Fast Channel Estimation in Transform Domain for Millimeter Wave Systems Based on MATLAB [Includes MATLAB Source Code]

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🔊Author Introduction: Graduate from a 985 university, researcher and developer in the field of MATLAB;

🚅 Motto: A journey of a thousand miles begins with a single step.

✅ Research Areas: Complete code, paper reproduction, program customization, journal writing, research collaboration

🏆 Code Acquisition Method: Method to obtain MATLAB code for the “Sea God Light”

For more MATLAB signal processing simulation content, click below👇

MATLAB Signal Processing (Advanced Version)

MATLAB Signal Processing Radar Communication (Milk Tea Price Version)

Introduction

📋📋📋 The table of contents is as follows: 🎁🎁🎁

Table of Contents

💥1 Overview

📚2 Code and Running Steps

🎉3 Running Results

🌈4 MATLAB Version and References

🔎5 Code Acquisition Method

🍅6 Simulation Consultation

1 Overview

See CSDN Sea God Light with the same title

**1 Principle of Channel Estimation in Transform Domain for Millimeter Wave Systems** Millimeter wave communication relies on large-scale antenna arrays for beamforming, but the sparsity of high-frequency signal paths leads to inefficiencies in traditional channel estimation methods. The Transform-Domain method utilizes the sparsity of signals in specific transform domains (such as Fourier domain, angle domain) to reduce estimation complexity through techniques like compressed sensing. The core principles include three aspects: 1. **Sparsity Assumption**: The millimeter wave channel can be represented as a superposition of a few dominant paths in the angle-delay domain, satisfying the sparsity condition. 2. **Transform Basis Design**: Projecting the time-domain channel into the sparse domain using discrete Fourier transform (DFT) matrices or overcomplete dictionaries (such as DCT, Kronecker product basis). 3. **Compressed Sensing Reconstruction**: Using algorithms like Orthogonal Matching Pursuit (OMP) and Approximate Message Passing (AMP) to recover the sparse channel from a small number of observations. The mathematical expression is:
\[ \mathbf{y} = \mathbf{\Phi}\mathbf{F}\mathbf{h} + \mathbf{n} \] where \(\mathbf{F}\) is the transform basis matrix, \(\mathbf{\Phi}\) is the observation matrix, and \(\mathbf{h}\) is the sparse channel vector. **2 Fast Channel Estimation Process** **Preprocessing Stage** – Construct the overcomplete dictionary matrix \(\mathbf{D} = \mathbf{U}_{\mathrm{Tx}}\otimes\mathbf{U}_{\mathrm{Rx}}\), where \(\mathbf{U}_{\mathrm{Tx/Rx}}\) is the antenna array response matrix at the transmitter/receiver. – Design the pilot sequence \(\mathbf{X}\) to satisfy the Restricted Isometry Property (RIP), typically using random phase pilots or Zadoff-Chu sequences. **Compressed Observation Stage** – Send pilot signals over \(T\) time slots, with the received signal represented as:
\[ \mathbf{Y} = \sqrt{\rho}\mathbf{W}^H\mathbf{H}\mathbf{F}\mathbf{X} + \mathbf{N} \] – Obtain compressed measurements \(\mathbf{y} = \mathrm{vec}(\mathbf{\Phi}\mathbf{Y})\) using a dimensionality-reducing observation matrix \(\mathbf{\Phi}\) (e.g., partial unit matrix). **Sparse Reconstruction Stage** – Use an improved OMP algorithm for path parameter estimation: 1. Initialize the residual \(\mathbf{r}_0 = \mathbf{y}\), support set \(\mathcal{S} = \emptyset\) 2. Iteratively select dictionary atoms: \[ i_k = \arg\max_i |\mathbf{D}_i^H\mathbf{r}_{k-1}| \] 3. Update the support set \(\mathcal{S} = \mathcal{S}\cup i_k\) and reconstruct the channel: \[ \mathbf{h}_k = (\mathbf{D}_{\mathcal{S}}^H\mathbf{D}_{\mathcal{S}})^{-1}\mathbf{D}_{\mathcal{S}}^H\mathbf{y} \] 4. Termination condition: residual energy falls below a threshold or reaches a preset number of paths. **Postprocessing Stage** – Perform inverse transformation on the estimated angle-delay domain channel \(\hat{\mathbf{h}}\):
\[ \hat{\mathbf{H}} = \mathbf{U}_{\mathrm{Rx}}\hat{\mathbf{h}}\mathbf{U}_{\mathrm{Tx}}^H \] – Improve time-varying channel tracking performance through interpolation or Kalman filtering. **3 Performance Optimization Techniques** **Low Complexity Algorithm Improvements** – Hierarchical Matching Pursuit (HMP): Divide large-scale antenna arrays into sub-arrays for hierarchical sparse reconstruction. – Structured OMP: Utilize the block sparse characteristics of millimeter wave channels to reduce search dimensions. **Hardware Adaptation Design** – Jointly optimize analog/digital observation matrices under hybrid beamforming architecture. – Design improved AMP algorithms for 1-bit ADC quantization. Under typical system parameters, this method can reduce pilot overhead to 10%-20% of traditional LS algorithms while maintaining NMSE below -15dB. Practical implementation requires balancing dictionary resolution, algorithm complexity, and estimation accuracy.

2 Code and Running Steps

2.1 Partial Code2.2 Running Steps

(1) Directly run main.m to generate the plot with one click

3Running Results

4MATLAB Version and References

1 MATLAB Version

2019b

2 References

[1] Ni Yiyang, Zhu Hongbo, Wang Yuxi. Overview of Millimeter Wave D2D Communication Technology for 5G [J]. Modern Electronic Technology. 2019

[2] Wan Yuan, Li Xingguo, Wang Hong. Application of Channel Coding Technology in Millimeter Wave Communication [J]. Journal of Ordnance and Guidance. 2006

3 Note

This section is excerpted from the internet for reference only. If there is any infringement, please contact for removal.

5 Code Acquisition Method

🏆CodeAcquisitionMethod:Method to obtain MATLAB code for the “Sea God Light”

6 Simulation Consultation

**🍅 Simulation Consultation

1 Various intelligent optimization algorithm improvements and applications**

1.1 PID Optimization

1.2 VMD Optimization

1.3 Distribution Network Reconstruction

1.4 Three-Dimensional Packing

1.5 Microgrid Optimization

1.6 Layout Optimization

1.7 Parameter Optimization

1.8 Cost Optimization

1.9 Charging Optimization

1.10 Scheduling Optimization

1.11 Price Optimization

1.12 Departure Optimization

1.13 Distribution Optimization

1.14 Coverage Optimization

1.15 Control Optimization

1.16 Inventory Optimization

1.17 Routing Optimization

1.18 Design Optimization

1.19 Location Optimization

1.20 Absorption Optimization

1.21 Site Selection Optimization

1.22 Operation Optimization

1.23 Assignment Optimization

1.24 Combination Optimization

1.25 Workshop Scheduling

1.26 Production Scheduling

1.27 Economic Scheduling

1.28 Assembly Line Scheduling

1.29 Reservoir Scheduling

1.30 Cargo Position Optimization

1.31 Bus Scheduling Optimization

1.32 Container Ship Loading Optimization

1.33 Pump Combination Optimization

1.34 Medical Resource Allocation Optimization

1.35 Visual Base Station and Drone Site Selection Optimization

**2 Machine Learning and Deep Learning Classification and Prediction**

**2.1 Machine Learning and Deep Learning Classification**

2.1.1 BiLSTM Bidirectional Long Short-Term Memory Neural Network Classification

2.1.2 BP Neural Network Classification

2.1.3 CNN Convolutional Neural Network Classification

2.1.4 DBN Deep Belief Network Classification

2.1.5 DELM Deep Learning Extreme Learning Machine Classification

2.1.6 ELMAN Recurrent Neural Network Classification

2.1.7 ELM Extreme Learning Machine Classification

2.1.8 GRNN General Regression Neural Network Classification

2.1.9 GRU Gated Recurrent Unit Classification

2.1.10 KELM Hybrid Kernel Extreme Learning Machine Classification

2.1.11 KNN Classification

2.1.12 LSSVM Least Squares Support Vector Machine Classification

2.1.13 LSTM Long Short-Term Memory Network Classification

2.1.14 MLP Multi-Layer Perceptron Classification

2.1.15 PNN Probabilistic Neural Network Classification

2.1.16 RELM Robust Extreme Learning Machine Classification

2.1.17 RF Random Forest Classification

2.1.18 SCN Stochastic Configuration Network Model Classification

2.1.19 SVM Support Vector Machine Classification

2.1.20 XGBOOST Classification

**2.2 Machine Learning and Deep Learning Prediction**

2.2.1 ANFIS Adaptive Neuro-Fuzzy Inference System Prediction

2.2.2 ANN Artificial Neural Network Prediction

2.2.3 ARMA Autoregressive Moving Average Model Prediction

2.2.4 BF Particle Filter Prediction

2.2.5 BiLSTM Bidirectional Long Short-Term Memory Neural Network Prediction

2.2.6 BLS Broad Learning System Prediction

2.2.7 BP Neural Network Prediction

2.2.8 CNN Convolutional Neural Network Prediction

2.2.9 DBN Deep Belief Network Prediction

2.2.10 DELM Deep Learning Extreme Learning Machine Prediction

2.2.11 DKELM Regression Prediction

2.2.12 ELMAN Recurrent Neural Network Prediction

2.2.13 ELM Extreme Learning Machine Prediction

2.2.14 ESN Echo State Network Prediction

2.2.15 FNN Feedforward Neural Network Prediction

2.2.16 GMDN Prediction

2.2.17 GMM Gaussian Mixture Model Prediction

2.2.18 GRNN General Regression Neural Network Prediction

2.2.19 GRU Gated Recurrent Unit Prediction

2.2.20 KELM Hybrid Kernel Extreme Learning Machine Prediction

2.2.21 LMS Least Mean Squares Algorithm Prediction

2.2.22 LSSVM Least Squares Support Vector Machine Prediction

2.2.23 LSTM Long Short-Term Memory Network Prediction

2.2.24 RBF Radial Basis Function Neural Network Prediction

2.2.25 RELM Robust Extreme Learning Machine Prediction

2.2.26 RF Random Forest Prediction

2.2.27 RNN Recurrent Neural Network Prediction

2.2.28 RVM Relevance Vector Machine Prediction

2.2.29 SVM Support Vector Machine Prediction

2.2.30 TCN Temporal Convolutional Network Prediction

2.2.31 XGBoost Regression Prediction

2.2.32 Fuzzy Prediction

2.2.33 Singular Spectrum Analysis Method SSA Time Series Prediction

**2.3 Machine Learning and Deep Learning Practical Application Prediction**

CPI Index Prediction, PM2.5 Concentration Prediction, SOC Prediction, Financial Warning Prediction, Yield Prediction, Parking Space Prediction, Pest Prediction, Steel Thickness Prediction, Battery Health Status Prediction, Power Load Prediction, Housing Price Prediction, Corrosion Rate Prediction, Fault Diagnosis Prediction, Photovoltaic Power Prediction, Trajectory Prediction, Aircraft Engine Life Prediction, Exchange Rate Prediction, Concrete Strength Prediction, Heating Furnace Temperature Prediction, Price Prediction, Traffic Flow Prediction, Resident Consumption Index Prediction, Air Quality Prediction, Grain Temperature Prediction, Temperature Prediction, Clear Water Value Prediction, Unemployment Rate Prediction, Electricity Consumption Prediction, Transport Volume Prediction, Manufacturing Purchasing Managers Index Prediction

**3 Image Processing Aspects**

**3.1 Image Edge Detection**

**3.2 Image Processing**

**3.3 Image Segmentation**

**3.4 Image Classification**

**3.5 Image Tracking**

**3.6 Image Encryption and Decryption**

**3.7 Image Retrieval**

**3.8 Image Registration**

**3.9 Image Stitching**

**3.10 Image Evaluation**

**3.11 Image Denoising**

**3.12 Image Fusion**

**3.13 Image Recognition**

3.13.1 Dial Recognition

3.13.2 Lane Line Recognition

3.13.3 Vehicle Counting

3.13.4 Vehicle Recognition

3.13.5 License Plate Recognition

3.13.6 Parking Space Recognition

3.13.7 Size Detection

3.13.8 Answer Sheet Recognition

3.13.9 Appliance Recognition

3.13.10 Fall Detection

3.13.11 Animal Recognition

3.13.12 QR Code Recognition

3.13.13 Invoice Recognition

3.13.14 Clothing Recognition

3.13.15 Chinese Character Recognition

3.13.16 Traffic Light Recognition

3.13.17 Iris Recognition

3.13.18 Fire Detection

3.13.19 Disease Classification

3.13.20 Traffic Sign Recognition

3.13.21 Card Number Recognition

3.13.22 Mask Recognition

3.13.23 Crack Detection

3.13.24 Target Tracking

3.13.25 Fatigue Detection

3.13.26 Flag Recognition

3.13.27 Grass Recognition

3.13.28 Face Recognition

3.13.29 Renminbi Recognition

3.13.30 ID Card Recognition

3.13.31 Gesture Recognition

3.13.32 Digit and Letter Recognition

3.13.33 Palm Recognition

3.13.34 Leaf Recognition

3.13.35 Fruit Recognition

3.13.36 Barcode Recognition

3.13.37 Temperature Detection

3.13.38 Defect Detection

3.13.39 Chip Detection

3.13.40 Behavior Recognition

3.13.41 Verification Code Recognition

3.13.42 Medicinal Material Recognition

3.13.43 Coin Recognition

3.13.44 Postal Code Recognition

3.13.45 Playing Card Recognition

3.13.46 Fingerprint Recognition

**3.14 Image Restoration**

**3.15 Image Compression**

**3.16 Image Steganography**

**3.17 Image Enhancement**

**3.18 Image Reconstruction**

**4 Path Planning Aspects**

**4.1 Traveling Salesman Problem (TSP)**

4.1.1 Single Traveling Salesman Problem (TSP)

4.1.2 Multiple Traveling Salesman Problem (MTSP)

**4.2 Vehicle Routing Problem (VRP)**

4.2.1 Vehicle Routing Problem (VRP)

4.2.2 Capacitated Vehicle Routing Problem (CVRP)

4.2.3 Capacitated + Time Window + Distance Vehicle Routing Problem (DCTWVRP)

4.2.4 Capacitated + Distance Vehicle Routing Problem (DCVRP)

4.2.5 Distance-Constrained Vehicle Routing Problem (DVRP)

4.2.6 Vehicle Routing Problem with Charging Stations + Time Windows (ETWVRP)

4.2.3 Vehicle Routing Problem with Multiple Capacities (MCVRP)

4.2.4 Distance-Constrained Multi-Vehicle Routing Problem (MDVRP)

4.2.5 Simultaneous Pickup and Delivery Vehicle Routing Problem (SDVRP)

4.2.6 Vehicle Routing Problem with Time Windows + Capacities (TWCVRP)

4.2.6 Vehicle Routing Problem with Time Windows (TWVRP)

**4.3 Multimodal Transport Problem**

**4.4 Robot Path Planning**

4.4.1 Obstacle Avoidance Path Planning

4.4.2 Maze Path Planning

4.4.3 Grid Map Path Planning

**4.5 Delivery Path Planning**

4.5.1 Cold Chain Delivery Path Planning

4.5.2 Takeout Delivery Path Planning

4.5.3 Mask Delivery Path Planning

4.5.4 Medicine Delivery Path Planning

4.5.5 Delivery Path Planning with Charging Stations

4.5.6 Chain Supermarket Delivery Path Planning

4.5.7 Vehicle Collaborative Drone Delivery Path Planning

**4.6 Drone Path Planning**

4.6.1 Aircraft Simulation

4.6.2 Drone Flight Operations

4.6.3 Drone Trajectory Tracking

4.6.4 Drone Swarm Simulation

4.6.5 Three-Dimensional Path Planning for Drones

4.6.6 Drone Formation

4.6.7 Cooperative Tasks for Drones

4.6.8 Drone Task Allocation

**5 Speech Processing**

**5.1 Speech Emotion Recognition**

**5.2 Sound Source Localization**

**5.3 Feature Extraction**

**5.4 Speech Coding**

**5.5 Speech Processing**

**5.6 Speech Separation**

**5.7 Speech Analysis**

**5.8 Speech Synthesis**

**5.9 Speech Encryption**

**5.10 Speech Denoising**

**5.11 Speech Recognition**

**5.12 Speech Compression**

**5.13 Speech Hiding**

**6 Cellular Automata Aspects**

**6.1 Cellular Automata Virus Simulation**

**6.2 Cellular Automata Urban Planning**

**6.3 Cellular Automata Traffic Flow**

**6.4 Cellular Automata Gas**

**6.5 Cellular Automata Personnel Evacuation**

**6.6 Cellular Automata Forest Fire**

**6.7 Cellular Automata Game of Life**

**7 Signal Processing Aspects**

**7.1 Fault Signal Diagnosis Analysis**

7.1.1 Gear Damage Identification

7.1.2 Asynchronous Motor Rotor Bar Fault Diagnosis

7.1.3 Rolling Element Inner and Outer Ring Fault Diagnosis Analysis

7.1.4 Motor Fault Diagnosis Analysis

7.1.5 Bearing Fault Diagnosis Analysis

7.1.6 Gearbox Fault Diagnosis Analysis

7.1.7 Three-Phase Inverter Fault Diagnosis Analysis

7.1.8 Diesel Engine Fault Diagnosis

**7.2 Radar Communication**

7.2.1 FMCW Simulation

7.2.2 GPS Anti-Jamming

7.2.3 Radar LFM

7.2.4 Radar MIMO

7.2.5 Radar Angle Measurement

7.2.6 Radar Imaging

7.2.7 Radar Positioning

7.2.8 Radar Echo

7.2.9 Radar Detection

7.2.10 Radar Digital Signal Processing

7.2.11 Radar Communication

7.2.12 Radar Phased Array

7.2.13 Radar Signal Analysis

7.2.14 Radar Early Warning

7.2.15 Radar Pulse Compression

7.2.16 Antenna Radiation Pattern

7.2.17 Radar Clutter Simulation

**7.3 Bioelectric Signals**

7.3.1 Electromyography (EMG)

7.3.2 Electroencephalography (EEG)

7.3.3 Electrocardiography (ECG)

7.3.4 Heart Simulation

**7.4 Communication Systems**

7.4.1 DOA Estimation

7.4.2 LEACH Protocol

7.4.3 Coding and Decoding

7.4.4 Variational Mode Decomposition

7.4.5 Ultra-Wideband Simulation

7.4.6 Multipath Fading Simulation

7.4.7 Cellular Networks

7.4.8 Pipeline Leakage

7.4.9 Empirical Mode Decomposition

7.4.10 Filter Design

7.4.11 Analog Signal Transmission

7.4.12 Analog Signal Modulation

7.4.13 Digital Baseband Signal

7.4.14 Digital Channel

7.4.15 Digital Signal Processing

7.4.16 Digital Signal Transmission

7.4.17 Digital Signal Denoising

7.4.18 Underwater Acoustic Communication

7.4.19 Communication Simulation

7.4.20 Wireless Transmission

7.4.21 Bit Error Rate Simulation

7.4.22 Modern Communication

7.4.23 Channel Estimation

7.4.24 Signal Detection

7.4.25 Signal Fusion

7.4.26 Signal Recognition

7.4.27 Compressed Sensing

7.4.28 Noise Simulation

7.4.29 Noise Interference

**7.5 Drone Communication**

**7.6 Wireless Sensor Localization and Layout**

7.6.1 WSN Localization

7.6.2 Height Estimation

7.6.3 Filter Tracking

7.6.4 Target Localization

7.6.4.1 Dv-Hop Localization

7.6.4.2 RSSI Localization

7.6.4.3 Intelligent Algorithm Optimization Localization

7.6.5 Integrated Navigation

**8 Power System Aspects**

Microgrid Optimization, Reactive Power Optimization, Distribution Network Reconstruction, Energy Storage Configuration