Super-Rectangular Cover Theory And Energy-Efficient Constellation Designs For Reliable MIMO-OWC Systems

Modern society has witnessed an explosively increasing demand of information,which has been triggering off an enormous expansion of wireless communications.As an extensively investigated area,radio frequency?RF?wireless communication has played an important role in our daily life.However,the ever increasing demand of data transmission almost makes the radio spectrum saturated.As an adjunct or alternative to RF communications,intensity modulation direct detection optical wireless communication?OWC?,due to its potential for bandwidth-hungry applications,has become a very important area of research.Since diverse factors resulted from atmospheric turbulence fluctuate the transmitted optical intensity signals through the free space channels,a multiple-input-multiple-output optical wireless communication?MIMO-OWC?system is usually deployed.For such a system,the theoretical framework and signal design techniques for reliable MIMO radio frequency?MIMO-RF?with bipolar signals and complex-valued Gaussian channel coefficients are not completely applicable since both the channel coefficients and transmitted signals of MIMO-OWC are nonnegative and the probability density function of its channel coefficients is hypergeometrical.Therefore,in this paper,our research focuses on the reliable transmission theory,the signal design criterion and energy-efficient constellation designs for MIMO-OWC systems.To sum up,our main contributions in this paper are listed as follows:1.Establishment of super-rectangular cover theory from the perspective of reliable signal detection.From the viewpoint of detection theory,a novel super-rectangular cover theory is developed to characterize the identifiability of the transmitted matrix signals for MIMO-OWC.In this theory,two concepts are introduced: 1)cover order,which is defined by the maximal side number of a super-rectangular covering the feasible domain decided by a quadratic form smaller than any given positive constant;and 2)cover length,which is the side length of the smallest super-rectangular.This theory states that a matrix signal of MIMO-OWC can be uniquely identified if and only if the cover order is equal to the transmitter aperture number and gives us an algebraic definition robust to the probability density function of the channel coefficients for the reliable transmission of MIMO-OWC systems.2.Diversity analysis of MIMO-OWC systems in presence of log-normal fading by specifically using super-rectangular cover theory.In particular,the super-rectangular cover theory is applied to the diversity analysis for space-time modulated MIMO-OWC systems over log-normal fading channels.For this system,the diversity gain has a geometrical interpretation as the cover order of the super-rectangular,which should be maximized,and the volume of this super-rectangular,as the diversity loss,should be minimized.Full-cover condition is proved to be necessary and sufficient for a full large-scale diversity gain.This criterion makes it possible for us to systematically design energy-efficient constellations.3.Diversity-optimal space constellation design for MIMO-OWC system by using Farey sequence in number theory and full large-scale diversity condition.We consider the design of space constellation for a MIMO-OWC system,in which channel coefficients are independent and non-identically log-normal distributed,with variances and means known at the transmitter and channel state information available at the receiver.Utilizing the super-rectangular cover based space constellation design criterion for MIMO-OWC with a maximum likelihood?ML?detector,we design a diversity-optimal space constellation?DOSC?that maximizes cover order and minimizes the cover volume and prove that the spatial repetition code?RC?with a diversity-optimized power allocation is diversity-optimal among all the high dimensional nonnegative space constellation schemes under a commonly used optical power constraint.In addition,we show that one of significant advantages of the DOSC is to allow low-complexity ML detection.Simulation results indicate that in high signal-to-noise ratio?SNR?regimes,our proposed DOSC significantly outperforms RC,which is the best space constellation currently available for such system.4.Energy-efficient space-time multi-dimensional constellation designs for MIMO-OWC: optimal linear space-time constellation,optimal non-linear space-time structure and interger-optimal space-repetitious time-collaborative modulation block code?SRTCM-BC?.Using our established super-rectangular cover error performance criterion,the optimal linear space-time constellation for block log-normal fading channels is proved to be RC with an optimal power allocation.Then,the optimal design of the non-linear space-time constellation is shown to be equivalent to constructing the optimal multi-dimensional constellation over AWGN channels,which is a classic and long-standing topic for modern wireless communication.For this reason,a specific integer-optimal multi-dimensional constellation from Diophantine equation theory is proposed and then,shown to be more energy-efficient than the commonly used nonnegative pulse amplitude modulation?PAM?constellation.5.Time-collaborative Golden Code design for MIMO-OWC over fast log-normal fading channels.For fast fading channels,a linear space-time constellation is constructed by collaborating the signals of two successive channel uses and proved to be related with the Golden number(5^1/2)/2?0.618,say,Golden Code.This Golden Code has an important property of non-increasing cover volume as constellation size increases and thus,presents encouraging error performances by comparing with the existing schemes in the currently available for MIMO-OWC systems in presence of fast-changing log-normal fading.6.Definition and optimal one-dimensional design of additively uniquely decomposable constellation group.For multiuser MIMO-OWC systems,a concept called an additively uniquely decomposable constellation group?AUDCG?is proposed in this paper to transmit multi-layer data through users' sub-constellation cooperation.Then,an optimal one-dimensional AUDCG is designed by minimizing the average optical power subject to a fixed minimum Euclidean distance.One of significant advantages of this optimal design is fast demodulation of the sum signal from a noisy received signal as well as fast decoding individual signal from the estimated sum signal.Another important advantage is that this design allows each user-constellation to be flexibly assigned to meet different priority requirements.Computer simulations indicate that our proposed design has better error performance than currently available time orthogonal transmission scheme for this application.