Capacity Analysis Of MIMO Visible Light Communication Systems

VLC is a communication method in which data is transmitted on visible light with a spectrum range of 430-790 THz.It has become one of the hot spots in the communication field because of its non-electromagnetic radiation,high speed,good safety and consideration of lighting.Compared with the traditional wireless communication signal,the visible light signal is a non-negative real signal,so it has been concluded that VLC cannot directly apply the traditional radio frequency complex signal.This paper studies the capacity of the VLC system.The main tasks are as follows:1.For the SISO-VLC system,the capacity problem under the constraint of the peak power of non-negative light intensity signals is considered.The input signal is a finite discrete signal.At this time,the system capacity can be expressed as a functional of the number of constellation points,the constellation point position vector,and the constellation point probability vector.In view of this optimization problem,the following conclusions are obtained: 1)When obtaining the optimal constellation design,the maximum and minimum optical power must be the modulation constellation points.2)When the number of constellation points is fixed and equal,the Lagrangian multiplier method is used to derive the necessary and sufficient conditions for the optimal constellation position to meet the capacity when the amount of mutual information reaches the capacity;3)The number of constellation points is given as 2.The analytical solutions of 3 and the change rule of the optimal solution when the number of constellation points is 4;4)Combining a large number of simulation results,a conjecture of the optimal solution is given for any number of constellation points.2.For the SISO-VLC system,consider the capacity problem when the average optical power of the optical signal is limited.Similarly,the input signal is a finite discrete signal.At this time,the optimization problem has equality constraints,and the Lagrangian multiplier method can be used to transform into a non-equal constraint problem.The main conclusions are as follows: 1)The equation constraint that the constellation position vector satisfies when the capacity is reachable is given.2)When the dimming target is less than0.5,the zero-value optical power must be the modulation constellation point,when it is greater than 0.5,the peak optical power must be the modulation constellation point;3)When the optical signal-to-noise ratio is fixed,the dimming factor is optimal if it is symmetrical.The position of the constellation point is symmetrical in the light intensity range;4)When the dimming factor is fixed,the influence of the optical signal-to-noise ratio on the position of the optimal constellation point;5)The analysis when the number of constellation points is equal to 2,3,and 4 solution.3.For decoupled MIMO-VLC system,the capacity problem under multi-dimensional finite discrete modulation is studied.The signal is a non-negative real signal and has an upper limit.The main conclusions are as follows: 1)When the constellation point is an optimization factor,the structure expression of the optimal multi-dimensional signal PDF and the addition relationship of the capacity are given,and the corresponding iterative algorithm is also designed;2)When the constellation point is fixed,it is given The PDF of the multi-dimensional signal when the constellation point is an exponent of 2 is discussed,and the optimal constellation design problem of decoupling MIMO-VLC is discussed.It is proved that the equality constraint is satisfied at the optimal time and the constellation point is in the two-dimensional plane.The law of position change when the value of is projected to one dimension is the same as the conclusion of the SISO-VLC system under equivalent conditions.4.For the non-decoupled MIMO-VLC system,input a multi-dimensional finite discrete signal,and consider the capacity and constellation design issues when the average power is limited.The main conclusions are: 1)The channel matrix is decomposed by SVD,and the solution of the MIMO channel can be equivalent to the capacity problem of several sub-channels;2)The invariance of the mutual information of the system before and after the decoupling is proved,and two The transformation formula of the solution in the solution space;3)For the decoupled sub-channels,under the equivalent constraint conditions,the constellation probability and the position are affected by the dimming factor and SNR are given by the functional analysis,and etc.are given.Equality constraints when the effective optimal solution capacity is reachable.