DMRS stands for 'Demodulation Reference Signal' User Input +---------------------------+ | # Subcarriers (Nsc)       | | # OFDM Symbols (Nsym)     | | DMRS length (Ldmrs)       | | # Channel taps            | | Noise std deviation       | +---------------------------+               |               v Generate DMRS Pilot Sequence +---------------------------+ | QPSK symbols of length Ldmrs | e.g., [1+j, -1+j, ...] +---------------------------+               |               v Frequency-Domain Mapping +---------------------------+ | Zero-pad DMRS to all Nsc   <-- Pilot insertion | DMRS on first Ldmrs, rest 0 | X[k] = [DMRS, 0, 0, ..., 0] +---------------------------+               |     ...

What is BLER (Block Error Rate)? Definition BLER (Block Error Rate) is the percentage of transmitted data blocks that are received incorrectly and fail error detection (CRC check) after decoding. It is a key performance metric in 4G and 5G wireless systems. Formula BLER = (Number of incorrectly received blocks) / (Total transmitted blocks) Example: If 100 transport blocks are transmitted and 10 fail CRC: BLER = 10 / 100 = 10% What is a Block? Data is transmitted in Transport Blocks (TB) Each TB contains multiple code blocks (LDPC coded) If CRC fails, the entire TB is considered erroneous Why is BLER Important? Determines throughput A...

OFDM Transmission in Practical LTE and 5G Systems Understanding the difference between baseband processing and real RF transmission in modern communication systems. 1. What We Study vs What Is Actually Transmitted In textbooks, the OFDM signal is written as: \[ x(t) = \sum_{k} X[k] e^{j 2\pi f_k t} \] This represents a complex baseband signal . However, antennas cannot transmit complex numbers. They transmit real RF signals . 2. Practical Transmitter Chain (LTE / 5G) In systems like LTE (4G) and 5G NR , the transmission process works as follows: Step 1: Digital Baseband Processing Bits QAM Mapping OFDM IFFT Add Cyclic Prefix The result is: \[ x_{BB}[n] = I[n] + j...

  MATLAB Code for Zak Transform (Time-Frequency Transform)  %% The code is developed by www.salimwireless.com clc; clear; close all ; %% Step 1: Parameters N = 16; % Total number of symbols M = 4; % Lattice rows (time slots) SNR_dB = 20; % Noise level modOrder = 4; % QPSK %% Step 2: Generate random QPSK symbols data = randi([0 modOrder-1], N, 1); txSymbols = pskmod(data, modOrder, pi/4); disp( 'Transmitted symbols:' ); disp(txSymbols); %% Step 3: Discrete Zak Transform (map to 2D lattice) lattice = zeros(M, N/M); for n = 0:N-1 m = mod(n, M) + 1; % row (time slot) k = floor(n / M) + 1; % column (frequency slot) lattice(m,k) = lattice(m,k) + txSymbols(n+1)*exp(-1j*2*pi*(k-1)*n/N); end % Optional: Apply simple phase rotation per column to illustrate Zak Transform %for k = 1:N/M % lattice(:,k) = lattice(:,k) .* exp(-1j*2*pi*(k-1)*(0:M-1)'/N); %end disp( 'Zak lattice:' ); disp(lattice); %% Step 4: Serialize lattice for transmissio...

Zak Transform Yes! There is a transform called the Zak Transform , though it’s much less commonly mentioned than the Fourier or Z-transform. It comes up mostly in signal processing, time-frequency analysis, and communications . 1. Definition The Zak Transform of a signal x(t) (continuous-time) is defined as: $$ Z_x(t, f) = \sum_{n=-\infty}^{\infty} x(t - nT) e^{j 2 \pi n f T} $$ Where: x(t) is the input signal T is a fixed period t is a continuous variable within [0, T) f is the frequency variable It essentially maps a 1D signal into a 2D representation in time-frequency space . 2. Key Properties Periodicity: $ Z_x(t + T, f) = e^{j 2 \pi f T} Z_x(t, f) $ Time-Frequency Analysis: Converts time-domain signal into a representation showing both time and frequency structure . Often used in Gabor frames, multicarrier communications, and OFDM . Invertible: There’s an inverse Zak Transform to recover x(t) . 4. Discrete Zak ...

MATLAB Code for OTFS (Orthogonal Time Frequency Space) %% Clear workspace clc; clear; close all ; %% Step 1: OTFS Parameters N_delay = 4; % Number of delay bins (rows) N_doppler = 4; % Number of Doppler bins (columns) N_sym = N_delay * N_doppler; modOrder = 4; % QPSK SNR_dB = 20; % Noise level %% Step 2: Generate random data symbols data = randi([0 modOrder-1], N_sym, 1); txSymbols = pskmod(data, modOrder, pi/4); disp( 'Transmitted Delay-Doppler symbols:' ); disp(reshape(txSymbols, N_delay, N_doppler)); %% Step 3: Map Delay-Doppler → Time-Frequency (ISFFT) % ISFFT: Inverse Symplectic Finite Fourier Transform % 1. Take IDFT along Doppler (columns) % 2. Take DFT along Delay (rows) ddSymbols = reshape(txSymbols, N_delay, N_doppler); % Step 3a: IDFT along columns (Doppler) tfGrid = ifft(ddSymbols, N_doppler, 2); %IFFT (accross columns) along Doppler → spreads in time (Delay → Time) %FFT (accross rows)along Delay → spreads in frequency (Delay → Frequency) % Step 3b: DFT along ...

DMRS-Based Channel Estimation in 5G NR 1. System Model (OFDM-Based 5G NR) After CP removal and FFT, the received signal at subcarrier k and OFDM symbol n: $$ Y(k,n) = H(k,n)X(k,n) + W(k,n) $$ Where: X(k,n): transmitted symbol H(k,n): channel frequency response W(k,n) ~ CN(0, σ²): AWGN Y(k,n): received symbol 2. Channel Representation Time-Domain Multipath Channel $$ h(\tau,t) = \sum_{l=0}^{L-1} \alpha_l(t)\delta(\tau - \tau_l) $$ Frequency-Domain Channel $$ H(k,n) = \sum_{l=0}^{L-1} \alpha_l(n)e^{-j2\pi k \Delta f \tau_l} $$ 3. Least Squares (LS) Channel Estimation $$ Y_{DMRS}(k,n) = H(k,n)X_{DMRS}(k,n) + W(k,n) $$ $$ \hat{H}_{LS}(k,n) = \frac{Y_{DMRS}(k,n)}{X_{DMRS}(k,n)} $$ Vector Form $$ \mathbf{Y} = \mathbf{X}\mathbf{H} + \mathbf{W} $$ $$ \hat{\mathbf{H}}_{LS} = (\mathbf{X}^H \mathbf{X})^{-1} \mathbf{X}^H \mathbf{Y} $$ LS Estimator Properties $$ E[\hat{H}_{LS}] = H $$ $$ Var(\hat{H}_{LS}) = \frac{\sigma^2}{|X|^2} $$...

For channel estimation in hybrid architecture: Here I will discuss communication between a BS (base station) and vehicles for mm Wave communication channel. Both N BS and N v have linear arrays (ULAs), with half-wavelength spaced antenna elements in a compact area uniformly. Let assume, f n is the beamforming vector at BS side. BS need to transmit a symbol, s , such that | s | 2 = 1. On the other hand, vehicle assigns a unit-norm measurement vector w m . Now, the signal received at MS (user) side is written by …………………………………………………..(vii) Where, H = N v X N BS matrix σ 2 = variance of white Gaussian noise …………………………………………………………….(viii) where α = channel gain a v (θ)= vehicle’s ULA array response for line of sight AOA (θ) a BS (φ)= For Line of sight AOD (φ), BS’s ULA steering vector response represented as ……………………………(ix) (Garcia, 2016) Equation (ix) showing phase difference in succeeding antenna elements of MIMO at vehicle and BS side, respectively. . …………………………………………...

Baseband precoding: Baseband precoding is to cancel interferences between multi stream in MIMO communication. Here in hybrid precoding each RF chains are connected to more than one antenna element. And each RF chain responsible of one data stream The signal that has been sent can be denoted as. x=Ds ........................................................(i) Where, x = transmitted signal vector D = N t X N r digital precoder s = N r X 1 symbol vector Now, received signal vector y at receiver side, y= √ρHDs + n …………………………….. (ii) Here, ρ = average received power H =channel matrix ( N r X N t ) n = additive white Gaussian noise vector Digital Beamforming for Multi-User scenario Here in above figure 6.2, BS uses N BS antennas and N BS RF chains for communication with U mobile stations (MSs) simultaneously. N MS antennas are there in each MS. The total number of data streams for communication is equal to the number of antennas on the receiver side, N MS U, wh...

Antenna array response In case of wireless communication signal reaches receiver thru multipath. Multipath signals are correlated if antenna elements are closely packed in a compact region. Figure 1: Illustration of multipath communication in wireless environment For a path l (say) is described along following parameters Angle of arrival θ r l ; Angle of departure θ t l ; Complex channel gain α l ; Figure 2: Directional cosine vectors at receiver side for transmission from Tx Figure 3: Antenna array response at different antenna array and simplified channel model Let assume, in the above figure 2, BS is transmitting at receiver side and receiver antenna array contain four ULA antenna elements. Then we can observe in the figure that to reach 2 nd element (from left) the signal has to travel more distance with compare to 1 st element. The extra path distance will be dcosθ or λ/2*cosθ as the antenna elements are spaced in half wave length interval. That’s why there wi...

UWB and mm-Wave Indoor Communication 8.1. Introduction: Higher frequency bands are intended for wireless and wired broadband networks. Since it allows for more spectrum coverage and higher bandwidth demands. To ensure that a wireless communication device performs well, it is essential to define the radio transmission channel. Wireless communication is also becoming popular in industrial operation day by day. It is needed to control appliances i.e, automated vehicles, machine to machine communication in factories, etc. compare to wired communication, and wireless communication is cost efficient. Fifth generation (5G) technology has gathered a great interest in industrial operation due to its low reliable latency. Industrial applications need more careful evaluation. Industrial environment faces a great quantity of reflective metal surfaces. So it is required to develop a suited physical layer for this particular environment. Indoor residential: This environment is suitable for home...

  Ray tracing Method Because of its advantages in industry, wireless networking is increasingly growing to new heights, with the ability to provide high-speed information sharing between handheld devices anywhere in the globe. Any empirically based radio propagation model is useful for a specific application. We can't adapt a model developed for one application to another, and these models lack the generality and ease of use that a simple theoretical formulation provides. As a result, deterministic models that can be used to various conditions without affecting the precision. It is basically based on EM wave propagation characteristics. Reflection and transmission Dielectric Boundary: For radio wave propagation, the physical properties of the walls and other materials for which it reflect and scatter radio waves are determined by boundary conditions. In practise, specifying information with precision less than the wavelength is impractical in dynamic environments. Ray tracing (site...