Skip to main content

Optimal Precoding for Millimeter wave Massive MIMO Systems


 

Optimal Precoding for Millimeter wave Massive MIMO Systems

In case of MIMO system we deploy multiple transmitter antennas at receiver side and multiple receiver antennas at receiver side. MIMO technology was introduced to support multiple simultaneous data streams between transmitter and receiver to multiply the capacity of a system. But there is also interference between multiple data streams. Precoding technique minimizes the interference between multiple data streams. 



What Exactly Precoding Technique is

We all are familiar with the channel matrix of an MIMO system, that looks like, =


\      R1     R2     R3     R4

T1  h11    h12     h13   h14

T2  h21    h22     h23   h24

T3  h31    h32     h33   h34

T4  h41    h42     h43   h44


Here, in the above figure channel matrix, is shown. In channel matrix it shown different gains between different antennas. Now, we see in the above matrix for example, h11 represents the channel gain between transmitter antenna, T1 and receiver antenna, R1 and h11 also means connection between the antennas as well. R1 also receives the signals from T2, T3, and T4 antennas too. So, there is some kind of interface between multiple data streams when we process the signal at receiver side. Here, precoding help us to reduce interference between multiple data streams. 



Optimal Precoding in MIMO

Typically, received signal at receiver side is represented as,

y = Hx + n       .....(i)

Where, is channel matrix gain

y = Received signal vector 

= Transmitted signal vector 

= Additive white Gaussian noise

Here, in the above equation you can image channel matrix, as same as above channel matrix where we've shown channel gains between TX side antennas T1, T2, T3, T4, and receiver side antennas, R1, R2, R3, R4, respectively. We've also talked about interference with T1's signal at R1 antenna due to transmission from T2, T2, and T3. 

Now, let imagine your channel matrix looks like that, =


\       R1     R2     R3     R4

T1   h11     0        0         0

T2     0     h22      0        0

T3     0       0      h33      0

T4     0       0       0       h44


Now in equation (i), if you the put the above channel matrix value then you see there is no interference with T1' signal with T2, T3, and T4's transmission at receiver R1. 

Similar approach is performed for optimal precoding technique we channel matrix is decomposed in to two unitary matrix U, V, and one diagonal eigen value matrix, Σ. We've already talked about "Singular Value Decomposition in MIMO Channel" in a separate article. 

There is matrix, Σwe operate row and column matrix in a such way that Σ becomes diagonal matrix where elements are in descending order. We do that by operating multiple operations in matrix as shown in the above mentioned article.

Generally, matrix is decomposed into, H = UΣVH

As and are unitary matrix so, multiplication of those matrix with its hermitian matrix itself are identity matrix. Alternatively, UUH = VVH = I



Signal Processing at Receiver Side for Optimal Precoding

During transmission we multiply original message signal vector with unitary matrix, V. So, now transmitted signal vector becomes, Vx. On the side at receiver side, received signal vector is multiplied with vector UH. So, as per above equation (i), received signal vector at receiver side as follows

y = UH (UΣVH) Vx + n

y= IΣIx + n

y = Σx +n 

Now, you see Σ is a diagonal matrix and signal vector, is multiplied with that diagonal matrix. So, you can observe there the simultaneous data streams between MIMO transmitter and receiver antennas without interference among them. Now we further do optimal power allocation to each antennas to maximize sum-rate or overall throughput as shown in a separate article. There is the URL link above.


# mimo beamforming

Why OFDM precoding modulation used in uplink?

People are good at skipping over material they already know!

View Related Topics to







Admin & Author: Salim

s

  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, ...

📘 Overview of BER and SNR 🧮 Online Simulator for BER calculation of m-ary QAM and m-ary PSK 🧮 Online Simulator for Constellation Diagram of m-ary QAM 🧮 Online Simulator for Constellation Diagram of m-ary PSK 🧮 MATLAB Code for BER calculation of M-ary QAM, M-ary PSK, QPSK, BPSK, ... 🧮 MATLAB Code for BER calculation of ASK, FSK, and PSK 🧮 MATLAB Code for BER calculation of Alamouti Scheme 🧮 Different approaches to calculate BER vs SNR 📚 Further Reading Modulation Constellation Diagrams BER vs. SNR BER vs SNR for M-QAM, M-PSK, QPSk, BPSK, ... 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 ...

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

https://www.salimwireless.com/2024/11/constellation-diagram-in-matlab.html 📘 Overview 🧮 Simulator 🧮 Noise Sensitivity, Bandwidth, Complexity, etc. 🧮 MATLAB Code for BER vs. SNR Analysis of ASK, FSK, and PSK 🧮 MATLAB Code for Constellation Diagrams of ASK, FSK, and PSK 🧮 Simulator for ASK, FSK, and PSK Generation 🧮 Simulator for ASK, FSK, and PSK Constellation 🧮 Some Questions and Answers 📚 Further Reading Modulation ASK, FSK & PSK Constellation MATLAB Simulink MATLAB Code Comparisons among ASK, PSK, and FSK    Comparisons among ASK, PSK, and FSK   Simulator for Calculating Bandwidth of ASK, FSK, and PSK The baud rate represents the number of symbols transmitted per second. Both baud rate and bit rate are same for binary ASK, FSK, and PSK. Select Modulation Type: ASK FSK PSK Baud Rat...

MATLAB Code for Pulse Amplitude Modulation (PAM) and Demodulation

📘 Overview & Theory 🧮 MATLAB Code 1 🧮 MATLAB Code 2 🧮 MATLAB Code for Pulse Amplitude Modulation and Demodulation of Digital data 🧮 Other Pulse Modulation Techniques (e.g., PWM, PPM, DM, and PCM) 📚 Further Reading   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('Amplitu...

Constellation Diagrams of ASK, PSK, and FSK

📘 Overview 🧮 Online Simulator for constellation diagrams of ASK, FSK, and PSK 🧮 Theory 🧮 MATLAB Codes 🧮 Simulator for constellation diagrams of m-ary PSK 🧮 Simulator for constellation diagrams of m-ary QAM 📚 Further Reading BASK (Binary ASK) Modulation: Transmits one of two signals: 0 or -√Eb, where Eb​ is the energy per bit. These signals represent binary 0 and 1.    BFSK (Binary FSK) Modulation: Transmits one of two signals: +√Eb​ ( On the y-axis, the phase shift of 90 degrees with respect to the x-axis, which is also termed phase offset ) or √Eb (on x-axis), where Eb​ is the energy per bit. These signals represent binary 0 and 1.  BPSK (Binary PSK) Modulation: Transmits one of two signals: +√Eb​ or -√Eb (they differ by 180 degree phase shift), where Eb​ is the energy per bit. These signals represent binary 0 and 1.    Simulator for BASK, BPSK, and BFSK Constellation Diagrams ...

Relationship between Gaussian and Rayleigh distributions

📘 Introduction, Gaussian Distribution, Relationship Between Gaussian and Rayleigh Distribution 🧮 How to mitigate Rayleigh fading? 🧮 Equalizer to reduce Rayleigh Fading (or Multi-path Effects) in MATLAB 🧮 MATLAB Code for Effects of AWGN and Rayleigh Fading in Wireless Communication 🧮 Simulator for the effect of AWGN and Rayleigh Fading on a BPSK Signal 📚 Further Reading Wireless Signal Processing Gaussian and Rayleigh distributions ...   The Rayleigh distribution in classical fading models (like wireless communication) arises from modeling the real and imaginary parts of a complex baseband signal as independent, zero-mean Gaussian random variables — under specific assumptions . 1. Gaussian Distribution  The Gaussian distribution has a lot of applications in wireless communication. Since noise in wireless communication systems is unpredictable, we frequently assume that it has a Gaussian distribution...

Channel Impulse Response (CIR)

Channel Impulse Response (CIR) 📘 Overview & Theory 📘 How does the channel impulse response affect the signal? 🧮 Online Channel Impulse Response Simulator 🧮 MATLAB Codes 📚 Further Reading 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(...

MATLAB Code for Constellation Diagram of QAM configurations such as 4, 8, 16, 32, 64, 128, and 256-QAM

📘 Overview of QAM 🧮 MATLAB Code for 4-QAM 🧮 MATLAB Code for 16-QAM 🧮 MATLAB Code for m-ary QAM (4-QAM, 16-QAM, 32-QAM, ...) 🧮 Online Simulator for M-ary QAM Constellations (4-QAM, 16-QAM, 64-QAM, ...) 📚 Further Reading   One of the best-performing modulation techniques is QAM [↗] . Here, we modulate the symbols by varying the carrier signal's amplitude and phase in response to the variation in the message signal (or voltage variation). So, we may say that QAM is a combination of phase and amplitude modulation. Additionally, it performs better than ASK or PSK [↗] . In fact, any constellation for any type of modulation, signal set (or, symbols) is structured in a way that prevents them from interacting further by being distinct by phase, amplitude, or frequency. MATLAB Script (for 4-QAM) % This code is written by SalimWirelss.Com % This is an example of 4-QAM. Here constellation size is 4 % or total number of symbols/signals is 4 % We need...

Online Simulator for Constellation Diagram of M-ary PSK

Constellation Diagram of M-ary PSK Bitstream (e.g. 1,0,1,1): Generate Message Modulation Order (M): M must be a power of 2 (e.g., 2, 4, 8, 16) Plot Constellation Diagram Explore Signal Processing Simulations Further Reading   Online Simulator for M-ary PSK Online Simulator for ASK, FSK, and PSK   Explore DSP Simulations