal power allocation. The design of the optimal non-linear STBC is shown to be equivalent to constructing the optimal multi-dimensional constellation. Specifically, a multi-dimensional constellation from Diophantine equations is proposed and then, shown to be more energy-efficient than the commonly used nonnegative pulse amplitude modulation constellation., Comment: Submitted to IEEE Transactions on Informaiton Theory

In this paper, we consider a multiple-input-multiple-output optical wireless communication (MIMO-OWC) system in the presence of log-normal fading. In this scenario, a general criterion for the design of full-diversity space code (FDSC) with the maximum likelihood (ML) detector is developed. This criterion reveals that in a high signal-to-noise ratio (SNR) regime, MIMO-OWC offers both large-scale diversity gain, governing the exponential decaying of the error curve, and small-scale diversity gain, producing traditional power-law decaying. Particularly for a two by two MIMO-OWC system with unipolar pulse amplitude modulation (PAM), a closed-form solution to the design problem of a linear FDSC optimizing both diversity gains is attained by taking advantage of the available properties on the successive terms of Farey sequences in number theory as well as by developing new properties on the disjoint intervals formed by the Farey sequence terms to attack the continuous and discrete variables mixed max-min design problem. In fact, this specific design not only proves that a repetition code (RC) is the optimal linear FDSC optimizing both the diversity gains, but also uncovers a significant difference between MIMO radio frequency (RF) communications and MIMO-OWC that space dimension alone is sufficient for a full large-scale diversity achievement. Computer simulations demonstrate that FDSC substantially outperforms uncoded spatial multiplexing with the same total optical power and spectral efficiency, and the latter provides only the small-scale diversity gain.

In this paper, we consider a multiple-input-multiple-output optical wireless communication (MIMO-OWC) system suffering from log-normal fading. In this scenario, a general criterion for the design of full large-scale diversity space code (FLDSC) with the maximum likelihood (ML) detector is developed. Based on our criterion, FLDSC is attained if and only if all the entries of the space coding matrix are positive. Particularly for $2\times 2$ MIMO-OWC with unipolar pulse amplitude modulation (PAM), a closed-form linear FLDSC satisfying this criterion is attained by smartly taking advantage of some available properties as well as by developing some new interesting properties on Farey sequences in number theory to rigorously attack the continuous and discrete variables mixed max-min problem. In fact, this specific design not only proves that a repetition code (RC) is the best linear FLDSC, but also uncovers a significant difference between MIMO radio frequency (RF) communications and MIMO-OWC that space-only transmission is sufficient for a full diversity achievement. Computer simulations demonstrate that FLDSC substantially outperforms spatial multiplexing with the same total optical power and spectral efficiency and the latter obtains only the small-scale diversity gain., Comment: accepted by ISIT 2015

In this letter, we consider intensity modulation/direct detection (IM/DD) channel in the visible light communication (VLC) systems with multiple transmitter phosphor-based white light emitting diodes (LED) and single receiver avalanche photo diode (APD). We proposed a Multiple Layer Phase Shift Linear Space-time Block Code (MLPS-LSTBC). We show that our proposed code for VLC has the following main features: (a) The symbol transmission rate is $N/(N+M-1)$, where $N$ is the number of transmitter LED and $M$ denotes the number of shift intervals contained by a single codeword per layer; (b) zero-forcing receiver can transform the virtual MIMO matrix channel into parallel sub-channels even without channel state information at the receiver side (CSIR); (c) Our MLPS-LSTBC can asymptotically enhance the spectral efficiency by $\min (M\text{,}N)$, which is attractive for LED-based VLC with limited electrical modulation bandwidth. By simulations, we achieve the record data rate of 1.5 Gb/s with the bit error rate performance below the FEC limit of $2\times10^{-3}$ via multiple 100-MBaud transmission of OOK signal., Comment: This paper has been withdrawn by the author due to a crucial error in the performance analysis