Direct Detection PSK systems have recently received a great attention, since they can be adapted for long haul transmissions along with optical amplifiers. However direct detection DPSK systems are susceptible to nonlinear phase noise and their performance is also affected by chromatic dispersion. The effects of nonlinear phaseshift on PSK components in a DPSK system are intensity dependent for Self Phase Modulation (SPM) and are random for cross-phase modulation (XPM). This disturbs the orientation of PSK components in the signal constellation diagram and the relationship is derived from Schrodinger equations. The addition of nonlinear phaseshift and chromatic dispersion leads to incorrect detection of bits at the receiver. In order to analyze the characteristic degradation, Bit Error Rate (BER) is used as a performance measure at the receiver side in the systems. In this thesis the bit error probabilities of direct detection system in presence of self-phase modulation and chromatic dispersion are evaluated separately. It has been observed that bit error probability of direct detection DPSK systems in the presence of SPM increases with increase in extinction ratio and decreases with photon chip count. In the presence of chromatic dispersion, bit error probability increases with OSNR but degrades with transmission distances. The bit error estimation analysis is a useful tool in designing direct detection system for long haul optical transmissions.