# HF Communication System using M-PSK Modulation and Adaptive Equalizers in ITU-R HF Multipath Fading Channel
### Brief description
This repo is dedicated to MATLAB Imitation Modeling for the BER of the HF Communication System using M-PSK modulation in the HF Communication Channel with multipath and signal fading.
The HF Communication System is constructed using objects and high-developed functions from MATLAB Communication and DSP Toolbox. The HF Channel is constructed based on [HF Ionospheric Channel Models](https://www.mathworks.com/help/comm/examples/hf-ionospheric-channel-models.html) by [`stdchan`](https://www.mathworks.com/help/comm/ref/stdchan.html) function according to [ITU-R Recommendation F.1487 "Testing of HF modems with bandwidths of up to about 12 kHz using ionospheric channel simulator"](https://www.itu.int/rec/R-REC-F.1487/en). For reducing signal fading and BER improving the HF Comm System uses [Adaptive Equalizers](https://www.mathworks.com/help/comm/ug/adaptive-equalizers.html).
The files in the repo can be useful for any communication engineer and MATLAB programmer, who is looking for examples of the BER Imitation Modeling of the Comm Systems.
## Content of the repo
The [HFCommSystem_LSModeling.mlx](HFCommSystem_LSModeling.mlx) contains detailed code and performs Imitation Modeling in the MATLAB Live Script Editor.
The [BERTool_MPSK.m](BERTool_MPSK.m), [BERTool_MPSK_Equalizer_T1.m](BERTool_MPSK_Equalizer_T1.m) and [BERTool_MPSK_Equalizer_T2.m](BERTool_MPSK_Equalizer_T2.m) are functions that used in the [BER Analyzer Tool](https://www.mathworks.com/help/comm/ug/bit-error-rate-ber.html#bsvziy0).
For the BER research and efficiency estimation presented files perform Imitation Modeling for the next cases:
* many types and conditions of the HF Comm Channel with multipath and signal fading, given in [`stdchan`](https://www.mathworks.com/help/comm/ref/stdchan.html) and [ITU-R Recommendation F.1487](https://www.itu.int/rec/R-REC-F.1487/en);
* two types of HF Receiver:
* without Adaptive Equalizer;
* with Adaptive Equalizer;
* two types of Adaptive Equalizer [structure](https://www.mathworks.com/help/comm/ug/equalization.html):
* [Linear Equalizer](https://www.mathworks.com/help/comm/ug/adaptive-equalizers.html#a1049736245);
* [Decision Feedback Equalizer](https://www.mathworks.com/help/comm/ug/adaptive-equalizers.html#a1049736296b1);
* two types of Equalizers adapting algorithm with training:
* [LMS](https://www.mathworks.com/help/comm/ug/adaptive-equalizers.html#d120e12871);
* [RLS](https://www.mathworks.com/help/comm/ug/adaptive-equalizers.html#d120e12917);
* two [training schemes](https://www.mathworks.com/help/comm/ug/adaptive-equalizers.html#mw_043c9308-c7a3-4243-9cdd-0eaa9563d70d) for the Adaptive Equalizer:
* T1 - training at the begining of each frame;
* T2 - one-time training at the begining of new BER point.
* As well there are many options to make research, e.g. for modulation order and symbol rate, and many options for signal analysis and visualization.
## BER Results
Here are some BER Results of Imitation Modeling presented in the next Graphs. The HF Comm System uses symbol rate 1000 baud and 2-PSK modulation. The other parameters are shown in the Graphs.
![BER 2-PSK with DF Equalizer in iturHFMQ Multipath Channel](./BERGraphs/BER_2-PSK_iturHFMQ.png)
![BER 2-PSK with DF Equalizer in iturHFMM Multipath Channel](./BERGraphs/BER_2-PSK_iturHFMM.png)
![BER 2-PSK with DF Equalizer in iturHFMD Multipath Channel](./BERGraphs/BER_2-PSK_iturHFMD.png)
As we see, DF Equalizer demonstrates BER reducing and noise immunity improving. The next research need to be conduct in purpose to find the optimal parameters of DF Equalizer.
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