# Maximal Ratio Combining Detection in OFDM Systems with Virtual Carriers Over V2V Channels
## 1 Introduction  
The integration of vehicular communication into novel networks has been a research topic for several years. Recently, some enabling technologies have been discussed to accelerate the integration of V2V systems into novel networks [1]. According to the 5G standard, novel technologies must integrate high data rates, low latency and reliability, wider coverage, low power, and low-cost communication services. Among others, virtualization, artificial intelligence (AI), mobile edge computing (MEC), non-orthogonal multiple access (NOMA), massive MIMO, MmWave, and full-duplex communications are promising technologies to satisfy these requirements [2, 3]. In particular, new technologies for real-time information transmission are an essential part of the emerging intelligent transportation systems (ITS). Novel networks will include vehicle-to-infrastructure (V2I) and vehicle-to-vehicle (V2V) communication links [4], which need to operate on doubly selective channels (DSC) at high transmission rates. These factors cause the systems based on orthogonal frequency division multiplexing (OFDM) to suffer from a severe problem known as intercarrier interference (ICI) [5, 6, 7]. In V2V communication systems, the ICI is accentuated by the high Doppler spread frequencies caused by the high mobility in the vehicular links [5, 8, 9, 10, 11]. ICI severely degrades the overall performance of OFDM-V2V systems, making channel estimation, data detection, and error correction tasks extremely challenging. Due to the computational complexity required to implement DSC channel equalization, data detection algorithms have been widely studied under this scenario. In the state of the art, it is common to find linear detectors, such as least squares (LS) or linear minimum mean squared error (LMMSE) detectors [6, 7, 12]. The performance of thesedetection schemes is inferior in terms of bit error rate (BER) compared to nonlinear detection schemes since they do not significantly reduce the inter-symbol interference (ICI) during the detection process, resulting in poor performance at low signal-to-noise ratio (SNR) levels in V2V channels. However, their main strength lies in their simple structure and computational complexity, making them viable for hardware implementation. On the other hand, nonlinear detection schemes use the finite cardinality of the transmitted symbols to improve their performance. This category includes the so-called ordered successive interference cancellation (OSIC) [13], decision feedback equalizers (DFE) [14], maximum likelihood (ML) detector [14; 15], etc. The performance of nonlinear detectors is much better than that of LMMSE in terms of BER, but this performance comes at the expense of a considerable increase in computational complexity, which makes it difficult to implement them in real-time systems. In order to reduce the complexity of these detection schemes, for the case of the ML detector, there are quasi-ML approximations that are based on hierarchical and selective search techniques, reducing the number of search sequences and computational complexity [16]. The price of these approximations is a loss in performance in terms of BER compared to the ML equalizer since there is a probability of eliminating the optimal estimation sequence in the early stages of the search. In conventional OFDM systems, a technique used to counteract ICI is deliberately sacrificing the spectral efficiency of the system, which is achieved by increasing redundancy in the transmitted data in forward error correction (FEC) stages [17; 18; 19], or using virtual carriers (VC), also known as guard symbols [20; 21; 22; 23; 24]. Several works [13; 20; 22] highlight the advantages of using VC during transmission, achieving an improvement in system performance in terms of BER and reducing the complexity required by linear/nonlinear detectors. However, the receivers reported in state-of-the-art detectors do not use the diversity of the received signal during the detection process.