Skip to main content
Home Wireless Communication Modulation MATLAB Beamforming Project Ideas MIMO Computer Networks Lab 🚀

Optimal Power Allocation in MIMO Transmission


 SVD-Based MIMO Transmission & Optimal Power Allocation



Optimal power allocation is defined as in a MIMO communication system we need to allocate more power to an independent stronger path and allocation of less power to a weaker path. By following this method we can achieve high throughput. Firstly, we talk about SVD-based MIMO. Then we discussed step by step how to find stronger or weaker communication paths between two MIMO antennas. 


Channel Matrix,



Let's assume, the first column in the above matrix is c1  .  c  and    c

are the 2nd and 3rd columns, respectively.


Here, columns are orthogonal for instance, i.e.,  c1Hc=0

Here, r=3, t=3  (r=number of Rx antenna; t=number of Tx antenna)


Now, c1


c2





Now, c1Hc2

 *



=0


Multiplication is 0 since the columns are orthogonal.



Step 1: We normalize each column

We get, H=


Here singular values are not in decreasing order.


Step 2: Now we arrange the singular values in decreasing order


H=



 



That implies,





Again assume, the first matrix is (unitary matrix), the middle one is Σ (eigenmatrix)and 3rd matrix is (unitary matrix).

Alternatively, UUH=I,     VHV=VVH=I


Σ =





In the above matrix, σ1=√52, σ2=√13, σ3=2, and Singular values are in decreasing order.


At receiver side   

            y ̃UHy =

           





At the transmitter side

  ͞x =V x ̃

Or,




Here, notation "x1~, x2~, x3~" represents original message signal vector


Transmit pre-processing or precoding at the receiver side

ỹ= Σx̃ + w̃

Or,




Here, "y~" represents the received signal vector and "w~" represents the noise vector


Now, 3 decoupled channel spatial multiplexing are as follows

ỹ1 = √52x̃1 + w̃1

ỹ2 = √13x̃2 + w̃2

ỹ3 = 2x̃3 + w̃3


Optimal Power allocation

To maximize sum-rate and to achieve the Shannon capacity,

P1=(1/λ- σ212)= (1/λ- σ2/52)

P2=(1/λ- σ222)= (1/λ- σ2/13)

P3=(1/λ- σ232)= (1/λ- σ2/4)

 

Consider the noise power, σ2= 0dB

                                         So, 10log10 σ2=0

                                              σ2=10^(0/10)=1

let P=total power=3dB

                  So, 10log10 P=3

                                      P=10^(3/10)=2 (approx.)

 

So, we must have

                 P1+P2+P3= 2

                (1/λ-1/52)+  (1/λ-1/13)+  (1/λ-1/4)=2

               Or, 1/λ=.7821

Now,

P1=10log10(1/λ- σ2/52)= 10log10(0.7821- 1/52)=-1.1755 dB

P2=10log10(1/λ- σ2/13)= 10log10(0.7821- 1/13)=-1.517 dB

P1=10log10(1/λ- σ2/4)= 10log10(0.7821- 1/4)=-2.74 dB

Power allocation decreases as gain σ2 decreases. So, we can say poor power to poor channel , more power to strong channel.



People are good at skipping over material they already know!

View Related Topics to







Admin & Author: Salim

profile

  Website: www.salimwireless.com
  Interests: Signal Processing, Telecommunication, 5G Technology, Present & Future Wireless Technologies, Digital Signal Processing, Computer Networks, Millimeter Wave Band Channel, Web Development
  Seeking an opportunity in the Teaching or Electronics & Telecommunication domains.
  Possess M.Tech in Electronic Communication Systems.


Contact Us

Name

Email *

Message *

Popular Posts

BER vs SNR for M-ary QAM, M-ary PSK, QPSK, BPSK, ...

Modulation Constellation Diagrams BER vs. SNR BER vs SNR for M-QAM, M-PSK, QPSk, BPSK, ... 1. What is Bit Error Rate (BER)? The abbreviation BER stands for bit error rate, which indicates how many corrupted bits are received (after the demodulation process) compared to the total number of bits sent in a communication process. It is defined as,  In mathematics, BER = (number of bits received in error / total number of transmitted bits)  On the other hand, SNR refers to the signal-to-noise power ratio. For ease of calculation, we commonly convert it to dB or decibels.   2. What is Signal the signal-to-noise ratio (SNR)? SNR = signal power/noise power (SNR is a ratio of signal power to noise power) SNR (in dB) = 10*log(signal power / noise power) [base 10] For instance, the SNR for a given communication system is 3dB. So, SNR (in ratio) = 10^{SNR (in dB) / 10} = 2 Therefore, in this instance, the signal power i

Comparisons among ASK, PSK, and FSK | And the definitions of each

Modulation ASK, FSK & PSK Constellation MATLAB Simulink MATLAB Code Comparisons among ASK, PSK, and FSK    Comparisons among ASK, PSK, and FSK Comparison among ASK,  FSK, and PSK Performance Comparison: 1. Noise Sensitivity:    - ASK is the most sensitive to noise due to its reliance on amplitude variations.    - PSK is less sensitive to noise compared to ASK.    - FSK is relatively more robust against noise, making it suitable for noisy environments. 2. Bandwidth Efficiency:    - PSK is the most bandwidth-efficient, requiring less bandwidth than FSK for the same data rate.    - FSK requires wider bandwidth compared to PSK.    - ASK's bandwidth efficiency lies between FSK and PSK. Bandwidth Calculator for ASK, FSK, and PSK The baud rate represents the number of symbols transmitted per second Select Modulation Type: ASK FSK PSK Baud Rate (Hz):

MATLAB code for BER vs SNR for M-QAM, M-PSK, QPSk, BPSK, ...

Modulation Constellation Diagrams BER vs. SNR MATLAB code for BER vs SNR for M-QAM, M-PSK, QPSk, BPSK, ...   MATLAB Script for  BER vs. SNR for M-QAM, M-PSK, QPSk, BPSK %Written by Salim Wireless %Visit www.salimwireless.com for study materials on wireless communication %or, if you want to learn how to code in MATLAB clc; clear; close all; % Parameters num_symbols = 1e5; % Number of symbols snr_db = -20:2:20; % Range of SNR values in dB % PSK orders to be tested psk_orders = [2, 4, 8, 16, 32]; % QAM orders to be tested qam_orders = [4, 16, 64, 256]; % Initialize BER arrays ber_psk_results = zeros(length(psk_orders), length(snr_db)); ber_qam_results = zeros(length(qam_orders), length(snr_db)); % BER calculation for each PSK order and SNR value for i = 1:length(psk_orders) psk_order = psk_orders(i); for j = 1:length(snr_db) % Generate random symbols data_symbols = randi([0, psk_order-1]

FFT Magnitude and Phase Spectrum using MATLAB

MATLAB Code clc; clear; close all; % Parameters fs = 100;           % Sampling frequency t = 0:1/fs:1-1/fs;  % Time vector % Signal definition x = cos(2*pi*15*t - pi/4) - sin(2*pi*40*t); % Compute Fourier Transform y = fft(x); z = fftshift(y); % Frequency vector ly = length(y); f = (-ly/2:ly/2-1)/ly*fs; % Compute phase phase = angle(z); % Plot magnitude of the Fourier Transform figure; subplot(2, 1, 1); stem(f, abs(z), 'b'); xlabel('Frequency (Hz)'); ylabel('|y|'); title('Magnitude of Fourier Transform'); grid on; % Plot phase of the Fourier Transform subplot(2, 1, 2); stem(f, phase, 'b'); xlabel('Frequency (Hz)'); ylabel('Phase (radians)'); title('Phase of Fourier Transform'); grid on;   Output  Copy the MATLAB Code from here % The code is written by SalimWireless.Com clc; clear; close all; % Parameters fs = 100; % Sampling frequency t = 0:1/fs:1-1/fs; % Time vector % Signal definition x = cos(2*pi*15*t -

Difference between AWGN and Rayleigh Fading

Wireless Signal Processing Gaussian and Rayleigh Distribution Difference between AWGN and Rayleigh Fading 1. Introduction Rayleigh fading coefficients and AWGN, or additive white gaussian noise [↗] , are two distinct factors that affect a wireless communication channel. In mathematics, we can express it in that way.  Let's explore wireless communication under two common noise scenarios: AWGN (Additive White Gaussian Noise) and Rayleigh fading. y = hx + n ... (i) The transmitted signal  x  is multiplied by the channel coefficient or channel impulse response (h)  in the equation above, and the symbol  "n"  stands for the white Gaussian noise that is added to the signal through any type of channel (here, it is a wireless channel or wireless medium). Due to multi-paths the channel impulse response (h) changes. And multi-paths cause Rayleigh fading. 2. Additive White Gaussian Noise (AWGN) The mathematical effect involves adding Gauss

Channel Impulse Response (CIR)

Channel Impulse Response (CIR) Wireless Signal Processing CIR, Doppler Shift & Gaussian Random Variable  The Channel Impulse Response (CIR) is a concept primarily used in the field of telecommunications and signal processing. It provides information about how a communication channel responds to an impulse signal.   What is the Channel Impulse Response (CIR) ? It describes the behavior of a communication channel in response to an impulse signal. In signal processing,  an impulse signal has zero amplitude at all other times and amplitude  ∞ at time 0 for the signal. Using a Dirac Delta function, we can approximate this.  ...(i) δ( t) now has a very intriguing characteristic. The answer is 1 when the Fourier Transform of  δ( t) is calculated. As a result, all frequencies are responded to equally by  δ (t). This is crucial since we never know which frequencies a system will affect when examining an unidentified one. Since it can test the system for all freq

MATLAB Code for Pulse Amplitude Modulation (PAM) and Demodulation

  Pulse Amplitude Modulation (PAM) & Demodulation MATLAB Script clc; clear all; close all; fm= 10; % frequency of the message signal fc= 100; % frequency of the carrier signal fs=1000*fm; % (=100KHz) sampling frequency (where 1000 is the upsampling factor) t=0:1/fs:1; % sampling rate of (1/fs = 100 kHz) m=1*cos(2*pi*fm*t); % Message signal with period 2*pi*fm (sinusoidal wave signal) c=0.5*square(2*pi*fc*t)+0.5; % square wave with period 2*pi*fc s=m.*c; % modulated signal (multiplication of element by element) subplot(4,1,1); plot(t,m); title('Message signal'); xlabel ('Time'); ylabel('Amplitude'); subplot(4,1,2); plot(t,c); title('Carrier signal'); xlabel('Time'); ylabel('Amplitude'); subplot(4,1,3); plot(t,s); title('Modulated signal'); xlabel('Time'); ylabel('Amplitude'); %demdulated d=s.*c; % At receiver, received signal is multiplied by carrier signal filter=fir1(200,fm/fs,'low'); % low-pass FIR fi