During symbol transmission we may use single carrier or multi-carrier modulation. In case ofrnsingle carrier transmission all users share the same transmission medium and this causes thernproblem of Inter Symbol Interference (ISI) which leads to error in reception. In case of multicarrierrntransmissionrntherernisrnMultiplernAccessrnInterferencern(MAI).rnInrnseveralrndigitalrncommunicationrnrnproblems,rnthernreceivedrnsignalrnisrngivenrnbyrnarnlinearrncombinationrnofrntherndatarnsymbolsrncorruptedrnbyrnrnchannelrnrneffects. So the received symbol may be affected by transmission channel noise,rninterference, distortion, bit synchronization problems, attenuation, and wireless multipath-fading.rnTherefore efficient demodulation and symbol detection strategies are very necessary. rnrnThis thesis work on symbol detection is done as per the request of Information Networks SecurityrnAgency (INSA) of Ethiopia. The industry wants to implement advanced digital receiver for localrnuse. So the industry main aim is to review, investigate, and implement efficient symbol detectionrnalgorithms.rnIn this paper we have considered a class of single carrier and multi-carrier symbol detectionrnalgorithms and compare their performance in terms of Bit Error Rate (BER) and Signal to NoisernRatio (SNR) of various modulation type and order. M-ary PSK and M-ary QAM have beenrnsimulated with optimum and sub-optimum detectors like Maximum-Likelihood (ML), MinimumrnMean Square Error (MMSE) and Zero Forcing (ZF) detector. rnFrom our findings, for the single carrier single user case for additive White Gaussian Noisern(AWGN) channel the BER at 15dB is 10rn, which is acceptable. Again for the case of RayleighrnFading channel at 35dB still we have a BER of 10rn-3rn. In the case of multicarrier multi user (MCCDMA)rnrndetection over Rayleigh fading channel, we have been shown how the three differentrndetectors behave in performance and complexity analysis. Finally, it can be seen that the mostrncomplex and the best performing detector, is the Maximum Likelihood detector.