Space time block coding is a method which is used in wireless communication in which multiple copies of data stream are transmitted through multiple antennas and to improve the reliability of the data transfer, the various received versions of the data are accomplished. The transmitted signal withstand refraction, scattering and reflection which traversing through difficult environment and then again corrupted by noise such as thermal noise so at the end some received copies of the data will be better than the others. This prolixity results in a higher chance of being able to use one or more of the received copies helpful in decoding the received signal. The Space time coding combines all the copies of the received signal in a most helpful way to extract as much information from each of them as possible.
For an OSTBC with NT transmit antennas, transmitting M complex symbols in L channel uses or time instants, the ST codewords are
Where Ck are complex symbols and rk are real symbols.
Table 3 describes [32, 33, 34, 35, 36, 37] the space time block codes study for different environments. In the study of Spectral efficiency Continuous Phase Modulation (CPM) [38] is introduced as STBCCPM gives advantage of spectral and power efficiency, both at the same time. In, this Quasi Orthogonal STBC is introduced, which provides spectral efficiency increment of 0.5 bits/s/Hz compared to the traditional Orthogonal STBC.
Another scheme i.e. Quasi Orthogonal STBC included with Minimum decoding complexity [MDCQOSTBC] [38] provides the distribution of power between the antennas in an even manner and change scalability for different transmit antennas is good and outperforms in terms of performance of decoding compared to traditional schemes. The enlargement of QOSTBC is used for improving the power scaling with 4 transmit antennas and single receive antenna and SNR Vs throughput is done using ML decoding and parameters are Alamouti code, QOSTBC and proposed code [39] while initially done for 2 transmit antennas to reduce the peak to minimum power ratio (PMPR) and guarantees full diversity. Simulation is done to analyze the performance of STBC for wireless communication [40] and with no extra processing, it outperforms for multiple transmit antennas considering Rayleigh fading channel along with Maximum Likelihood decoding.
Cooperative Diversity is a very important technique nowadays to improve the system capacity and to handle fading efficiently so that the area to provide the services will increase [41, 42, 43] Cooperative Relaying System (CRS) is proposed with STBCNOMA. With using STBC i.e. CRSNOMA the results in terms of performance gain degrades and placing relay between the transmitter and receiver improves the performance and power allocation scheme is proposed which is suboptimal. Similarly, Cooperative Spectrum sharing is required [44] so a cooperative spectrum sharing algorithm is designed in two phase and the results show improvement both in ergodic capacity and outage performance than the traditional scheme. Somehow, capacity of mobile link can be analyzed in a channel, say Rayleigh fading channel [45] coherence interval is computed according to the number of transmit antenna if the receiver know the propagation coefficients. SNR values range from 0,6,12 dB and a single transmitter and receiver antenna is used.
A new scheme proposed for Square STBC [46] in this there is no knowledge of CSI on the transmitter and receiver. This provides less error probability and complexity compared to already existing differential unitary STBC. Other than Conventional Differential STBC, Non constant modulus constellation i.e. QAM is proposed which provides improvement in SNR gain and SER in comparison to conventional Differential STBC using transmitter antenna 2 or 4 and receive antenna is 1 in number and two constellations are considered i.e. 16PSK and 16QAM. Differential STBC can also be proposed with non constant modulus constellation [47] with a lot of advantages over conventional differential STBC in terms of gain, SNR, SER performance.
4.1 STBC with MIMO
STBC MIMO system with Orthogonal Frequency Division Multiplexing (OFDM) is investigated to get reduced Peak to average power ratio (PAPR) [48] using Selective Mapping (SLM) Technique which provides improved PAPR as compared to other scheme like partial transmit sequence (PTS) and the overall BER performance is improved. STBC can also be used with massive MIMO [49] and large MIMO systems [50] also and analysis is done in broadcasting with coherence interval which is limited in nature and different Orthogonal STBC are compared in terms of outage capacity. In [50], a technique is proposed in which by properly using Orthogonal STBC that are small in dimension and null space is used to derive a decoder so that at last analysis are done to receive SNR and Symbol error rate(SER) is also extracted.
Till now, each analysis gives ergodic capacity and outage performance dependency but still there is still a scope of independency [51], a closed form approximation is simply done for many fading channels i.e. Rayleigh, Ricean, Nakagami, Weibull etc and it is also useful for MIMO and shows that the ergodic and outage capacities does not depend upon a number of transmit antennas and channel parameters if high number of antennas are considered. Non Orthogonal Amplify and forward (NAF) MIMO technique is proposed [52] but for half duplex and all the relays here are employed with a multiple number of antennas and provides full diversity.
Table 3
Some Protocols made along with assumptions − 3
Paper

Evaluation Tool

Number of antennas

MUD

Key Assumptions

Result
Parameters

Vahid[32], 1999

Simulation

N

Maximum Likelihood

Rayleigh/Ricean

Transmission
Rate

Sumeet[33],
2000

Analysis

M Rx
> 1 Tx

Maximum Likelihood

Rayleigh

Spectral
Efficiency

Mathias[34], 2001

Analysis + Simulation

2Tx


Rayleigh/Multipath

Closed loop
power control

Hao[35],2005

Analysis

N Tx
M Rx

Maximum Likelihood

Rayleigh/Ricean/
Nakagami

Capacity and
Error probability

Mandana[36],
2015

Simulation + Analysis

2 Tx

Maximum Likelihood

Rayleigh

Bit error rate

Kazuyuki[37],
2017

Simulation

2 and 4 Tx

CPM

Rayleigh

Spectral Efficiency

In the presence of relay assisted MIMO, the performance of STBC along with Vertical bell labs layered space time (VBLAST) in which all the sequences are transmitted from different antennas, Multi layered STBC (MLSTBC) and Hybrid STBC VBLAST that combines the features of STBC along with VBLAST [53] and their capacities are compared. The results show MLSTBC display higher at low SNR(10 to 15 dB) and Hybrid STBC VBLAST indicates significant improvement in capacity and gain as compared to rest at high SNR (above 15dB).
By using the proposed algorithm [54], 2M diversity order can be achieved with two transmit and over two receive antennas, and Rayleigh fading is used SNR Vs BER. Another algorithm for interference cancellation based on Bayesian analysis [55] having two antennas each at transmitter and receiver, the results does not vary as [56, 57] using 4 transmit and receive antennas and in another one using two transmit antennas and constellation used are QPSK, 16QAM and 256 QAM but in this prediction of the performance is possible of decoding algorithms according to SNR w.r.t BER.
4.2 Alamouti Code
The Generalization of Alamouti [58] scheme assumes Rayleigh fading for two transmit antennas and ML decoding providing full rate and full transmit diversity and maximum rate is achieved for real constellation (PAM) and inferior rate for complex constellation (QAM, PSK) for many transmit antennas.
An approach is proposed for improving the code efficiency [59] for high data rates and increasing the spectral efficiency, also assuming ML decoding. Conventionally, two transmit antennas are used in Alamouti but a case is specified in which 4 transmit antennas and single receive antenna is considered [60] and performance is compared with conventional Alamouti code so, there is performance gain in proposed code as compared to the previous one using Rayleigh fading.
There are so many newly developed algorithms, one of them is Alamouti BLAST for multiuser detection [61] for decoding of single user and multi user Quasi orthogonal STBC and with ML decoding full diversity at transmitter and receiver is achieved [62] i.e. NM where N is number of transmit antennas and M is number of receive antennas and as the number of receive antennas increases, it certainly degrade the bit error rate and subsequently the diversity gain improves in Alamouti space time codes [63]. Orthogonal STBC that allows linearization of transceiver signal is a very well known case of alamouti code [64]. The sum rates for NOMA can be improved for two point system [65] by using superposition coding mainly coordinated superposition coding (CSC) and for providing better rate of transmission to the users present at the edges of the cell, alamouti code are included with CSC.
4.2.1 Alamouti code with STBC and MIMO
The best known Space time block code is Golden STBC [66], frequency selective channels are used and performing Golden STBC with OFDM and without OFDM is compared and it is analyzed that the Golden STBC with OFDM provides low Peak to average power ratio (PAPR) as compared to Alamouti code with OFDM.
Table 4
Result of Shobhit[66], SNR Vs BER
Parameters

Antennas

Constellation used

Result

Alamouti STBC & Golden STBC

2 Tx and 1 Rx

16 PSK

2.5 dB

Golden STBC with and without OFDM

2 Tx and 2 Rx

QPSK

3 dB

Alamouti STBCOFDM and Golden STBC  OFDM

2 Tx and 2 Rx

16 PSK

5 dB

There are Double STBC OFDM system proposed in [67] and for this system MIMO ML decoding is combined with Decision feedback equalization (DFE) and this proposed scheme shows improvement in performance compared to conventional MIMO detector. However, Rather than Rayleigh or frequency selective channel it uses Nakagamim fading channel [68] and it shows that the diversity order of the system just doubles if downlink NOMA with Alamouti code is used in Nakagamim environment and error performance analysis in Nakagamim is done [69] of Alamouti and Coordinated interleaved orthogonal design (CIOD) STBC, a closed form approximate formula is derived to evaluate the coding gain and diversity order.
However, if there is need to use omnidirectional codes in Massive MIMO, then two types of omnidirectional codes are proposed [70] i.e. precoded alamouti code and other one is Quasi Orthogonal STBC. The complexity of decoding i.e. ML decoding is more in precoded QOSTBC with a diversity order of 4 whereas precoded Alamouti code provides diversity order of 2 with no complexity issue and even fast decoding.
The Alamouti scheme initially with 4 transmit antennas is used but if there are more than 4 antennas [71] then without sacrificing much gain, it can be achieved but here Zero forcing, MMSE and ML decoding techniques are compared for 2 and 4 transmit antenna alamouti code. MMSE shows little improvement as compared to ZF whereas ML outperforms both the schemes.
Equalization in Alamouti STBC is done [72] but in conventional case it can be done if the number of receive antennas is equal to the number of transmit antennas but in practical case Widely Linear (WL) equalizer is designed which shows an improvement in gain compared to the conventional one.