International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 12 Issue: 10 | Oct 2025 www.irjet.net p-ISSN: 2395-0072
Performance Analysis of a 4×4 MIMO-OFDM Wireless Communication System using MMSE Equalization and Pilot-Based LS Channel Estimation
Akshat Gupta
Student , Department of Electronics and Communication Engineering , JSSATE Noida , U.P. , India
Abstract - This paper presents a MATLAB-based simulation and performance analysis of a 4×4 MIMO-OFDM wireless communication system employing QPSK modulation. The system operates under frequency-selective Rayleigh fading channels and incorporates pilot-based LS channel estimation and MMSE equalization. Key performance metrics, including Bit Error Rate (BER), average system capacity, and per-subcarrier SNR/capacity, are evaluated across a range of SNR values. The results provide a practical benchmark for future 5G/6G system simulations and education.
MATLAB implementation: https://github.com/akshat-137/ 4x4-MIMO-OFDM-Wireless-Communication-System-Simulation
Key Words: MIMO,OFDM,LSChannelEstimation,MMSE,MATLAB,WirelessCommunication,5G
1.INTRODUCTION
OrthogonalFrequencyDivisionMultiplexing(OFDM)iswidelyadoptedinmodernwirelesscommunicationsystemsdueto its robustness against multipath fading and efficient spectral utilization. Multiple-Input Multiple-Output (MIMO) technology leverages multiple transmit and receive antennas to enhance link reliability and spectral efficiency. The combinationofMIMOwithOFDMformsthebackboneof4GLTE,5GNR,andemerging6Gsystems.
Thisstudysimulatesa4×4MIMO-OFDMsysteminMATLAB.Thesystemincorporates:
•Pilot-basedLSchannelestimationforaccuratechannelcharacterization.
•MMSEequalizationtomitigatenoiseandinter-symbolinterference.
Thesimulationevaluates:
•BitErrorRate(BER)versusSNR.
•Averagesystemcapacityacrosssubcarriers.
•Per-subcarrierSNRandcapacitydistributions
2. SYSTEM MODEL
2.1 Block Diagram
Fig. 1 : Blockdiagramof4×4MIMO-OFDMsystem
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 12 Issue: 10 | Oct 2025 www.irjet.net p-ISSN: 2395-0072
2.2 Transmitter
QPSKsymbolmapping:s∈{1+j,1−j,−1+j,−1−j}
OFDMmodulationviaIFFT:
(1)
Wherexn isthetime-domainOFDMsignalandXk isthesymbolonthek-thsubcarrier.Cyclicprefix(CP)isaddedto preventinter-symbolinterference
2.3 Channel
Frequency-selectiveRayleighfadingwithL=6tapsandexponentialpowerdelayprofile: Pl = exp(−l) , l=0,1,...,L−1 (2)
WherePlrepresentsthepowerofthel-thmultipathcomponent,followinganexponentialdecay.
2. 4 Receiver
CPremovalandFFTfollowedbypilot-basedLSchannelestimation:
HˆLS istheestimatedchannelmatrixusingpilotsymbols andreceivedpilots
MMSEequalizationpersubcarrier:
3. SIMULATION PARAMETERS
Table -1: SimulationParameters
Parameters Value
Subcarriers 64
CyclicPrefix 16
Modulation QPSK
TransmitxReceive 4x4
PilotSymbols 4
ChannelTaps 6
SNRRange 0-24dB
Equalizer MMSE
ChannelEstimation LS(Pilot–based)
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 12 Issue: 10 | Oct 2025 www.irjet.net p-ISSN: 2395-0072
4. RESULT AND ANALYSIS
Observation: BER decreases significantly with increasing SNR, while average capacity grows almost logarithmically, demonstrating the spatial multiplexing gain of 4×4 MIMO.
Table -2 : CommandWindowOutput:BERandAverageCapacityvsSNR
Fig. 2 : BERvsSNRfor4x4MIMO-OFDMsystem:ConfirmsMMSEequalizationmitigateschannelnoise.
Fig. 3 : AveragesystemcapacityvsSNR:Capacityincreasessteaditly,showingMIMOspatialmultiplexing.
International Research Journal of Engineering and Technology (IRJET) e-ISSN:
Volume: 12 Issue: 10 | Oct 2025 www.irjet.net
Fig. 4: Per-subcarriercapacityvariationshowingfrequency–selectivefadingeffects.
Fig. 5: Per-subcarrierSNRvariationillustratingmultipathfadingeffects.
Fig. 6: QPSKConstellationafterMMSEEqualization,confirmingaccuratechannelestimation.
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 12 Issue: 10 | Oct 2025 www.irjet.net p-ISSN: 2395-0072
5. CONCLUSION
This work presents a simulation and performance analysis of a 4×4 MIMO-OFDM system under frequency-selective Rayleigh fading. BER decreases with increasing SNR, while average capacity confirms the spatial multiplexing gain. Persubcarrier SNR and capacity plots reflect realistic channel behavior, and the QPSK constellation after MMSE equalization validatesthechannelestimationaccuracy.
These results demonstrate the practical feasibility of MIMO-OFDM for 4G LTE, 5G NR, and beyond. Future work may includehigher-ordermodulation,advancedcoding,adaptivebit-loading,andevaluationundermobilityeffects.
APPENDIX: MATLAB IMPLEMENTATION
1. % OFDMModulation
2. tx=ifft(sym_tx,subcarriers,1);
3. tx_cp=[tx(end–cp+1:end,:,:);tx];
4.
5. % LSChannelEstimation
6. H_est(:,k,j)=Y_pilot(:,j)./pilot_symb(j);
7.
8. % MMSEEqualization
9. W=(H_est’*H_est+noise_var*eye(Tx))\H_est’;
10. X_hat=W*Y;
11.
12. % BERandAverageCapacity
13. BER(idx)=total_error/total_bits;
14. Capacity(idx)=sum(C_subcarrier(:))/(subcarriers*data_symbols*num_frames);
Listing 1 : KeyMATLABImplementation
REFERENCES
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International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 12 Issue: 10 | Oct 2025 www.irjet.net p-ISSN: 2395-0072
[10]M.S.Alouini,”PerformanceAnalysisofMIMO-OFDMSystemsOverFadingChannels,”IEEETransactionsonVehicular Technology,2018.
[11] A. Gupta, 4x4 MIMO-OFDM Wireless Communication System Simulation, GitHub: https:// github.com/akshat137/4x4-MIMO-OFDM-Wireless-Communication-System-Simulation,2025.
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