# Evaluating the Performance of Quasi and Rotated Quasi OSTBC System with Advanced Detection Techniques for 5G and IoT Applications

## Introduction

Wireless Internet, cellular video, e-mail, etc. requires tremendous speed. For such high-speed applications, wireless networks have become the promising field of modern engineering. High data rates and capacity requirement for long-term evolution (LTE) and 5G networks are still a challenging task for researchers due to severe restriction in the wireless communication channels. These restrictions are caused due to an enormous number of users getting access to the network. This results in interuser interference and intersymbol interference. Use of additional nodes between base stations and mobile users to decrease the path loss further leads to additional interference known as intermodal interference. The challenge for researchers is to resolve these issues to get smooth communication between base station and users. Thus, researchers are involved in solving various problems arising in a communication channel like multipropagation fading, intersymbol interference, and distortion of one’s own signal.

In spatial multiplexing, the signal is transmitted in such a way that a receiver receives numerous copies of an original signal in three dimensions viz space, frequency, and time. Thus, it increases the number of paths between transmitter and receiver and probability that two or more paths will experience the fade at same time. If some path is experiencing a fade, a signal can be switched to another route. This increases the spatial diversity gain and reduces multipath fading. If a multiple input multiple output (MIMO) system is using N, and N_{r} transmit and receive antennas, respectively, the total number of independent fading links available will be N,N_{r}. The spatial multiplexing gain thus means a linear increase in data rate.

To approach the need of a MIMO wireless channel system is to exploit space-time coding, constructed with multiple antennas at the transmitter side. This system provides an efficient technique for utilizing the diversity provided by the time and space for fading suppression purpose increasing capacity, data rate, and spectral efficiency. However, it is not simple to implement because complexity rises in an exponential manner by incrementing the antenna elements either at the transmitting or receiving end.

MIMO schemes are mainly divided into spatial multiplexing, spatial diversity, and beamforming. Beamforming technique is related to the concept of the smart antenna. Spatial multiplexing schemes gain data bit transmission speed due to parallel transmission and are used to get the high data rate, although spatial diversity technique decreases the signal fading effect by reducing BER. It is clear from the above discussion that it is impossible to achieve both the benefits simultaneously. This is done with the help of two-dimension coding, that is, in space and time domain proposed by (Tarokh et al. 1998) to generate core relation between the signals achieved from numerous transmitting antennas at different time slots called space- time codes. Basically, space-time codes are classified as space-time block codes and space-time trellis codes, and in this chapter, essential emphasis is on orthogonal space-time block codes (OSTBC).

Space-time block codes are the orthogonal codes, that is, columns from the channel matrix are orthogonal to each other with a simple and optimal linear decoding scheme at the front end. The only standard STBC that can achieve full transmission rate and full diversity was introduced by (Alamouti 1998). In this phenomenon, two antennas are deployed at the back end of system. Further. Alamouti space-time block codes (STBC) are modified by employing more antennas at the transmitter side, but achieving 100% diversity and code rate becomes too difficult. Tarokh et al. (1999) proved that using the calculations and examples of the set of STBCs with more than two transmit antenna cannot achieve rate 1 code; it can be a maximum of * ^{3}A.* In order to obtain the 100% diversity gain, Jafarkhani (2001) brought in a generalized method known as quasi orthogonal space-time block code (QOSTBC) arrangement utilizing four antennas at the transmitting side, by pairing symbols. But the limitation of this pairing was that the matrix columns at the transmitter end did not follow the orthogonality principle, hence full diversity was not achieved. Most of the literature so far has not been able to achieve the full diversity, while selecting the symbols from the same constellation phases using various phase modulations. Thus, we have to rotate the symbols using various rotation factors to minimize the hamming distance in both spatial and temporal domain. These rotation-based codes are termed as rotated Q-OSTBC (Ahmadi, Talebi, and Shahabinejad 2014).

Typically, it was realized that a new scheme known as maximum-likelihood (ML) technique can be implemented to decode these codes, giving superior performance among all conventional decoders (Alabed, Paredes, and Gershman 2011). This chapter first reviews the realization of different STBC MIMO systems with ML detector with respect to BER and SNR. Alamouti (1998) generated complex orthogonal codes for two antennas at transmitter employing a ML detection algorithm at the receiver. The simplicity is due to the orthogonal codes. Similarly, it was performed with higher-order STBCs for more than two transmit antennas, and the literature suggests that computational complexity of the decoding algorithm rises at 4G and 5G modulation schemes like 256 QAM ,1024 QAM. and OQAM for newly generated codewords. Finally, some different decoding methods have been proposed to reduce the complexity.

An alternative approach was proposed (Wolniansky et al. 1998) by employing the V-BLAST algorithm at the receiver. It is a simple detection technique to exploit the spectral efficiency and capacity of the next generation wireless system using a well- defined antenna system employed at back and front end. Spectral efficiency close to 40 bits/sec/Hz in space research centers with interference suppression and successive interference cancellation techniques are achieved using this algorithm. Foschini (1996) proposed a Diagonal Bell Laboratories Layered Space-Time architecture specified as D-BLAST. This further enhances the capacity and information rate. This architecture provides the benchmark for MIMO wireless communications. V-BLAST architecture is the simplest version designed to reduce the computational complexity inherently occurring in D-BLAST systems. Practical implementation of this architecture in MIMO wireless systems can achieve spectral efficiencies more than 40 bits/sec/Hz. V-BLAST finds practical application in MIMO systems because of its immense spectral efficiency, simplicity, and ease to implement on any test bed or VLSI kits. In V-BLAST algorithm researchers introduced numerous concepts based on coding theory and system model to design the BLAST system. This included space-time block coding. There is ordered successive interference cancellation (OSIC) and many decoding schemes used at receivers such as ML decoding (Azzam and Ayanoglu 2009). This process involves much improved performance for V- BLAST systems. Two important receiver decoding steps based on detecting and decoding of symbols is performed in a layered way successively. To avoid the interference and to nullify it, researchers introduce successive interference cancellation mechanism at the receiver site.

This chapter mainly focuses on decoding algorithm based on sphere decoder, also termed the Fincke-Pohst algorithm, proposed by Pohst and later advanced by Fincke