How calculate Energy efficiency in massive MIMO with antenna selection ?

What is the formula of Energy efficiency (Bits/joule) with this code (using matrix)? Basically, this code selects the optimal sub-matrix from a capacity point of view. I want it to be the same except with energy efficiency thank's.

%%%%%%%%%%%OPTIMAL ANTENNA SELECTION

Ns=4;

Nr=16;

SNR=6;%dB

SNR= 10^(SNR/10);

simulation=10;

capacityOfAver=[];

for Lr=1:8

capacityOfSum=0;

antennaSubset=nchoosek([1:Nr],Lr);

for sim=1:simulation

H=sqrt(1/2)*(randn(Nr,Ns)+1j*randn(Nr,Ns));

capacityOfSubsetMax=0;

for k=1:nchoosek(Nr,Lr);

indexOfChannel=antennaSubset(k,:);

H_sel=H(indexOfChannel,:);

capacityOfSubset=log2(det(eye(Ns)+SNR/Ns*(H_sel'*H_sel))) ;

if(capacityOfSubset>capacityOfSubsetMax)

capacityOfSubsetMax=capacityOfSubset;

end

end

capacityOfSum=capacityOfSum+capacityOfSubsetMax;

capacityOfAver=[capacityOfAver,capacityOfSum/simulation];

end

%plot

X=[0:8];

plot(X,[0,capacityOfAver]);

xlabel('Lr');

ylabel('capacity(bit/s/Hz)');

grid on;

hold on;

Answer 1

[Mrutyunjaya Hiremath]

The Energy Efficiency (EE) is usually measured in bits per joule (bits/J) and is calculated as follows:

Energy Efficiency (EE) = Capacity (C)/Energy Consumption (E)​

Modifying the Code for Energy Efficiency

When considering energy efficiency, you need to model the energy consumption of the selected antennas. Let’s assume that each selected antenna consumes energy Ea​ (joules/bit), and there is a fixed energy consumption Ef​ (joules/bit) for the system.

The energy consumption E for a selection of Lr​ antennas can be modeled as:

E = Ef ​+ Lr ​⋅ Ea​

Subsequently, the energy efficiency can be calculated as follows:

Energy Efficiency (EE) = Capacity (C)/ E​

Here’s the modified MATLAB code to select the optimal sub-matrix from an energy efficiency point of view:

Ns=4;
Nr=16;
SNR=6; %dB
SNR= 10^(SNR/10);
simulation=10;
Ea = 0.1; % Energy consumption per antenna (joules/bit)
Ef = 1; % Fixed energy consumption (joules/bit)

energyEfficiencyAver=[];

for Lr=1:8
    energyEfficiencySum=0;
    antennaSubset=nchoosek([1:Nr],Lr);
    for sim=1:simulation
        H=sqrt(1/2)*(randn(Nr,Ns)+1j*randn(Nr,Ns));
        energyEfficiencySubsetMax=0;
        for k=1:nchoosek(Nr,Lr);
            indexOfChannel=antennaSubset(k,:);
            H_sel=H(indexOfChannel,:);
            capacityOfSubset=log2(det(eye(Ns)+SNR/Ns*(H_sel'*H_sel)));
            E = Ef + Lr * Ea; % Total Energy Consumption
            energyEfficiency = capacityOfSubset / E; % Energy Efficiency Calculation
            if(energyEfficiency > energyEfficiencySubsetMax)
                energyEfficiencySubsetMax = energyEfficiency;
            end
        end
        energyEfficiencySum = energyEfficiencySum + energyEfficiencySubsetMax;
    end
    energyEfficiencyAver=[energyEfficiencyAver, energyEfficiencySum/simulation];
end

% Plot
X=[0:8];
plot(X,[0,energyEfficiencyAver]);

Warning: Imaginary parts of complex X and/or Y arguments ignored.

xlabel('Lr');
ylabel('Energy Efficiency (bits/J)');
grid on;
hold on;