Hybrid Optimized LMMSE-Based Channel Estimation with Low Power Trellis Coded Modulation

Figures & data

Table 1. Review on conventional LMMSE based CE models: features and challenges.

Author [citation]	Adopted scheme	Features	Challenges
(Charrada 2018)	LMMSE-SVR method	High-speed estimation Increased throughput Improved QoS	The learning step complexity was not reduced.
(Li et al. 2018)	Jakes model	Less signal-to-noise ratios Minimum BER	Need to consider the choice of the PS factor.
(Dai et al. 2021)	LSE algorithm	Reduced training resources Low costs High spectral efficiency	Need to develop the low-resolution super-resolution CE scheme.
(Boukhedimi, Kammoun, and Alouini 2019)	Massive MIMO system	Low Rician factors Higher SE gains Stronger LoS signals	The processing approach does not constitute the achievable capacity limitation.
(Xiong, Wei, and Zhang 2018)	Massive MIMO system	Small loss Better BER performance	The adopted scheme does not need the IQI parameters exact value.
(Ali et al. 2020)	RS-LS and D-LS Algorithm	Better throughput Minimum error Low computational complexity	NDMRS and NPUSCH hopping were not considered in the adopted model.
(Sorna Keerthi and Meena Alias Jeyanthi 2018)	Trellis Coded FF Optimized LMMSE model	Low complexity High spectral efficiency Reduced error	Heuristic algorithm does not give optimum solutions.
(Jeya and Amutha 2019)	OSBS-CE algorithm	Improved channel capacity Low SNR	Need to consider more transmitters and also receivers in this work.

Figure 1. Architectural diagram of the proposed model.

Figure 2. TCM model.

Figure 3. 8 × 8 MIMO without precoding.

Figure 4. 8 × 8 MIMO with precoding.

Figure 5. Interleaved subcarrier mapping.

Figure 6. Localized subcarrier mapping.

Figure 7. Flowchart of the proposed channel estimation algorithm.

Figure 8. Convergence analysis of proposed method over other existing schemes (a) PSK; (b)QAM.

Figure 9. BER analysis of proposed method over other existing schemes (a) PSK; (b) QAM.

Figure 10. Channel MSE analysis of adopted method over other existing schemes (a) PSK; (b) QAM.

Figure 11. Analysis on PSK magnitude response for (a) LMMSE channel matrix; (b) LSE channel matrix (c) proposed AAA model.

Figure 12. Analysis on QAM magnitude response for (a) LMMSE channel matrix (b) LSE channel matrix (c) proposed AAA model.

Table 2. Statistical analysis: proposed vs. traditional models for PSK.

Metrics	Proposed TCM + MAEHO model	TCM + MFO (Mirjalili 2015)	TCM + EHO (Elhosseini et al. 2019)	TCM + WOA (Mirjalili and Lewis 2016)	TCM + FF (Wang et al. 2017)
Best	0.00082	0.00082	2.98$\times {10}^{-05}$	2.98$\times {10}^{-05}$	0.000744
Median	0.001206	0.01352	0.000744	2.98$\times {10}^{-05}$	0.02622
Standard Deviation	0.000157	0.013912	0.000292	0.000408	0.010401
Worst	0.001206	0.02622	0.000744	0.00082	0.02622
Mean	0.001142	0.01352	0.000625	0.000293	0.021974

Table 3. Statistical analysis: proposed vs. traditional models for QAM.

Metrics	Proposed TCM + MAEHO model	TCM + MFO (Mirjalili 2015)	TCM + EHO (Elhosseini et al. 2019)	TCM + WOA (Mirjalili and Lewis 2016)	TCM + FF (Wang et al. 2017)
Best	2.98$\times {10}^{-05}$	0.00082	0.000744	2.98$\times {10}^{-05}$	0.000744
Median	0.001206	0.00082	0.000744	2.98$\times {10}^{-05}$	0.02622
Standard Deviation	0.00048	0.000157	0	0.000323	0.010401
Worst	0.001206	0.001206	0.000744	0.00082	0.02622
Mean	0.00101	0.000885	0.000744	0.000162	0.021974

Table 4. Error analysis: proposed vs. traditional models for PSK.

Metrics	Proposed TCM + MAEHO model	TCM + MFO (Mirjalili 2015)	TCM + EHO (Elhosseini et al. 2019)	TCM + WOA (Mirjalili and Lewis 2016)	TCM + FF (Wang et al. 2017)
MSE	0.000117	0.000898	0.000625	0.000352	0.000547
RMSE	0.010825	0.029974	0.025	0.01875	0.023385
MAE	0.000117	0.000898	0.000625	0.000352	0.000547
PSNR	39.311	30.465	32.041	34.54	32.621

Table 5. Error analysis: proposed vs. traditional models for QAM.

Metrics	Proposed TCM + MAEHO model	TCM + MFO (Mirjalili 2015)	TCM + EHO (Elhosseini et al. 2019)	TCM + WOA (Mirjalili and Lewis 2016)	TCM + FF (Wang et al. 2017)
MSE	0.067344	0.07418	0.070664	0.068477	0.076406
RMSE	0.25951	0.27236	0.26583	0.26168	0.27642
MAE	0.067344	0.07418	0.070664	0.068477	0.076406
PSNR	11.717	11.297	11.508	11.645	11.169

Table 6. Analysis on computational time.

Methods	Time (sec)
MFO	232.14
EHO	212.45
WOA	198.75
FF	187.98
MAEHO	152.32

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