All classes MIMO-OFDM Channel Estimation Deep Learning Syllabus · Episode 3 of 6

Class MIMO-OFDM Channel Estimation Deep Learning #3: Classical Estimators: Least Squares and MMSE

0 views

Tutorial on MIMO-OFDM channel least squares and LMMSE estimators with Python: interpolation, covariance, eigen decomposition, NMSE. Episode 3 of the massive MIMO-OFDM channel estimation deep learning series.

Software: Python (NumPy, SciPy, PyTorch, Matplotlib)
Level: Advanced
Duration: ± 9 min
Series total: 57 min · 6 videos
Published: October 25, 2026

Episode 3 of 6 · view syllabus

Download PDF (6 PDF pages)

0 downloads

Download Project File· 380 KB Unlock All Premium Classes ▶ Watch the video lesson0 plays

▶ Video Lesson

Watch every step above performed live, with English narration.

0 plays

Class book

Page 1 / 6

Class MIMO-OFDM Channel Estimation Deep Learning #3: Classical Estimators: Least Squares and MMSE: Cover: Class MIMO-OFDM Deep Learning Channel Estimation #3: Classical Estimators: Least Squares and MMSE

Class MIMO-OFDM Channel Estimation Deep Learning #3: Classical Estimators: Least Squares and MMSE: Before you start, steps list, and Step 1

Class MIMO-OFDM Channel Estimation Deep Learning #3: Classical Estimators: Least Squares and MMSE: Step 2: LMMSE with eigen decomposition

Class MIMO-OFDM Channel Estimation Deep Learning #3: Classical Estimators: Least Squares and MMSE: Step 3: NMSE vs SNR

Class MIMO-OFDM Channel Estimation Deep Learning #3: Classical Estimators: Least Squares and MMSE: Step 4: NMSE Curve & Estimation Example

Class MIMO-OFDM Channel Estimation Deep Learning #3: Classical Estimators: Least Squares and MMSE: Done: Final Result and Further Practice

Cover: Class MIMO-OFDM Deep Learning Channel Estimation #3: Classical Estimators: Least Squares and MMSE

Click a page or use ◀ ▶ to turn · swipe on mobile · to enlarge

Want to go deeper?

Join one of our courses or ask us directly on WhatsApp.

Download PDF· 0 downloads View the full 6-episode syllabus View MIMO-OFDM Channel Estimation Courses Ask on WhatsApp

Recommended classes for you

Picked from the software, topic, and level of “Class MIMO-OFDM Channel Estimation Deep Learning #3: Classical Estimators: Least Squares and MMSE”.

18 episodesFree preview

Python · Beginner–Advanced

Machine Learning Python

18 video lessons with PDF guides, 3 h 41 min in total. Starts with: Introduction to Machine Learning & First Model.

3 h 41 min 61 0

View class

Deep Learning CNN-LSTM Pneumonia Detection

6 episodesFree preview

Python · Intermediate–Advanced

Deep Learning CNN-LSTM Pneumonia Detection

6 video lessons with PDF guides, 57 min in total. Starts with: Chest X-ray Dataset: Loading, Exploration & Data Splitting.

57 min 22 0

View class

EKG Arrhythmia Classification Wavelet Deep Learning

6 episodesFree preview

Python · Intermediate–Advanced

EKG Arrhythmia Classification Wavelet Deep Learning

6 video lessons with PDF guides, 56 min in total. Starts with: EKG & EEG Signals: Characteristics and Public Datasets (MIT-BIH).

56 min 2 0

View class

50 episodesFree preview

Agentic AI · Beginner–Intermediate

Agentic AI Without Coding

50 video lessons with PDF guides, 14 h 29 min in total. Starts with: Chatbots, Automation, and AI Agents: What's the Difference?.

14 h 29 min 66 0

View class

100 episodesFree preview

Claude · Beginner–Advanced

Claude from Zero to Expert

100 video lessons with PDF guides, 15 h 1 min in total. Starts with: What Claude Is and How It Differs from ChatGPT and Gemini.

15 h 1 min 62 0

View class

6 episodesFree preview

Python · Intermediate–Advanced

Transfer Learning for Leaf Disease

6 video lessons with PDF guides, 1 h 5 min in total. Starts with: PlantVillage Dataset: Folder Structure, Class Distribution & Data Split.

1 h 5 min 9 0

View class

6 episodesFree preview

Python · Intermediate–Advanced

5G Deep RL Resource Allocation

6 video lessons with PDF guides, 1 h 1 min in total. Starts with: Concept of 5G/6G Resource Allocation: Resource Block, Power, User.

1 h 1 min 0 0

View class

Reinforcement Learning for Robot Manipulator

6 episodesFree preview

Python · Intermediate–Advanced

Reinforcement Learning for Robot Manipulator

6 video lessons with PDF guides, 49 min in total. Starts with: Forward and Inverse Kinematics of a 2-DOF Robotic Arm.

49 min 1 0

View class

Need more than a video?

Other ways we can help with Python.

Learn with a mentor

Scheduled AI & Machine Learning courses with live guidance and a certificate.

Course

Multi-Objective Optimization Course: NSGA-II, MOPSO & Hybrid Algorithms (Python)

Course

ECG Arrhythmia Classification Course with Wavelet & Deep Learning (PyTorch)

Course

ANFIS + PSO/GA Course for Non-Linear Time Series Forecasting (Python)

See all in AI & Machine Learning →

Have it built for you

No time to learn Python? Our team can do the project for you.

Service

Python Machine Learning — Prediction Models, Customer Segmentation, Fraud Detection & AI Apps

Service

AI Image Creation with Stable Diffusion — Unlimited Custom Visual Production

★ 4.9

Service

AI Image & Video Creation with Leonardo AI — All-in-One Visuals for Business

★ 4.9

See all in AI & Machine Learning →

Get notified about new Python classes

At most one email a week. Unfollow anytime with one click.

Transcript

The full narration of this video. The current sentence is highlighted while the video plays; click any sentence to jump there.

Show transcript

Introduction

Here is the final result, 2 classical channel estimators. List scores hit the NMSI minus 9 dB regardless of SNR, while LMMSI keeps improving up to minus 21 dB. The average LMMSI is almost 7 dB more accurate. Let's get started. Hello, welcome to episode three of the massive MIMO FDM channel estimation series with Deep Neural Networks. Before using Deep Learning, we need a strong classical benchmark. List scores are the simplest one, and LMMSI is optimal for linear estimators when channel statistics are known.

Step 1: Least Squares & Interpolation

Create a file estimator.py List scores in the pilot subquerier simply divide the received signal by the known pilot. Since the pilot is valued at 1, the estimation is the same as the received signal. The subquerier between pilots is filled with linear interpolation, and the subquerier after the last pilot is extrapolated. The frequency covariance function calculates the correlation matrix between 64 subqueriers from the training data, that is, the average of H times H hermitian.

Step 2: LMMSE with Eigen Decomposition

The LMMC function calculates RHP multiplied by inverse RPP plus sigma squared I, multiplied by the LS estimate. This matrix weights each pilot according to its correlation with the target subquerier and the draw level. Since each sample can have a different SNR, we use the Agen decomposition, RPP equals U lambda U hermitian, so the inverse for any sigma is just 1 over lambda plus sigma squared, and 12,000 samples can be calculated at once in half a second.

Step 3: NMSE vs SNR

Create a file test underscore estimator.py and run it. At -10 dB, LS is very poor, NMSI at +9 dB, meaning the error is larger than the channel itself, while LMMSI is at -0.8 dB. At 0 dB, LS is -0.5 and LMMSI is -4.6 dB. At 20 dB, LS hits -9.2 due to interpolation error, while LMMSI reaches -21 dB. The average LMMSI is 6.96 dB better.

Step 4: NMSE Curve & Estimation Example

Let's look at the graph. The LS curve flattens at high SNR, because interpolation error cannot be eliminated by increasing power. The LMMSI curve continues to decrease. The right graph shows one antenna at 10 dB SNR, the red LS point is scattered, its interpolation line is rigid, while LMMSI smoothly follows the actual channel. However, LMMSI only uses correlation between subcarriers, and has not yet utilized correlation between 32 antennas.

Done!

Done. We have built the least-squares estimator with interpolation and LMMSI with frequency covariance and agent decomposition, and compared their NMSE. In the next episode, we will build a CNN which utilizes the correlation between antennas and subcarriers simultaneously. Currently working on a thesis, dissertation, or research in the field of telecommunications and artificial intelligence? Cerdas Inovasi Digital helps implement communication system research from OFDM and multipath channels, massive MIMO simulations, least squares and MMSE estimators, up to deep learning-based channel estimation with PyTorch, as well as opening Python programming courses for electrical engineering and telecommunications. Want to master the entire series, from basic OFDM up to NMSI and BER evaluation? All 6 episodes, complete with step-by-step PDF guides and source code, are available to premium tutorial subscribers. Subscribe starting at Rp69.000 per month, save 28% with the 12-month package, or one-time payment of Rp999.000 for lifetime access. Want just one class? Buy a single class with lifetime access. Subscribe now at the premium page CerdasInnovasiDigital.com Contact us via WhatsApp, or visit CerdasInovasiDigital.com Thank you for watching, See you in the next episode. Thank you for watching. See you in the next episode.

Ask the class material

Type a question or keyword; we find the part of this episode that explains it and jump the video there.

My notes

Notes are saved with the current video time and are only visible to you.

Questions & answers

Stuck on a step? Ask here; the instructor and other learners can answer.

No questions yet.

Your instructor

Cerdas Inovasi Digital Team

Software developers, BIM & 3D engineers, and AI practitioners

53 video classes1,296 episodes

We build software, BIM models, games and AI automations for clients every day, and turn that hands-on work into step-by-step classes: every step is shown on screen and comes with a PDF guide you can keep.

See our clients →

Memuat

▶ Video Lesson

Recommended classes for you

Need more than a video?

Transcript

0:03Introduction

0:44Step 1: Least Squares & Interpolation

2:29Step 2: LMMSE with Eigen Decomposition

3:43Step 3: NMSE vs SNR

5:28Step 4: NMSE Curve & Estimation Example

7:05Done!

Ask the class material

My notes

Questions & answers

Your instructor

▶ Video Lesson

Recommended classes for you

Need more than a video?

Transcript

0:03Introduction

0:44Step 1: Least Squares & Interpolation

2:29Step 2: LMMSE with Eigen Decomposition

3:43Step 3: NMSE vs SNR

5:28Step 4: NMSE Curve & Estimation Example

7:05Done!

Ask the class material

My notes

Questions & answers

Your instructor

Introduction

Step 1: Least Squares & Interpolation

Step 2: LMMSE with Eigen Decomposition

Step 3: NMSE vs SNR

Step 4: NMSE Curve & Estimation Example

Done!

Introduction

Step 1: Least Squares & Interpolation

Step 2: LMMSE with Eigen Decomposition

Step 3: NMSE vs SNR

Step 4: NMSE Curve & Estimation Example

Done!