## 4 Low Complexity Non-Linear Detection
### Two Approaches for Non-Linear Data Detection
#### 4.2.2 Near ML Detection
Of the 64 subcarriers that compose an OFDM symbol, 48 are used for the data transmitting. This allows the use of eight modulation schemes which permit the handling of transmission speeds between 3 and 27 Mbps and a frame length of \(L_{F}=37\) OFDM signals. In this article, we present results using the following parameters: a 4-QAM modulation scheme, \(N_{c}=4\) for the Near ML search tree, convolutional coding of length \(L_{c}=7\), a code rate of \(Rc=1/2\) and \(B=27\) main diagonals, with \(\lambda=8,\lambda_{c}=5\). The channel was implemented using the filtered method explained in [28]. The channel power delay profile (PDP) consists of six uncorrelated paths defined by \(p(\tau)=\delta(\tau-m\tau_{0})e^{\frac{\tau}{W_{0}}}\) where \(0<\tau<1.6\) us, \(\tau_{0}=0.1\) us and \(m=\{0,1,\dots,\}\). The parameters that were used to generate the V2V channel are reported in [3], where V2V channel models consider vehicle velocities of \(v=100\) Km/h. The number of OFDM symbols transmitted by each evaluated SNR level is equal to \(1.6\times 10^{5}\). Figure 10 shows the BER vs. \(E_{b}/N_{0}\), under a vehicular scenario with NLOS (no-line-of-sight). To emulate this scenario, a channel with Rayleigh fading was considered with a power delay profile, decreasing exponentially with root mean square (RMS) delay time \(\tau_{RMS}=0.4\) us and \(f_{D}=1\) kHz. This model is similar to the one called \"RTV-Expressway\" described in [2]. The dotted lines show the system performance with linear detectors, using the pilot assignment shown in Figure 1 for the iterative estimation of the channel. The solid line is assigned to the performance of our proposed system with Near ML non-linear detection. The tests show that the linear detection approach needs at least three iterations in order for a floor error not to be found. In the case of the proposed Near ML non-linear detection, no iteration is needed to achieve this. It can be seen that the proposed Near ML detection largely surpasses the LMMSE detection approach proposed in [3]. Figure 10: BER vs. Eb/No comparison of the Near ML detection proposed and LMMSE detection for a frame length \(L_{F}=37\) and full 802.11p compliant (no postamble). The channel model uses a Jake’s Doppler profile for each channel tap. The power delay profile is exponentially decaying with RMS delay spread of 0.4 μs and frequency Doppler spread of 1 kHz modeling a Rayleigh fading NLOS scenario. In order to more clearly quantify the Near ML and OSIC detection performance with respect to the DFTS-OFDM-LMMSE detection, tests were completed without the use of the convolutional encoder. Additionally, both the OSIC and Near ML detection were evaluated using QR decomposition with ZF and MMSE as criteria. Figure 9 shows the BER vs. SNR comparison of the proposed algorithms that includes frequency dispersion. With the exception of the ZF-OSIC detection, the proposed algorithms present better performance compared with LMMSE detection with ideal channel. In one particular case above SNR = 15 dB, the MMSE-OSIC suboptimal detection and the MMSE-Near ML detection surpass the LMMSE detection by 2.5 and 5 dB, respectively. It is important to mention that the tendency shown by both proposed detectors does not exhibit the undesirable error floor. Figure 11 shows the performance of the proposed iterative receiver. With just two iterations completed in the proposed receiver, a performance similar to the ideal channel, in terms of BER, is achieved. This represents a substantial decrease in the number of iterations required by the receivers reported in state of the art, which require at least five iterations to achieve a performance similar to the ICI-free condition. ## 8 Conclusions

This article has presented a low computational complexity receiver that achieves both the extraction of frequency diversity, as well as efficient ICI mitigation in V2V communication systems.