###### Abstract
Aiming to deal with the aforementioned issues, this paper focuses on the performance comparison among HS-OFDM, OCDM, SCCP, and OTFDM schemes in the presence of the CP length violation and the STO in data communication performed by base-band PLC systems, in which the media is characterized by frequency-selective channel frequency response (CFR). The main contributions of this study are as follows. We present:  
* A presentation of a unified formulation from which the HS-OFDM scheme, OCDM, SCCP, and OTFDM schemes are derived for baseband systems, as well as a deduction of closed-form expressions for the estimated signal, signal-to-interference-plus-noise ratio (SINR), and SINR upper-bound when frequency domain equalizers (i.e., complete zero-forcing (C-ZF), modified zero-forcing (M-ZF), and single-tap zero-forcing (ST-ZF) [27]) are considered. * Numerical analyses to compare closed-form expressions with the Monte Carlo simulation and different types of frequency domain equalizers; we show that the STO might benefit data communication systems when the CP length violation occurs. * Performance analyses comparing HS-OFDM, OCDM, SCCP, and OTFDM in terms of the achievable data rate, which considers uniform power allocation (UA) and optimal power allocation (OA), and bit error probability (BEP) with adaptive modulation when the frequency domain equalizer is used to deal with linear time-invariant (LTI), PLC, and channel impulse response (CIR), which is frequency selective and corrupted by the presence of additive noise modeled as a white or colored random process. Our major findings are:* The unified formulation allows us to derive HS-OFDM, OCDM, SCCP, and OTFDM schemes easily. Consequently, we advocate that it can support future designs of transceivers based on multi-schemes. Moreover, the closed-form expressions can correctly characterize the performance of these schemes. Consequently, it is unnecessary to perform Monte Carlo simulations. * For all schemes, the STO might benefit the system performance when the CP length violation occurs. In other words, small values of STO can relieve the interference caused by the CP length violation. In the scenario without the CP length violation, we show the transmission block will not be degraded by the interference caused by the channel spreading if the sum of the CP length with the STO is bigger than the length of PLC CIR minus one. * Similar behavior is observed in the narrowband PLC systems using the aforementioned schemes when the C-ZF scheme, M-ZF, and ST-ZF are applied. For instance, the C-ZF scheme and ST-ZF always attain the best and the worst performances for all schemes, respectively. * Regarding the achievable data rate analysis, we see that without interference (i.e., no CP length violation and no STO), the HS-OFDM scheme always attains the highest achievable data rate, followed by OTFDM. In the sequel, we have SCCP and OCDM, which yield the same achievable data rate. On the other hand, under the interference's presence, the HS-OFDM scheme attains the highest achievable data rate when the total transmission power belongs to a certain range of values. Above this range of values, OTFDM attains the highest achievable data rate. Moreover, HS-OFDM offers the lowest achievable data rate upper bound while SCCP attains the highest. * The BEP analyses for all scenarios with interference show that OCDM attains the lowest bit error probability. It is followed by HS-OFDM, SCCP, and OTFDM, in this order. Note that SCCP and OTFDM attain similar BEP performances and have higher lower bounds. On the other hand, in the absence of interference, the best BEP performances are attained by OCDM and SCCP, followed by OTFDM, with HS-OFDM being the worst. The rest of this paper is organized as follows: Section 2 details the system model; Section 3 focuses on the transmitter and receiver general mathematical formulation, which includes the CP length violation and the STO; it also discusses the types of interference that corrupt the data communication system.