# Signal Detection for GSTFIM Systems with Carrier Frequency Offset +
###### Abstract  
Generalized space-time-frequency index modulation (GSTFIM) inherits the drawbacks of the conventional orthogonal frequency-division multiplex (OFDM), such as being sensitive to carrier frequency offset (CFO). For a robust design against this problem, in this contribution, a novel construction of a message passing (MP)-aided detector is developed for GSTFIM systems to combat the influence of CFO, while offering a flexible tradeoff between transmission performance and computational complexity. Through complexity analysis and simulation results, we demonstrate that, in the context of CFO, with a careful design, the developed MP detector is capable of approaching traditional GSTFIM with maximum likelihood (ML) detection, and of offering better performance at lower complexity compared to its minimum mean-square-error (MMSE)-aided counterpart. m 202  
Meanwhile, as an evolution of traditional MIMO-OFDM technology, GSTFIM inherits the disadvantages of original OFDM, such as the sensitivity to ICI caused by carrier frequency offset (CFO). Although this problem may be slightly alleviated due to its sparse 3D structure, as described in current research, the influence on GSTFIM caused by CFO remains a huge challenge, especially in the context of high-mobility scenarios. As a result, the performance of original GSTFIM will be degraded seriously when CFO is considered in practical transmission. In the current literature, a series of techniques has been developed as in [13; 14; 15; 16] for traditional MIMO-OFDM systems. Specifically, for spatial modulation OFDM systems, some CFO compensation techniques at the receiver side were also presented such as in [17; 18; 19]. However, the above structure cannot be directly utilized in the special structure of GSTFIM. For GSTFIM and index modulation, in order to achieve the performance bound of the optimal detector while fully exploring the sparse structure [20], the concept of message-passing (MP) has been widely considered for low-complexity signal detection [21; 22; 23]. Recently, we conceived a class of minimum mean-square-error (MMSE) detectors [24] with the capability to combat CFO. However, the attained BER performance still requires improvement while the computational complexity is high for practical implementation. Against the above background, this paper considers the design of a robust detector for enhancing the BER performance of GSTFIM systems, in the context of an iterative process. The detailed contribution is summarized as follows. Firstly, the iterative detection concept is introduced for general GSTFIM detectors. Specifically, the a priori probabilities of the GSTSK symbols are computed for general GSTFIM detectors, then, a priori probabilities of the GSTSK symbols of all the subcarriers are replaced with posterior probabilities, and the detectors continue the iterative process. After several numbers of iterations, the GSFTIM symbols are ultimately reconstructed. Secondly, two kinds of methods are developed for detector construction. The first method is based on a single carrier, where the probability of the subcarriers in the same GSFTIM symbol is compared to determine whether the symbol on each subcarrier is a GSTSK symbol or an all-zero matrix. The second method is based on block carriers, where the GSFTIM symbols are reconstructed by comparing the probabilities of GSFTIM symbols, which are obtained by the sum probability of several subcarriers in the GSFTIM symbol. Lastly, the idea of message-pass is utilized in signal detection in GSTFIM systems with an iterative process. In general, we conclude that the proposed two methods, as single carrier and block carrier processing, can adapt the MMSE detector in [24] toward a flexible detector configuration. Most important of all, by combining MP and an iterative process, we demonstrate that the developed MP-aided detector can approach the BER performance of maximum likelihood (ML), and outperform MMSE-based detectors with reduced computational complexity. The remainder of this paper is organized as follows.