Both spectral and power efficiencies of the Time Interleaved Block Windowed Burst OFDM (TIBWB-OFDM) transmission scheme are limited due to the windowing operation performed in the transmitter. Although this operation is required to reduce out of band (OOB) emissions, it results in temporal extension of the OFDM-based blocks and increases the signal peak-to-average power ratio (PAPR). A new TIBWB-OFDM transceiver scheme is studied in this paper, where adjacent OFDM sub-blocks are allowed to overlap in time. This leads to a smaller overall block, increasing the spectral efficiency and decreasing the PAPR of the transmitted signals, when compared with standard TIBWB-OFDM. These efficiency gains are obtained at the expense of interference between sub-blocks, which deteriorates the bit error rate (BER) performance. To avoid this BER degradation, we propose several embodiments (non-iterative and iterative) of the the receiver that include frequency domain equalizers and time domain interference cancellation algorithms to cope with channel effects and interference introduced by the overlapping operation, respectively.