# Performance of Differential-Phase OFDM Systems over Selective Multipath Fading Channels
## 1 Introduction
To decrease or eliminate the overlap between the adjacent frames, a guard period, which could be a cyclic prefix or zero padding, i.e., a period of silence with no transmission, with a duration of \(T_{g}\), can be added between successive frames. This will extend the actual frame duration to \(T_{f}=T_{u}+T_{g}\). When possible, \(T_{g}\) should be chosen to be greater than the maximum delay in the multipath fading channels. The ratio of the useful frame duration to the total frame duration represents the efficiency in the transmitted power: \(\eta=T_{u}/T_{f}\). Another advantage of increasing the number of orthogonal carriers is to make the subchannel bandwidth small compared to the coherence bandwidth of the channel \((\Delta f)_{c}\) in the frequency-selective channels, i.e., \(\Delta f=W/N\ll(\Delta f)_{c}\)[4]. Such a condition will enable transmitted symbols to experience almost flat fading (frequency non-selective) which will significantly decrease the complexity of the receiver and allow for a simple equalization process. In a previous effort, the author et al. have studied the performance of enhanced cooperative coding for OFDM systems in frequency flat channels. However, this paper studies uncoded OFDM systems in frequency-selective channels with potential future expansion to this work to include cooperative coding for OFDM systems [10]. In this paper, differential-phase modulation has been chosen to study the performance of OFDM over frequency-selective multipath fading channels. The reason for choosing the differential-phase scheme rather than the coherent-phase scheme is that the differential-phase technique does not require channel estimation or equalization. Channel estimation mandates transmitting pilot symbols which will significantly increase the complexity of the receiver. The price paid by the differential scheme is the requirement of a higher signal-to-noise ratio (SNR) to achieve the same probability of error as for coherent-phase detection. On the other hand, differential-phase modulation can be coherently demodulated and differentially decoded. This method is called quasi-coherent detection which can improve the performance of the system given the same level of SNR [11; 12]. The authors in [11] have concluded that transmitting the pilot symbol in coherent-phase OFDM schemes will cause additional loss of around 1.5 dB which justifies the use of differential-phase modulation. Even with the precautions taken when designing the OFDM system, interference problems are likely to occur but with less severity when compared to single carrier systems. However, interference problems will degrade the performance of the system, and the system will require more procedures to be employed at the receiver side. Due to the nature of fading channels, the orthogonality between subcarriers may cease, causing a specific type of interference known as the Inter-Channel-Interference (ICI). The guard period between the frames is designed to prevent or reduce interference between adjacent OFDM frames. The next section presents the performance of OFDM-encoded differential phase shift keying signals in the presence of multipath frequency-selective Nakagami-\(m\) channels. In particular, there will be a focus on the degradation of the system performance in the presence of ISI, ICI, and additive Gaussian noise.