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

Class Estimation of MIMO-OFDM Channels Using Deep Learning #6: NMSE and BER vs SNR Evaluation, Comparison of All Estimators

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Tutorial on evaluating NMSE and BER for massive MIMO-OFDM channel estimation: LS, LMMSE, CNN, maximum ratio combining with Python. Episode 6, the closing part of the massive MIMO-OFDM deep learning channel estimation series.

Software: Python (NumPy, SciPy, PyTorch, Matplotlib)
Level: Advanced
Duration: ± 8 min
Series total: 57 min · 6 videos
Published: October 25, 2026

Episode 6 of 6 · view syllabus

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Introduction

Here is the final result, the bit error rate of data received by 32 antennas with the channel results from each estimator. At SNR-5dB, CNN produces a bit error rate 2.4 times lower than LMMSI and 5 times lower than list squares. Let's start. Hello, welcome to the final episode of the massive MIMO FDM channel estimation series with Deep Neural Networks. NMSI measures the accuracy of the estimation, but users feel the bit error rate. Today we will send real data, combining 32 antennas with maximum ratio combining using the estimated channel, and see the impact.

Step 1: BER with MRC 32 antennas

Create an evaluation .py file, we use 1000 test channels. The function bermRC sends QPSK symbols across all subcarriers, receives them at 32 antennas with draw, then combines them with maximum ratio combining. The number of conjugate channel estimates multiplied by the received signal, divided by the number of squared magnitude channel estimates. An incorrectly estimated channel causes incoherent combining and symbol shift. For each SNR from minus 10 to 10 decibels, we calculate NMSI and BIR for perfect CSI, LS, LMMSI, and CNN. Run. With perfect CSI, BIR is already 1.2 times 10 to the power of minus 3 at minus 5 decibels thanks to the 32 antenna gain. At the same SNR, LS is 8.8 times 10 to the power of minus 2, LMMSI is 4.2 times 10 to the power of minus 2, and CNN is 1.8 times 10 to the power of minus 2. BIR-CNN is 0.42 times BIR-LMMSI and 0.2 times BIR-LS. At 5 decibels, LS is still stuck at 4 times 10 to the power of minus 3, while CNN is 1.6 times 10 to the power of minus 5.

Step 2: NMSE & BER Curve

Continue with the NMSI and BIR graphs. Let's look at the graphs. The NMSI-CNN curve is always below LMMSI across the entire range. On the BIR graph, the dashed black line for perfect CSI is the best benchmark, and CNN is the closest to it. The LS curve flattens at high SNR because its interpolation error causes floor error. The horizontal difference between curves indicates power savings. For the same BIR, CNN requires about 1-2 decibels less power than LMMSI.

Done!

Done, and the series is complete. We have built a complete research on massive MIMO-FDM channel estimation, OFDM, Massive MIMO Channels and Dataset, List Squares and LMMSI, Hybrid CNN with dilation, effect of pilots and SNR, up to evaluation of NMSE and BER. For further research, try channels with mobility and Doppler effect, transformer architecture, multi-user estimation with pilot contamination, or more realistic 3GPP-CDL models. Thank you for following this series. 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 simulation, List Squares and LMMSI 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 evaluation of NMSE and BER? All 6 episodes, complete with PDF step-by-step guides and source code, are available for 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. Thank you for watching, see you in the next episode.

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Transcript

0:03Introduction

0:45Step 1: BER with MRC 32 antennas

4:45Step 2: NMSE & BER Curve

6:10Done!

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Transcript

0:03Introduction

0:45Step 1: BER with MRC 32 antennas

4:45Step 2: NMSE & BER Curve

6:10Done!

Ask the class material

My notes

Questions & answers

Your instructor

Introduction

Step 1: BER with MRC 32 antennas

Step 2: NMSE & BER Curve

Done!

Introduction

Step 1: BER with MRC 32 antennas

Step 2: NMSE & BER Curve

Done!