There have been many matching pursuit algorithms (MPAs) which handle the sparse signal recovery problem, called compressed sensing (CS). In the MPAs, the correlation step makes a dominant computational complexity. In this paper, we propose a new fast correlation method for the MPA when we use partial Fourier sensing matrices and partial Hadamard sensing matrices which are widely used as the sensing matrix in CS. The proposed correlation method can be applied to almost all MPAs without causing any degradation of their recovery performance. Also, the proposed correlation method can reduce the computational complexity of the MPAs well even though there are restrictions depending on a used MPA and parameters.

Clipping is an efficient and simple method that can reduce the peak-to-average power ratio (PAPR) of orthogonal frequency division multiplexing (OFDM) signals. However, clipping causes in-band distortion referred to as clipping noise. To resolve this problem, a novel iterative estimation and cancellation (IEC) scheme for clipping noise is one of the most popular schemes because it can significantly improve the performance of clipped OFDM systems. However, IEC exploits detected symbols at the receiver to estimate the clipping noise in principle and the detected symbols are not the sufficient statistic in terms of estimation theory. In this paper, we propose the post-processing technique of IEC, which fully exploits given sufficient statistic at the receiver and thus further enhances the performance of a clipped OFDM system as verified by simulations.

Orthogonal frequency division multiplexing with index modulation (OFDM-IM) is a novel scheme where the information bits are conveyed through the subcarrier activation pattern (SAP) and the symbols on the active subcarriers. Specifically, the subcarriers are partitioned into many subblocks and the subcarriers in each subblock can have two states, active or idle. Unfortunately, OFDM-IM inherits the high peak-to-average power ratio (PAPR) problem from the classical OFDM. The OFDM-IM signal with high PAPR induces in-band distortion and out-of-band radiation when it passes through high power amplifier (HPA). Recently, there are attempts to reduce PAPR by exploiting the unique structure of OFDM-IM, which is adding dither signals in the idle subcarriers. The most recent work dealing with the dither signals is using dithers signals with various amplitude constraints according to the characteristic of the corresponding OFDM-IM subblock. This is reasonable because OFDM subblocks have distinct levels of robustness against noise. However, the amplitude constraint in the recent work is efficient for only additive white Gaussian noise (AWGN) channels and cannot be used for maximum likelihood (ML) detection. Therefore, in this paper, based on pairwise error probability (PEP) analysis, a specific constraint for the dither signals is derived over a Rayleigh fading channel.

By exploiting the inherent sparsity of wireless channels, the channel estimation in an orthogonal frequency division multiplexing (OFDM) system can be cast as a compressed sensing (CS) problem to estimate the channel more accurately. Practically, matching pursuit algorithms such as orthogonal matching pursuit (OMP) are used, where path delays of the channel is guessed based on correlation values for every quantized delay with residual. This full search approach requires a predefined grid of delays with high resolution, which induces the high computational complexity because correlation values with residual at a huge number of grid points should be calculated. Meanwhile, the correlation values with high resolution can be obtained by interpolation between the correlation values at a low resolution grid. Also, the interpolation can be implemented with a low pass filter (LPF). By using this fact, in this paper we substantially reduce the computational complexity to calculate the correlation values in channel estimation using CS.

Many selected mapping (SLM) schemes have been proposed to reduce the peak-to-average power ratio (PAPR) of orthogonal frequency division multiplexing (OFDM) signal sequences. In this paper, an efficient selection (ES) method of the OFDM signal sequence with minimum PAPR among many alternative OFDM signal sequences is proposed; it supports various SLM schemes. Utilizing the fact that OFDM signal components can be sequentially generated in many SLM schemes, the generation and PAPR observation of the OFDM signal sequence are processed concurrently. While the u-th alternative OFDM signal components are being generated, by applying the proposed ES method, the generation of that alternative OFDM signal components can be interrupted (or stopped) according to the selection criteria of the best OFDM signal sequence in the considered SLM scheme. Such interruption substantially reduces the average computational complexity of SLM schemes without degradation of PAPR reduction performance, which is confirmed by analytical and numerical results. Note that the proposed method is not an isolated SLM scheme but a subsidiary method which can be easily adopted in many SLM schemes in order to further reduce the computational complexity of considered SLM schemes.

It is known that in the selected mapping (SLM) scheme for orthogonal frequency division multiplexing (OFDM), correlation (CORR) metric outperforms the peak-to-average power ratio (PAPR) metric in terms of bit error rate (BER) performance. It is also well known that four times oversampling is used for estimating the PAPR performance of continuous OFDM signal. In this paper, the oversampling effect of OFDM signal is analyzed when CORR metric is used for the SLM scheme in the presence of nonlinear high power amplifier. An analysis based on the correlation coefficients of the oversampled OFDM signals shows that CORR metric of two times oversampling in the SLM scheme is good enough to achieve the same BER performance as four times and 16 times oversampling cases. Simulation results confirm that for the SLM scheme using CORR metric, the BER performance for two times oversampling case is almost the same as that for four and 16 times oversampling cases.