# Linear Approximation Signal Detection Scheme in MIMO-OFDM Systems
## 1 Introduction  
Multiple input multiple output-orthogonal frequency division multiplexing (MIMO-OFDM) system, which is a combination of the MIMO and OFDM, is a core technology for high speed mobile communication systems. The MIMO systems provide a high channel capacity and high data rate, without additional bandwidth and high transmit power when compared to single input-single output (SISO) systems [1; 2]. However, received signal is a mixed form of the several distorted transmit signals that go through the fading channel. At the receiver, maximum likelihood (ML) detection has optimal error performance [3; 4]. The ML calculates the squared Euclidean distance (SED) between the received signals and all of the reference signals in the constellation. However, the ML cannot be implemented in the huge MIMO-OFDM system due to very high complexity. Unlike the ML, the zero-forcing (ZF), which is popular for linear detection can be implemented easily in the huge MIMO-OFDM system [5; 6; 7; 8]. Also, ZF based decision fusion schemes have been studied for low complexity in huge MIMO systems [9; 10]. However, the error performance for the linear detection scheme is poor as the number of transmit antennas increases and its error performance is not acceptable in real-time systems. The decision feedback equalizer (DFE) and QR decomposition-\(M\) algorithm (QRD-\(M\)), which are nonlinear detection schemes, have higher error performance than the linear detection schemes [11; 12; 13; 14; 15; 16; 17; 18]. Among several nonlinear detection schemes, the DFE and the QRD-\(M\) use QR receiver for low complexity. However, the complexity for the nonlinear detection scheme increases exponentially as the number of transmit antennas increases, and these algorithms cannotbe implemented in the huge MIMO-OFDM systems. Specifically, the complexity for the QRD-\(M\) increases exponentially when the modulation order is high, due to tree structures. In [19; 20; 21; 22], many detection algorithms were developed to reduce the complexity for tree search algorithms. In [19; 20; 21], the proposed algorithms are based on sphere decoding (SD) and \(K\)-best decoding. These algorithms have a very lower complexity than the conventional detection scheme and the ML, with similar error performance. Specifically, [19; 20] represented complexities as the average number of metric operations at all layers with respect to signal-to-noise ratio (SNR). Also, the average number of metric operations is decreased very sharply according to increased SNR. However, the number of metric operations converges to certain point and the decrease of the complexity is limited although the value of SNR goes to infinity. Also, [22] proposed the semidefinite relaxation (SDR) based scheme. However, the complexity order is still high to use in the huge MIMO-OFDM system.  
In this paper, linearly approximate signal detection scheme is proposed for easy implementation in the huge MIMO-OFDM system. The proposed scheme is composed of three stages. The first stage is partial ZF, which is a core scheme to reduce the whole complexity for the proposed algorithm. The purpose of the partial ZF is that it divides one \(N\times N\) MIMO-OFDM system into several \(2\times 2\) MIMO-OFDM systems. After the partial ZF, the number of \(2\times 2\) MIMO-OFDM systems is \(N/2\). The second and the third stages are DFE and QRD-\(M\) to increase the error performance because noise power may be increased in the partial ZF. Also, the DFE and the QRD-\(M\) are applied to \(2\times 2\) MIMO-OFDM systems, and it does not require high complexity. Due to the partial ZF, the whole complexity for the proposed algorithm increases linearly according to the increased number of transmit antennas.