# Analytical Framework of CP-Free Multiuser OFDM System for Coordinated Multi-Point at mmWave
## 1 Introduction
### Related Works  
Several studies on signal detection and channel estimation in CP-free OFDM systems and massive multiple-input multiple-output (MIMO) have been reported in the literature. The authors in [13] used single bit analog-to-digital converters (ADCs) for both single-input single-output (SISO) and MIMO systems in frequency selective channel to accurately obtain the maximum likelihood sequence estimation channel equalizer in mmWave massive MIMO (mMIMO) communications. Their observations revealed that the acute nonlinear distortion of single bit ADCs can be successfully nullified using an adequate number of receive antennas. The authors in [14] formulate such a repetitive receiver for an mMIMO system that utilizes Bayesian theory as well as a strategy for the neutralization of parallel intrusion. The consequence of their work proves that the performance of the minimum mean square error (MMSE) signal detection technique was not satisfying in terms of bit error rate (BER) and latency processing performances. The comprehensive study in [15] proposed a system with a virtual carrier using the MIMO-OFDM concept to identify proper the repetition index scheme-oriented subspace  
Figure 1: Dual connectivity of user equipment (UE) with macro eNB and small-cell eNB. channel. Such a study was carried out for the conversion of the white noise into nonwhite noise using the repetition index scheme as well as the conversion of nonwhite noise back to white noise using Cholesky factorization. The numerical simulation shows the superiority of the repetition index scheme-oriented channel identification over other compared methods. Another study in [16] introduced a reservoir computing structure for MIMO-OFDM symbol detection, known as a windowed echo state network (WESN). Their numerical evaluations propose that only a certain number of training symbols can be utilized for the effective reduction of model mismatch and improvement in symbol identification performance by WESN. The authors in [17] proposed two neural networks, one for channel estimation and another one for signal detection. Both the networks are associated with a CP-free OFDM system utilizing a novel artificial intelligence (AI)-supported receiver. Such a receiver provided low complexity and significant robustness over the existing algorithms. In [18], authors explored a model-driven neural network for CP-free MIMO-OFDM data detection. The authors in [19] investigated the linear MMSE channel estimator for CP-free single carrier MIMO (SC-MIMO) under frequency-selective channel and also proposed a new iterative receiver for quantized CP-free uplink wideband SC-MIMO for uncorrelated or correlated Rayleigh and Rician fading channels. In [20], authors proposed a generalized sidelobe canceller equalizer using QR decomposition for CP-Free MIMO-OFDM systems and also reduced the complexity of maximum likelihood detection. Another study [21] proposed a CP-free MIMO generalized frequency division multiplexing system for high data rate transmission in frequency selective fading channels. A brief summary of these works is illustrated in Table 1.  
Despite the limited number of researches and applications, there are many challenges in CP-free multiuser OFDM communication systems. Due to the multiuser interference, the performance of CP-free multiuser OFDM is quite limited. Thus, the CoMP-JT transmission method and complex Hadamard transform (CHT) with block diagonalization (BD) channel precoding are very important. The CHT codes are orthogonal spreading codes whose applications are very much effective in reducing user's interfering signals. It is known from the literature that the Hadamard matrices have been considered as a very promising tool and are applicable in MIMO systems, due to its simple and efficient implementation with the use of fast algorithm [22]. The computational complexity is \(N\log_{2}(N)\) for an \(N\)-point CHT matrix [23]. Besides, BD is a well-known linear precoding scheme that usually provides good performance.