CN111565071B - Optimum power distribution method of ACO-OFDM in VLC system - Google Patents

Abstract

The invention provides an optimal power distribution method of ACO-OFDM in a VLC system, which is used for solving the Energy Efficiency (EE) of asymmetric amplitude limiting optical orthogonal frequency division multiplexing (ACO-OFDM) of Visible Light Communication (VLC). The present invention first derives the achievable rates for capacity-achieving gaussian distributed input and actual limited alphabet input. However, considering quality of service, power and dimming control constraints, the non-convex EE maximization problem of ACO-OFDM VLC with gaussian distributed input and limited letter input, respectively, is further analyzed and solved. The present invention solves these problems by the proposed Dinkelbach type iterative algorithm. The performance of the proposed optimal power allocation scheme for EE maximization was verified by numerical analysis.

Description

Optimum power distribution method of ACO-OFDM in VLC system

Technical Field

The invention relates to the field of visible light communication, in particular to an optimal power distribution method of ACO-OFDM in a VLC system.

Background

Conventional Radio Frequency (RF) communication is facing the situation of spectrum tightening, and thus, the demand for wireless data traffic is exponentially increasing. In addition, the amount of energy consumed by wireless devices is enormous, exceeding 3% of the global energy consumption, and by 2020, it accounts for about 5% of the total global carbon dioxide emissions. Thus, both spectrum and energy resources are severely limited by next generation wireless communications. With the push of low cost and widely installed lighting infrastructure with Light Emitting Diodes (LEDs), Visible Light Communication (VLC) has become a promising green indoor Communication solution, enabling simultaneous lighting and wireless data transmission. VLC systems are a powerful complement of RF systems for enabling high-speed wireless data transmission due to their inherent advantages, such as rich license-free spectrum, high security and no interference with existing RF systems.

Although VLC techniques bring considerable benefits, in high-rate VLC systems, because the modulation bandwidth of LEDs is only tens of MHz at all times, severe Inter Symbol Interference (ISI) may exist as multipath transmission. To alleviate the ISI problem, Orthogonal Frequency Division Multiplexing (OFDM) has been adopted as a Physical layer (PHY) standard to be implemented by 4G RF communication, which can achieve high bandwidth efficiency and excellent anti-fading performance. However, as the VLC system uses an Intensity Modulation and Direct Detection (IM/DD) scheme, information of the VLC is represented by light Intensity, and thus a transmitted signal should be true and non-negative. Therefore, the conventional RF OFDM cannot be directly applied to the VLC system. To mitigate the ISI problem, VLC systems propose asymmetric limiting optical OFDM (ACO-OFDM) and direct current offset optical OFDM (DCO-OFDM). To generate a non-negative transmit signal, ACO-OFDM cancels the negative component of the signal, while DCO-OFDM adds a Direct Current (DC) offset and then clips the negative portion of the signal to zero. Further, the ACO-OFDM transmits data symbols through only odd subcarriers, and the DCO-OFDM transmits data symbols through all subcarriers. ACO-OFDM with single polarization signal mode can achieve lower bit error rate compared to DCO-OFDM with clipping noise. Due to the DC offset, DCO-OFDM requires a higher signal-to-noise ratio in low order modulation, which makes it less efficient than ACO-OFDM. The spectral efficiency of both the ACO-OFDM and the U-OFDM is half of that of the DCO-OFDM. Enhanced U-OFDM (eU-OFDM) is proposed to compensate for the spectral efficiency loss in U-OFDM by combining multiple U-OFDM streams into a single time domain stream signal.

For high-speed VLC OFDM systems, both the achievable rate expression and the optimal power allocation scheme are essential characteristics. Neither the classical shannon capacity formula nor the power allocation scheme of RF OFDM systems can be directly applied to VLC OFDM systems due to the limitation of monopolarity. By introducing the signal-to-noise-plus-distortion ratio, the direct current offset and the information bearing power are jointly optimized, so that the achievable rate of the DCO-OFDM is improved to the maximum extent. Under the constraint of average optical power, an information rate result and a water-filling power distribution scheme of the ACO-OFDM system are provided. The authors investigated the SNR performance of asymmetrically clipped DC offset optical OFDM (ADO-OFDM), which has higher optical power efficiency than conventional ACO-OFDM and DCO-OFDM. In the known document, information rates of unipolar OFDM, such as DCO-OFDM, ACO-OFDM and U-OFDM, are derived under the constraints of average optical power, and capacities of near high SNR are obtained, and by optimizing the power allocation, using various multi-component schemes, such as ADO-OFDM and eU-OFDM, under the constraints of bandwidth and average optical power, it is known that the document studies the ACO-OFDM, the effective information rates of SEE-OFDM and DCO-OFDM assess the excess bandwidth that clipping operations cause to the achievable rates. Under the constraints of average and dynamic optical power, authors in the known literature analyze the performance of DCO-OFDM and ACO-OFDM systems in terms of error vector magnitude, signal-to-noise ratio and achievable data rate. Adaptive hierarchical ACO-OFDM with variable layers is studied in the known literature, where the optimal layer quantity should be adaptively varied with SNR. In the known literature, the authors have analyzed the achievable rates of ACO-OFDM and DCO-OFDM under the nonlinear distortion and electrical power constraints of the LEDs. By deriving the probability density function of the received signal, authors in the known literature have investigated the lower bound of Asymmetric and Symmetric Clip Optics (ASCO) -OFDM and ADO-OFDM channel capacities.

However, most of the VLC studies described above aim to improve achievable throughput, while there is little concern about energy efficiency. Energy efficiency of VLC systems based on amorphous user-to-network association structures is designed in known literature, where amorphous batteries are shown to achieve higher energy efficiency than conventional battery structures. By analyzing the additional power consumption and data rate capabilities, authors in the known literature have studied the power loss at the VLC transmit end using OFDM and Pulse Amplitude Modulation (PAM) modulation schemes, respectively. For VLC systems, the relationship of energy efficiency, defined as the data rate per unit power consumed by the LED, to spectral efficiency is studied in the known literature. In the known literature, the authors analyzed and compared the energy efficiency and spectral efficiency of ACO-OFDM, PAM-DMT, DCO-OFDM, ADO-OFDM, HACO-OFDM and LACO-OFDM. Although the search for VLC systems has been greatly emphasized. But there is little concern about the energy efficiency of VLC systems. For communication systems, energy efficiency is typically defined as the ratio of the achievable data rate to the total power consumption. From the known literature, it is known that for VLC the energy consumption serves at least two purposes: lighting and data transmission. In the known literature, it is focused on maximizing the energy efficiency problem of visible light communication systems. By using the Dinkelbach's algorithm and Lagrange method, the optimal power consumption of the PA can be obtained in a closed form in SISO and MISO systems.

Through the joint design of unit formation and system-level power distribution, the amorphous structure of the ACO-OFDM VLC system can realize higher EE than the conventional unit structure. To ensure that quality of service (QoS) is provided at an affordable energy, EE is present^[32]Conventional and OFDM-based hybrid VLC modulation schemes are investigated.

However, the current research EE for ACO-OFDM is based on Gaussian distribution input. As mentioned earlier, gaussian distributed input is difficult to generate in practice, while the actual input is always limited alphabetic input, which is rarely studied in the literature.

Disclosure of Invention

The purpose of the invention is as follows: to solve the technical problems in the background art, the present invention provides an optimum power allocation method for asymmetric amplitude limiting optical orthogonal frequency division multiplexing (ACO-OFDM) in a Visible Light Communication (VLC) system, so as to maximize energy efficiency ee (energy efficiency) of the ACO-OFDM VLC system having gaussian distribution input and limited alphabet input. The present invention systematically analyzes the signal processing modules of a typical ACO-OFDM VLC system. Based on the frequency domain analysis, the gaussian distribution rate of the considered system is first derived from the point of view of the channel capacity, with the gaussian distribution input from the point of view of the channel capacity and the finite alphabet input from the point of view of the actual modulation. Furthermore, for the two inputs described above, a corresponding dimming control was developed for the ACO-OFDM VLC system. In addition, an explicit EE expression is proposed with Gaussian distribution input and limited alphabet input, respectively. The problem of maximizing EE has been studied under the constraints of maximum transmission power and minimum data rate requirements, which is a non-convex problem. This problem can be solved by applying the Dinkelbach type algorithm and the interior point algorithm.

The VLC system comprises 2N subcarriers, signals are only sent through odd subcarriers, no signal is sent on even subcarriers, and a transmitting end of the system executes the following steps:

step 1: the information bit stream generated by the signal generator is converted into parallel sub-streams through a serial-parallel converter;

step 2: modulating the parallel sub-streams converted in the step 1 by a multi-system quadrature amplitude modulation (M-QAM) scheme;

and step 3: applying inverse fast Fourier transform and zero clipping to the frequency domain signal X to obtain a non-negative digital signal

And 4, step 4: passing the digital signal through an analog-to-digital converter

Is converted into an analog signal and then emitted through visible light;

and 5: by using the direct detection IM/DD scheme, the transmitted information of the system is represented by signal strength, which is real and non-negative;

step 6: at the receiver, the received visible light is converted into an analog electrical signal by a photodetector and then converted into a digital signal by an analog-to-digital converter;

and 7: the digital signal is demodulated into information bits by an M-QAM demodulator using a fast fourier transform.

The step 2 comprises the following steps: at the transmitting end of the system, to ensure the actual output of the IFFT, the input of the IFFT module (i.e., the inverse fast fourier transform part) is Hermitian (Hermitian, meaning conjugate symmetry) symmetry, i.e.:

wherein X_iRepresenting the modulated signal on the ith subcarrier, X_2i-1Is a normalized unit power input, i.e. average power

Conjugate symmetry on odd carriers;

let p be_iRepresents the allocated power of the ith subcarrier, wherein

P is the total electrical transmit power; according to the table formula (1), power division factor { p_iSatisfy:

wherein p is_2(N-i)-1Indicating power factor on odd carrier, then transmit electric power constraint is rewritten as

After IFFT operation, digital signal x_kExpressed as:

wherein j represents a formula in inverse Fourier of the discrete signal and represents a complex number; re represents the real part of the complex number; k represents a kth digital signal;

according to equation (3), the obtained time domain signal satisfies the antisymmetry as follows:

x_k＝-x_k+N, (4)

wherein k is 1.., N;

since the transmitted signal is non-negative, the truncation ignores the negative signal, i.e., the non-negative signal

Comprises the following steps:

the non-negative signal obtained in step 3 needs to adopt dimming control to meet the actual requirement of illumination, and order P_oRepresents the average optical power threshold, and η ∈ (0, 1)]Represents a dimming level, and dimming control is represented as:

in step 4, the analog signal is transmitted through visible light, and needs to pass through a VLC channel, which is as follows:

let H_iRepresents the channel gain of the ith subcarrier, which includes both line-of-sight and scatter links, as shown below

H_i＝H_L,i+H_D,i, (7)

Wherein H_L,iIs the channel gain of the line-of-sight link for the ith subcarrier, and H_D,iIs the channel gain of the scattering link for the ith subcarrier, i 1.

Channel gain H of line-of-sight link of ith subcarrier_L,iExpressed as:

wherein g is_LIs a generalized Lambertian emission model, f_iDenotes the frequency of the ith subcarrier, τ is the delay between two subcarriers, τ ═ d-c, d is the distance between the transmitter and the receiver, c is the speed of light, i 1.., 2N;

the generalized Lambertian emission model g_LExpressed as:

where m is the order of lambertian emission, i.e. m ═ ln2/ln (cos Φ)_1/2)，Φ_1/2Representing the half-power angle, A_rRepresenting the effective receiving area of the photodetector,

and theta denotes an incident angle and an irradiation angle from the LED to the PD, respectively (i.e., the LED emits light of different intensities to perform photoelectric conversion, and then passes through a photodetector at a receiving end),

and

the optical filter gain and the concentrator gain of the receiver, respectively, and Ψ denotes the field angle of the receiver;

channel gain H of scattering link of ith subcarrier_D,iExpressed as:

wherein eta_DIs the power efficiency of the scattered signal.

In step 6, an optimal power allocation scheme is designed to maximize the energy efficiency of the system under the constraints of user quality of service requirements and electrical and optical power, and the EE maximization problem of the system is expressed as:

where r is the minimum achievable rate requirement.

In step 6, when the input is a gaussian input distribution, the problem (15) is solved as follows:

setting input signal X_2i-1Subject to independent complex Gaussian distributions, i.e.

Time domain signal x according to IFFT operation expression (3)_kStill subject to a Gaussian distribution, i.e.

The average optical power is expressed as:

wherein the parameters

In addition, by substituting (16) into (15), the dimming control is re-expressed as:

according to Shannon's theorem, the rate R can be reached_G({p_2i-1}) is expressed as:

substituting the reachable rate expression (18) of Gaussian input distribution to obtain the energy efficiency EE_G({p_2i-1}) is:

the energy efficiency maximization problem with the gaussian input distribution of the system is written as:

y represents a viable cluster of issues (20):

wherein the parameters

Parameter(s)

Introducing a new function f ({ p)_2i-1}) are as follows:

where q is a given real-valued parameter, by calculating the equation f ({ p)_2i-1Y) 0 at the root of the actionable domain, to obtain the optimal solution to the problem (20);

for a given q, with respect to p_2i-1The convex sub-problem of (a) is expressed as:

for a given q, the question (20) is about p_2i-1By making the function f ({ p)_2i-1}) is 0, i.e.

Thus obtaining:

next, the feasible solution of problem (23)

Projection into a feasible set y, resulting in an optimal power distribution scheme for the problem (23)

Specifically represented by the formula:

wherein

To represent

Projection in subspace γ.

In step 6, when the input is in the process of inputting bounded characters, solving the problem (15) in the following way:

setting input signal from discrete constellation set

Of order M, wherein X_2i-1,kIs the constellation point of the (2i-1) th subcarrier, the achievable rate R of the bounded input distribution_F({p_2i-1}) is written as:

wherein the parameters

Which is used to measure the constellation point X_2i-1,nAnd X_2i-1,kThe difference between the above-mentioned two methods,

is the noise Z_2i-1(iii) a desire; from the known literature, R_F({p_2i-1Is allocated power p)_2i-1A concave function of (d);

according to expression (5), the average optical power of the transmitted signal is written as:

wherein

Depending on the particular modulation scheme (e.g., the example of 4-qam, x)_iValues are 1+ j, 1-j, -1+ j, -1-j, the mean value is 1, and (27) is substituted into (6), and the dimming control constraint is expressed as:

according to the inequality

And an intermediate parameter a_iNot less than 0, the dimming control constraint is rewritten as:

for a bounded signal input, the expression for the achievable rate is given by (15), and the energy efficiency EE of the bounded input signal_F({p_2i-1}) is expressed as:

next, the dimming control constraint is expressed as

The bounded input maximization energy efficiency problem under power and rate constraints is then expressed as:

in step 6, the lower-bound optimal energy efficiency problem of the mutual information is solved by the following method:

mutual information of the system I_2i-₁({p_2i-1}) is expressed as:

wherein the parameters

The upper limit of the desired term in equation (32) is:

wherein the inequality (31) is based on the Jense inequality, (31) the second term is a desire for gaussian noise Z;

let I_L({p_2i-1}) represents a lower bound on the (2i-1) th sub-carrier for mutual information, in which system there is a lower bound R for achievable rate of symbol entry_L({p_2i-1}) is expressed as:

wherein, I_L({p_2i-1}) denotes the power p of the 2i-1 th sub-carrier in the lower bound case of mutual information_2i-1Mutual information of (2);

using the lower bound of mutual information (32), the energy efficiency function of the system is expressed as:

therein, EE_L({p_2i-1Denotes the power p for the 2i-1 th sub-carrier in the case of the mutual information boundary_2i-1As a function of energy efficiency;

the energy efficiency EE problem (15) is re-expressed as:

in step 7, after applying the fast fourier transform, a frequency domain signal is obtained:

let Y_2i-1Represents a signal received in the frequency domain of the 2i-1 th subcarrier, which is given by:

where the coefficient 1/2 indicates that only half of the subcarriers send information; z_2i-1Representing additive white Gaussian noise with an average value of 0, i.e.

W_2i-1Represents the bandwidth of the (2i-1) th subcarrier;

let R_2i-1({p_2i-1}) denotes the rate of the (2i-1) th subcarrier, which is expressed as:

R_2i-1({p_2i-1})＝I(X_2i-1；Y_2i-1) (12)

wherein I denotes mutual information, R_ACOThe total rate of the ACO-OFDM system is expressed by the formula:

meanwhile, the energy efficiency EE of the system is defined as the ratio of capacity to total power consumption, expressed as:

wherein

Electric power, P, representing sub-carriers_cIndicating the loop power consumption of the entire system, EE ({ p)_2i-1} is a function of energy efficiency with respect to power.

Has the advantages that:

the invention provides an optimal power distribution scheme under the constraints of transmission power and dimming control, which is used for solving the Energy Efficiency (EE) of asymmetric amplitude limiting optical orthogonal frequency division multiplexing (ACO-OFDM) of Visible Light Communication (VLC). We propose an explicit EE expression with gaussian distributed input and limited alphabet input, respectively. Furthermore, the problem of maximizing EE has been studied under the constraints of maximum transmission power and minimum data rate requirements, which is a non-convex problem. This problem can be solved by applying the Dinkelbach type algorithm and the interior point algorithm.

Drawings

The foregoing and/or other advantages of the invention will become further apparent from the following detailed description of the invention when taken in conjunction with the accompanying drawings.

FIG. 1 is a block diagram of a transmitting end of an asymmetric amplitude-limited optical orthogonal frequency division multiplexing ACO-OFDM system;

fig. 2 is Ε_G，ΕΕ_FE_LIs different in the distribution power p_iChannel gain H with subcarrier i_iA schematic diagram of the relationship of (1);

fig. 3 e Ε_G，ΕΕ_FE_LA relation diagram with an electric power threshold value P;

FIG. 4 shows the power threshold P-1 (W) and the optical power threshold P₀E 0.003(W)_G，ΕΕ_FE_LAnd a velocity threshold r.

Detailed Description

The present invention addresses the lack of workable, optimal power allocation schemes to maximize EE for ACO-OFDM VLC systems with gaussian distributed input and limited alphabetic input.

Fig. 1 shows a block diagram of the transmitting end of the ACO-OFDM system, i.e. how the signal model is generated, the specific steps are as follows:

step 1: the information bit stream is first converted into parallel sub-streams by a serial-to-parallel (S/P) converter.

Step 2: modulating through an M-QAM scheme;

namely:

X_2i＝X_2(N-i)-2＝0,

wherein X_iRepresenting the modulated signal on the ith subcarrier, X_2i-1Is a normalized unit power input, i.e.

Let p be_iRepresents the allocated power of the ith subcarrier, wherein

P is the total electrical transmit power. According to expression (1), power division factor { p_iShould satisfy

p_2i＝p_2(N-i)-2＝0,

p_2i+1＝p_2(N-i)-1≥0,i＝0,...,N/2-1.

Thus, the transmitted electric power constraint may be rewritten as

And step 3: after applying Inverse Fast Fourier Transform (IFFT) and zero clipping, the signal

Is non-negative

Time domain signal x_kCan be expressed as:

according to expression (3), the obtained time-domain signal satisfies the antisymmetry, as follows:

x_k＝-x_k+N,

wherein k is 1.

Since the transmitted signal should be non-negative, the truncation process ignores the negative signal, i.e.:

for VLC systems, dimming control has been employed to meet lighting requirements^[46,47]The actual requirements of (2). Let P_oRepresents the average optical power threshold, and η ∈ (0, 1)]Indicating a dimming level. The dimming control is expressed as:

and 4, step 4: after passing the signal through an analog-to-digital converter (D/A), the digital signal

Converted to an analog signal and then transmitted through visible light.

And 5: by using the IM/DD scheme, transmission information of the VLC system is represented by signal strength, which is real and non-negative.

Step 6: at the receiver, the received visible light is converted to an analog electrical signal by a Photodetector (PD) and then converted to a digital signal by an analog-to-digital converter (a/D).

And 7: after applying a Fast Fourier Transform (FFT), the signal is demodulated into information bits by an M-QAM demodulator.

And (3) channel model:

VLC channels are typically characterized by line of sight (LOS) links and multiple reflections of light from surrounding objects such as walls, floors, and windows. In this study, the present invention employs a common frequency domain VLC channel model that is not limited to a finite order of reflection.

Let H_iRepresents the channel gain for the ith subcarrier, which includes both line-of-sight and scatter links, as follows:

H_i＝H_L,i+H_D,i,

wherein H_L,iIs the channel gain of the line-of-sight link, and H_D,iIs the channel gain of the scattering link, i 1.

Line-of-sight link H_L,iExpressed as:

wherein g is_LIs a generalized Lambertian emission model, f_iDenotes the frequency of the ith subcarrier, and τ is the delay between the two, where τ is d/c.

d is the distance between the transmitter and the receiver, c is the speed of light, i 1. Generalized lambertian radiator g_LCan be expressed as

Where m is the order of lambertian emission, i.e. m ═ ln2/ln (cos Φ)_1/2)，Φ_1/2Representing the half-power angle, A_rRepresenting the effective receiving area of the photodetector,

and theta denotes an incident angle and an irradiation angle from the LED to the PD respectively,

and

respectively the optical filter gain and the concentrator gain of the receiver. Ψ denotes the field angle (FOV) of the receiver.

Channel gain H of a scattering link_D,iAs follows:

wherein eta_DIs the power efficiency of the scattered signal.

Performance indexes are as follows:

after modulation at the transmitting end, the signal is transmitted over an optical channel. At the receiver, it performs an FFT to obtain a frequency domain signal. However, due to the effect of zero frequency truncation, it is known in the known literature that the amplitude of the frequency domain signal at the receiver is half the amplitude at the transmitter. Let Y_2i-1Represents a signal received in the frequency domain of the 2i-1 th sub-carrier, which is given by

Where the coefficient 1/2 indicates that only half of the subcarriers send information. Z_2i-1Represents additive white gaussian noise with an average of 0, such as:

W_2i-1indicating the bandwidth of the (2i-1) th subcarrier.

Let R_2i-1({p_2i-1}) denotes the rate of the (2i-1) th subcarrier, which can be expressed as

R_2i-1({p_2i-1})＝I(X_2i-1；Y_2i-1),

R_ACORepresents the total rate of the ACO-OFDM system, which can be expressed as

Meanwhile, EE of the ACO-OFDM VLC system is defined as a ratio of capacity to total power consumption, expressed as:

wherein

Electric power, P, representing sub-carriers_cRepresenting the power consumed by the loop of the overall system.

Energy efficiency study after distribution by gaussian input:

suppose an input signal X_2i-1Subject to independent complex Gaussian distributions, e.g.

After operation according to IFFT, time domain signal x_kStill subject to a Gaussian distribution, i.e.

In addition, the average optical power is expressed as:

wherein

The dimming control is re-expressed as:

according to Shannon's theorem^[49]Reachable rate R_G({p_2i-1}) is expressed as:

the energy efficiency EE is obtained from the reachable rate expression of Gaussian input distribution_G({p_2i-1}) is:

the problem of maximizing energy efficiency with respect to the gaussian input distribution of an ACO-OFDM system is therefore written as:

for the objective function, its numerator is the variable p_2i-1With denominator being related to p_2i-1So that the objective function is with respect to p_2i-1A pseudo-concave function of (a). With linear constraints, the problem of energy efficiency is the linear concave fraction problem^[56]It is non-convex. To avoid non-convexity, Dinkelbach algorithm can be adopted^[57–59]The problem is solved by converting the problem energy efficiency problem into a series of convex sub-problems. In particular, an optimal solution to the energy efficiency problem may be obtained by solving these convex sub-problems by iteration. γ represents a feasible set constraint of energy efficiency issues:

wherein the parameters

Parameter(s)

Introducing a new function f ({ p)_2i-1}) are as follows:

where q is a given real-valued parameter, which can be obtained by iteration. Next, by calculating the equation f ({ p)_2i-1Y) 0 at the root of the actionable domain, an optimal solution to the energy efficiency problem may be obtained.

For a given q, with respect to p_2i-1Can be represented as

For a given q, the energy efficiency problem is with respect to p_2i-1A convex function of (a). Thus, by letting the function f ({ p)_2i-1}) is 0, i.e.

Can obtain

Then, will

Projection into feasible set y, resulting in problem (4-6) optimal power distribution scheme

Specifically, it can be represented by the following formula

Wherein

To represent

Projection in subspace γ.

Formula (4-8) defines the operable region y. For smaller electrical transmit power budgets, EE maximization shows the same water-filling solution. However, when the budget is large enough, the optimum EE power algorithm will limit the transmit power level once the maximum EE is reached.

Finally, the problem of EE maximization of Gaussian distribution input can be solved through a Dinkelbach type algorithm. Under the limited iteration times, the Dinkelbach type algorithm can be used for ensuring the convergence to the optimal solution of the problem (4-8).

Energy efficiency study under bounded character input:

in practice, a typical input signal is a discrete signal constellation point, such as M-ary phase shift keying (M-psk) or quadrature amplitude modulation of order M (M-QAM), rather than the ideal Gaussian signal. The input signal is set to be derived from discrete constellation points of order M. Setting the input from a discrete constellation set

Of order M, wherein X_2i-1,kIs the constellation point of the (2i-1) th subcarrier. Thus, the achievable rate R of the bounded input distribution_F({p_2i-1}) can be written as

Wherein

Which is used to measure the constellation point X_2i-1,nAnd X_2i-1,kThe difference between the above-mentioned two methods,

is the noise Z_2i-1The expectation is that. R_F({p_2i-1Is allocated power p)_2i-1A concave function of (a).

The average optical power of the transmitted signal is written as:

wherein

Depending on the particular modulation scheme, the dimming control constraint is expressed as:

according to the inequality

And a is_iNot less than 0, the dimming control constraint is rewritten as:

optical power constraints are denoted as such.

For bounded signal inputs, an expression for the achievable rate may be given as such. Thus, the energy efficiency EE of the bounded input signal_F({p_2i-1}) is expressed as:

second, the dimming control constraint can be expressed as a constraint

Therefore, the bounded input maximization energy efficiency problem under power and rate constraints is expressed as:

there is no closed form expression for the achievable rates for the above problems, since for input power, R is_F({p_2i-1Is aA strictly concave function. In combination with the feasible set of convexes formed by linear constraints, the above problem is a concave linear differentiable problem, and therefore it can also be solved with Dinkelbach.

Energy efficiency issues at the lower bound of mutual information:

for bounded input signals, the optimal power allocation scheme includes integral calculations from- ∞ to + ∞ of MMSE. This calculation can be obtained by monte carlo simulations, but at the cost of high computational complexity. To balance complexity and performance, the present invention further develops a low complexity power allocation scheme.

First, mutual information of ACO-OFDM is expressed as:

wherein

Further, the upper limit of the desirable term in the above is:

wherein the above inequality is based on the Jense inequality.

Let I_L({p_2i-1}) represents the lower bound of mutual information on the (2i-1) th subcarrier. Thus, in a visible light communication ACO-OFDM communication system, the lower bound of the achievable rate of bounded symbol input is expressed as:

in the objective function, the integral needs to be solved with high computational complexity. To reduce the computational complexity, a lower bound of mutual information is used, and the energy efficiency function of the corresponding system is expressed as:

furthermore, the EE problem is re-expressed as:

the problem is also a concave linear differentiable problem, since the lower bound of achievable rates is concave and differentiable. Meanwhile, the above problem can be solved by using a Dinkelbach algorithm.

Examples

The present embodiment provides simulation results to verify the results of the present invention and from the optimal energy efficiency problem with gaussian and bounded input distributions.

The ACO-OFDM VLC system includes 4 LEDs, and other basic parameters of the VLC system are listed in table 1.

TABLE 1

Definition	Value
		Number of subcarriers，N	64
Transmit angle，θ	60°
		FOV，Ψ	90°
Lambertian emission order，m	1
		Dimming level，η	1
Half power angle，Φ1/2	60°
		PD collection area，Ar	1cm2
Circuit power consumption，Pc	0.1W
		Angle of arrival/departure，ψ	45°
Noise PSD，σ2	10-18A2/Hz
		Modulation order，M	4-QAM
Bandwidth of(2i-1)subcarrier，W2i-1	1MHz

In table 1, starting from the second row, the parameters of each row are: subcarrier number, transmission angle, reception field of view, lambertian transmission order, dimming level, half-power angle, effective reception area of the photodetector, circuit power consumption, arrival/departure angle, PSD noise, modulation order, and subcarrier bandwidth.

FIG. 2 shows the energy efficiency EE of a Gaussian input distribution_GEnergy efficiency EE for bounded character input_FEnergy efficiency EE of the lower bound of mutual information_LWith respect to the channel gain Hi of the subcarrier i (left ordinate in fig. 2 is the distributed power, right ordinate is the channel gain, abscissa is the subcarrier), wherein the electrical power threshold P is 2(W) and the optical power threshold P is 2(W)₀0.003(W) and the rate threshold r 1 (bit/sec/Hz). FIG. 2 shows, due to the power allocation strategy in (51) and (52), EE_GThe allocated power of the subcarrier i is proportional to its channel gain. EE_FAnd EE_LThe allocated power of subcarrier i depends on the channel gain and the MMSE function. In particular, the proposed algorithm avoids allocating too much power to the subcarriers to maximize the system EE.

FIG. 3 depicts EE, respectively_G，EE_FAnd EE_LRelation to electric power threshold value P (energy efficiency on ordinate and power threshold value on abscissa in FIG. 3), optical power threshold value P₀0.003(W) and P₀Infinity (no optical power constraint), where the rate constraint r is 0.1 (bits/sec/Hz). FIG. 3 shows that, with increasing P, EE_G，EE_FAnd EE_LFirst increasing and then remaining constant. The reason for the case with optical power constraint is that, as the electrical power P increases, EE_GEEF and EE_LConstrained by luminous power P₀Limit of 0.003 (W); for the case of no optical power limitation, the best EE remains constant when it reaches an optimum value. Moreover, Ε_FE_LThe gap between them decreases as the power threshold P increases. FIG. 3 also shows that the EE performance for limited letter input is significantly higher than for Gaussian distribution input.

Fig. 4 depicts a circuit having a power threshold P-1 (W) and an optical power threshold P₀E 0.003(W)_G，ΕΕ_FE_LAnd a rate threshold r. As shown in fig. 4 (the ordinate in fig. 4 is energy efficiency, the abscissa is rate threshold), Ε e_FAbove Ε_LE_G. Furthermore, EE for the three cases first remains constant and then decreases as the rate threshold r increases. This is because the power allocation performed when the value of the rate threshold r is smallThe rate requirements can be met more easily and hence EE does not change. For the high rate threshold r, the resource allocation in the system becomes less feasible when allocating power, as it is forced to consume more power to meet the strict rate constraints, and therefore the best EE is reduced. Moreover, Ε_FE_LThe gap between decreases as the rate threshold r increases. Fig. 4 also verifies that the EE performance for limited alphabetic input is significantly higher than for gaussian distributed input. In fact, a scheme designed for gaussian input increases the transmit power in some subcarriers even if the highest modulation order is reached.

The present invention provides a method for allocating optimum power of ACO-OFDM in VLC system, and a plurality of methods and approaches for implementing the technical solution, and the above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, a plurality of improvements and modifications may be made without departing from the principle of the present invention, and these improvements and modifications should also be regarded as the protection scope of the present invention. All the components not specified in the present embodiment can be realized by the prior art.

Claims (5)

1. An optimal power allocation method for ACO-OFDM in VLC system, wherein said VLC system includes 2N sub-carriers, signal is transmitted only via odd sub-carrier, no signal is transmitted on even sub-carrier, the transmitting end of the system executes the following steps:

step 1: the information bit stream generated by the signal generator is converted into parallel sub-streams through a serial-parallel converter;

step 2: modulating the parallel sub-streams converted in the step 1 by an M-QAM scheme;

and step 3: applying inverse fast Fourier transform and zero clipping to the frequency domain signal X to obtain a non-negative digital signal

And 4, step 4: passing the digital signal through an analog-to-digital converter

Is converted into an analog signal and then emitted through visible light;

and 5: by using a direct detection scheme, the transmitted information of the system is represented by signal strength, which is real and non-negative;

step 6: at the receiver, the received visible light is converted into an analog electrical signal by a photodetector and then converted into a digital signal by an analog-to-digital converter;

and 7: applying fast Fourier transform to the digital signal, the digital signal being demodulated into information bits by an M-QAM demodulator;

the step 2 comprises the following steps: at the transmitting end of the system, to ensure the actual output of the IFFT, the input of the IFFT module is Hermitian symmetry, i.e.:

wherein X_iRepresenting the modulated signal on the ith subcarrier, X_2i-1Is a normalized unit power input, i.e. average power

Conjugate symmetry on odd carriers;

let p be_iRepresents the allocated power of the ith subcarrier, wherein

P is the total electrical transmit power; according to the table formula (1), the power is distributed { p_iSatisfy:

wherein p is_2(N-i)-1Assigned power on odd carriers, the transmit electric power constraint is rewritten as

After IFFT operation, digital signal x_kExpressed as:

wherein j is a plurality; re represents the real part of the complex number; k denotes the kth digital signal, α_2i-1Represents a normalized power allocation factor;

according to equation (3), the obtained time domain signal satisfies the antisymmetry as follows:

x_k＝-x_k+N, (4)

wherein k is 1.., N;

since the transmitted signal is non-negative, the truncation ignores the negative signal, i.e., the non-negative signal

Comprises the following steps:

the non-negative signal obtained in step 3 needs to adopt dimming control to meet the actual requirement of illumination, and order P_oRepresents the average optical power threshold, and η ∈ (0, 1)]Represents a dimming level, and dimming control is represented as:

in step 4, the analog signal is transmitted through visible light, and needs to pass through a VLC channel, which is as follows:

let H_iRepresents the channel gain of the ith subcarrier, which includes both line-of-sight and scatter links, as shown below

H_i＝H_L,i+H_D,i, (7)

Wherein H_L,iIs the channel gain of the line-of-sight link for the ith subcarrier, and H_D,iIs the channel gain of the scattering link for the ith subcarrier, i ═ 1., 2N;

channel gain H of line-of-sight link of ith subcarrier_L,iExpressed as:

wherein g is_LIs a generalized Lambertian emission model, f_iDenotes the frequency of the ith subcarrier, τ is the delay between two subcarriers, where τ is d/c, d is the distance between the transmitter and the receiver, c is the speed of light, i is 1.

The generalized Lambertian emission model g_LExpressed as:

where m is the order of lambertian emission, i.e. m ═ ln2/ln (cos Φ)_1/2)，Φ_1/2Representing the half-power angle, A_rRepresenting the effective receiving area of the photodetector,

and theta denotes an incident angle and an irradiation angle from the LED to the PD respectively,

and

respectively, the optical filter gain and the concentrator gain of the receiver, Ψ representing the receptionThe field angle of the device;

channel gain H of scattering link of ith subcarrier_D,iExpressed as:

wherein eta_DIs the power efficiency of the scattered signal;

in step 6, an optimal power allocation scheme is designed to maximize the energy efficiency of the system under the constraints of user quality of service requirements and electrical and optical power, and the EE maximization problem of the system is expressed as:

where R is the minimum achievable rate requirement, R_2i-1Indicates the achievable data rate, P, of the ith sub-carrier_cRepresenting the power consumed by the loop of the overall system.

2. A method according to claim 1, characterized in that in step 6, when the input is a gaussian input distribution, the problem (15) is solved by:

setting input signal X_2i-1Subject to independent complex Gaussian distributions, i.e.

Time domain signal x according to IFFT operation expression (3)_kStill subject to a Gaussian distribution, i.e.

The average optical power is expressed as:

wherein the parameters

In addition, by substituting (16) into (15), the dimming control is re-expressed as:

according to Shannon's theorem, the rate R can be reached_G({p_2i-1}) is expressed as:

substituting the reachable rate expression (18) of Gaussian input distribution to obtain the energy efficiency EE_G({p_2i-1}) is:

W_2i-1represents the bandwidth of the 2i-1 th subcarrier;

the energy efficiency maximization problem with the gaussian input distribution of the system is written as:

y represents the actionable domain constraint of issue (20):

wherein the parameters

Parameter(s)

Introducing a new function f ({ p)_2i-1}) are as follows:

where q is a given real-valued parameter, by calculating the equation f ({ p)_2i-1Y) 0 at the root of the actionable domain, to obtain the optimal solution to the problem (20);

for a given q, with respect to p_2i-1The convex sub-problem of (a) is expressed as:

for a given q, the question (20) is about p_2i-1By making the function f ({ p)_2i-1}) is 0, i.e.

Thus obtaining:

next, the feasible solution of problem (23)

Projection into the actionable domain y, resulting in an optimal power distribution scheme for the problem (23)

Specifically represented by the formula:

wherein

To represent

Projection in subspace γ.

3. A method according to claim 2, characterized in that in step 6, when the input is at bounded character input, the problem (15) is solved by:

setting input signal from discrete constellation set

Of order M, wherein X_2i-1,kIs the constellation point of the (2i-1) th subcarrier, the achievable rate R of the bounded input distribution_F({p_2i-1}) is written as:

wherein the parameters

Which is used to measure the constellation point X_2i-1,nAnd X_2i-1,kThe difference between the above-mentioned two methods,

is the noise Z_2i-1(iii) a desire; r_F({p_2i-1Is allocated power p)_2i-1A concave function of (d); y is_2i-1Represents a signal received in the frequency domain of the 2i-1 th subcarrier;

according to expression (5), the average optical power of the transmitted signal is written as:

wherein

Depending on the particular modulation scheme, substituting (27) into (6), the dimming control constraint is expressed as:

according to the inequality

And an intermediate parameter a_iNot less than 0, the dimming control constraint is rewritten as:

for a bounded signal input, the expression for the achievable rate is given by (15), and the energy efficiency EE of the bounded input signal_F({p_2i-1}) is expressed as:

next, the dimming control constraint is expressed as

The bounded input maximization energy efficiency problem under power and rate constraints is then expressed as:

4. the method according to claim 3, characterized in that in step 6, the lower bound optimal energy efficiency problem of mutual information is solved by:

mutual information of the system I_2i-1({p_2i-1}) is expressed as:

wherein the parameters

The upper limit of the desired term in equation (32) is:

wherein the inequality (31) is based on the Jense inequality, the second term of equation (31) being the expectation with respect to the Gaussian noise Z;

let I_L({p_2i-1}) represents a lower bound on the (2i-1) th sub-carrier for mutual information, in which system there is a lower bound R for achievable rate of symbol entry_L({p_2i-1}) is expressed as:

wherein, I_L({p_2i-1}) denotes the power p of the 2i-1 th sub-carrier in the lower bound case of mutual information_2i-1Mutual information of (2);

using the lower bound of mutual information (32), the energy efficiency function of the system is expressed as:

therein, EE_L({p_2i-1}) denotes the power p for the 2i-1 th sub-carrier in the case of a mutual information boundary_2i-1As a function of energy efficiency;

the energy efficiency EE problem (15) is re-expressed as:

5. the method according to claim 4, characterized in that in step 7, after applying the fast Fourier transform, a frequency domain signal is obtained:

let Y_2i-1Represents a signal received in the frequency domain of the 2i-1 th subcarrier, which is given by:

where the coefficient 1/2 indicates that only half of the subcarriers send information; z_2i-1Representing additive white Gaussian noise with an average value of 0, i.e.

W_2i-1Represents the bandwidth of the (2i-1) th subcarrier;

let R_2i-1({p_2i-1}) denotes the rate of the (2i-1) th subcarrier, which is expressed as:

R_2i-1({p_2i-1})＝I(X_2i-1；Y_2i-1) (12)

wherein I denotes mutual information, R_ACOThe total rate of the ACO-OFDM system is expressed by the formula:

meanwhile, the energy efficiency EE of the system is defined as the ratio of capacity to total power consumption, expressed as:

wherein

Electric power, P, representing sub-carriers_cIndicating the loop power consumption of the entire system, EE ({ p)_2i-1} is a function of energy efficiency with respect to power.

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