6G Vision and Challenges: Complexity Analysis of M-MIMO Rate-less Based System with Various Pre- Coding Schemes

Due to the expected essential role of the rate-less digital fountain codes and MassiveMulti-Input Multi-Output (M-MIMO) techniques in the 5G and 6G mobile wireless networks, this paper investigates the performance of M-MIMO enhancing system employing the Raptor code. The proposed M-MIMO-Raptor code based system has been tested over the different wireless communications channel conditions with respect to the various Frequency Doppler (FD). The various promising technologies for the beyond 5G and 6G have been presented with focusing on the advanced error control techniques. The flexible adaptive interleaved pre-code based on the channel conditions is suitable for 6G mobile wireless networks which integrates the various environments of the communications. The complexity of the advanced and fixed code rate schemes is discussed. Several computer simulation experiments are carried out for evaluating the performance of M-MIMO-rate-less code system. These experiments prove the superiority of the presented wireless rate-less system compared to the fixed rate wireless system due to the improved results of BER and the throughput values which are utilized as a performance evaluating metrics. Theoretical analysis of the M-MIMO throughput proves the enhancing of M-MIMO utilizing the rateless Raptor code and its applicability for the next mobile wireless networks generations.


Introduction
The mobile wireless communications systems utilize the MIMO to improve its performance and achieve available maximum capacity. On the other hand, the adaptive encoding packet technique is a tool for enhancing the performance of the wireless communications systems. This tool depends on employing the different error control schemes for encoding the transmitted packets with the different code rate according to the channel conditions. The adaptive packet approach can achieve good error performance, optimizing the capacity and low power consumption. Hence, the adaptive packet technique represents the idea of fountain codes, where it provides a variable code rate but with more complexity. The adaptive code rate concept achieves the rate-less code error control schemes. The rate-less fountain code is error control scheme with a variable code rate is applied within the MIMO system for enhancing the performance of the mobile wireless communication systems [1].
In the M-MIMO system, there are several antennas are employed for transmitting and receiving processes for improving the quality of the wireless link and increasing its capacity. The reliability of the wireless systems utilizing the MIMO can be enhanced by the spatial diversity achieve significant capacity gains over conventional single antenna systems. There are many approaches are employed for improving the MIMO system performance such as the OFDM combining within the MIMO to enhance the capacity, employing the error control technique for improving the error performance and interleaving techniques [2][3].
In this research paper, the merging between the classical-fixed code rate error control schemes and the variable code rate fountain code schemes is proposed. Also, the proposed combined error control schemes are performed with the different interleaving techniques.
The rate-less fountain codes are suitable for enhancing the error performance over the realtime signals transmission, these error control schemes are tested with the chaotic interleaving. The chaotic interleaving is an efficient data randomizing tool, it is built and designed based on the 2-D Baker map, the randomizing mechanism is carried out by secret key. This secret key is flexible length, which is determined according to the size of transmitted packets [4].
Therefore, the proposed technique aims to improve the M-MIMO systems error performance and enhance the system security through the different secret keys of the chaotic interleaving, it can be changed for every transmitted packet. Utilizing the erasure error control codes achieves improving the real-time signals quality over the noisy and unreliable fixed and mobile communications channels. On the other hand, the unequal-error protecting techniques leads to enhance the power efficiency of the wireless communication systems due to the automatic adjusting of the code rate based on the communication channels conditions [5].
In this paper, the channel coding schemes overview are presented in section 2. In section 3, related work overview is presented. Section 4 describes the computational complexity of the various FEC techniques. Overview of the promising technologies of next mobile generation are presented in Section 5. The proposed model of rate-less based M-MIMO system is described in section 6. related works and recent Raptor code research are presented. In section 7, the simulation results of the proposed rate-less based M-MIMO system with different error control schemes and interleaving techniques are discussed. Simple throughput analytical analysis with considering the rate less features is presented. The conclusion is presented in section 8.

Channel Coding Techniques Overview
In this section, the different types of the error control schemes are discussed. Also, the computational complexity of the various Forward Error Correction (FEC) techniques has been described for the classical FEC schemes which have fixed code rate and the advanced rate-less FEC schemes which have variable code rate. Figure 1 shows the various error control schemes.  contains two main categories, the block codes and the convolutional codes [6].

-Rate-less Fountain Codes
The advanced FEC schemes are an efficient tool for enhancing the real-time signal transmission quality over the unreliable wireless channel. It can be considered hybrid FEC and embedded adaptive packet techniques [7].

-Automatic Repeat reQuest (ARQ)
The ARQ approach is simpler error control schemes, it depends on received data checking at the receiver by parity check bits or CRC schemes. The ARQ utilizes these techniques for detecting the error only, in case of error detecting, the receiver requests retransmitting the corrupted packet again. This error handling method is not suitable for real-time wireless signal transmission. The rate-less fountain codes includes in its mechanism the ARQ concepts.

-Pseudo Coding techniques
The pseudo coding techniques is lower complex scheme performed by randomizing the processed data. It is an efficient for the image and audio over the correlated fading channels.

-Hybrid Techniques
The hybrid techniques are built based on merging and combining the different techniques. there are different types of hybrid techniques, the simpler [8].

-Adaptive Techniques
The adaptive technique includes the adaptive FEC and adaptive packet approaches.
The adaptive technique achieves the flexibility for choosing the best choice of encoding tool and transmitted packets format based on the wireless link channel condition for enhancing the throughput and error performance. also, the adaptive packet can be employed for reducing the consumed power and decreasing the ARQ times [9].

Related Works Overview
The rate-less error control schemes are considered promising tool for combating the errors and improving the error performance of the next generations of the mobile wireless networks. In this section, the related works of the research papers which are discussed the utilizing of the digital rate-less fountain codes and its advantages in the MIMO and the 5G network.
The digital rate-less fountain code is used for enhancing the performance of the OFDM-based Raptor code utilizing in [10]. In this research paper, the Raptor rate-less code is used with the various modulation techniques to improve the OFDM system error performance. Also, the different types of the digital fountain codes are discussed. The complexity of the rate-less codes compared to the traditional and classic fixed code rate channel coding schemes has been presented [10].
In [11], the near future 5G "Fifth generation" of the mobile wireless network is considered. This research paper discussed the expected eavesdropping threats in 5G mobile wireless network. This threats can be combated by the classical cryptography techniques, these classic approaches are not efficient due to its overhead complexity. The physical-Layer Security (PLS) based is an efficient approach for resisting the eavesdropping over the 5G networks. The PLS-based approach is utilized to achieve improving in the security and error performance of the 5G mobile wireless networks using fountain code within the massive MIMO system. In this research paper, the risks of intruder are reduced using the rate-less raptor code and data punctuation for retrieving the transmitted packets before the attacker. The Raptor code is utilized for enhancing the security and reliability of the massive-MIMO system [12].
In [13], application of the advanced Forward Error Correction (FEC) techniques such as rate-less Raptor codes with the inner LT code and outer LDPC codes are studied and investigated. The first type of fountain codes is the LT code, it is also, the main partition in Raptor codes structures as shown in Figure 2-a. There are various parameters determine the code rate and the decoding algorithm, these parameters are studied for choosing the suitable for Raptor codes with respect to the systematic property and various code rates. Also, the different modulation techniques are utilized with the Raptor codes and code rate variation.
The experiments in this paper revealed that the Raptor code performs better with the BPSK than the QPSK scheme with considering the same code rate and decoding algorithm.
The rate-less Raptor coding technique has been proposed for reducing the interference and protecting the transmitted video signals in [14]. The proposed scheme is evaluated over the multipath and varying conditions communication channels, Raptor code is implemented in this paper by LDPC and LT codes. Also, the rate-less error control schemes are proposed for achieving the reliability and enhancing the efficiency of the mobile wireless 5G communications. The multi-links method has been presented utilizing the rate-less error control technique to improve the wireless link reliability and efficient usage of the network resources [15].
Enhancing the performance of the Wireless Body Area Network (WBAN) is proposed in [16], this paper proposed utilizing Raptor code as an efficient error control scheme. The proposed technique based on the rate less code is used for improving the life time of the network. The WBAN is a Wireless Sensor Network (WSN) specified for the medical applications. Hence, the power source is the main constraint of the WBAN, this research paper enhances the energy efficiency and reliability of this wireless networks by utilizing Raptor code .

Raptor Codes Description
The structures of Raptor code are given in Figure 2-a, It contains two error control schemes are merged for achieving the Raptor code. The process of decoding is shown in  Figure 3 Steps of the Raptor codes Decoding process.

Raptor Coding Process
The encoding process of the rate-less Raptor cod includes two cascaded encoding process utilizing the inner and outer encoder. The coding process stages can be described as follows [17]: The intermediate symbol ( ′ ) is the encoded form of source symbol ( ′ ), it is also, input the second encoding process.
The second step is encoding the k ′ symbols by the inner LT code. for generating the output symbols (O/S), these encoded symbols is denoted by (C), it is expressed by Eq. (3): Notes that:-is the original/ source symbol is the intermediate symbol, encoded ′ and input of inner code, ′ > is the output symbols and encoded ′ , > ′ .

Channel Effects Investigating
In this section, the effects of the wireless communications channel is presented on the transmitted encoded packets. Suppose that the received signal ( ) is expressed by Eq. (4), where, refers to the codeword, and represents the Gaussian noise.
= + The LLR is calculated using the formula of Eq. (5):- where, 2 is the variance of Gaussian noise, ~(0, 2 ), it is the noise of the communication channel, its mean = 0 and the variance equals 2 .

Decoding Process
The decoding processes of the Raptor code are presented in this section. This process contains two decoding steps as previous described in encoding process, which are the inner and outer decoding. The Sum Product Algorithm (SPA) is used for decoding the inner and outer encoded symbol utilizing Tanner graph. The LLR of the received encoded symbol is given in the formula Eq. (6) [18]:- where:-: is the variable Node, its symbols are denoted by (V/S). : is the check nodes ( ), it is the output symbols of the ( ).
Let's, there are one codeword, with the E b /N o , R, hence, its energy can be calculated by :- Raptor codes can be represented by :-Raptor Code (k, C, Ω(ɛ), where, the k is the source symbol, C is the output of outer encoded, and Ω(ɛ), where, C is the pre-code with message length k, n is the block length and Ω(ɛ) is a degree of distribution of LT code, it is determined by ɛ.

Throughput Analysis Utilizing Fountain Codes
The throughput analyzing has been discussed with presence the rate-less fountain codes, in this section. The fountain codes have the positive effects, which are cleared through the simple presented theoretical analysis. The previous section presents the computer simulation experiments and its results. These experiments are carried out using the Zero forcing equalizer, it evaluated the proposed technique over the M-MIMO system with the modulation technique variation [35].
The throughput is important metric for measuring the wireless communications systems performance. It is defined as the amount of corrected data success to received at a time interval. According to the throughput definition, it mathematical expression is given in Eq.

(20) as follows:-
The throughput is affected by the Packet Error Probability (PEP) and the packet length as shown in Eq. (20) [35].
(1 ) The throughput can be expressed also, as in Eq. (21), It can be expressed as follows: The s T symbol is the period, the symbol I is the length of transmitted data, and j p is the probability of failure decoding 1 through j times. It is given in Eq. (22). 1 Decoding failure in the transmission Decoding failure in the transmission BLER where the BLER denotes the block error rate achieved after the jth transmission.
The average packet delay, δ, is the expected time that elapses from the moment the packet is first transmitted over the channel to the moment the packet is successfully decoded. It is given by: The

Computational Complexity of the Various FEC Techniques
The complexity of the error protection systems is the amount of its required operations and its additional memory, logic and arithmetic which are needed for performing the encoding and decoding processes. Therefore, the computational complexity of these systems affects the amount of power consumption and the required time. Also, there are another terms refer to the complexity of the error corrections schemes which are the time complexity, hardware and power complexity. In this section, some simple notes about the complexity parameters of the various error control schemes are presented.
The block codes is represented by this form "Code (n, k, t), where k is the length of data-word 'encoder input' (number of bits in data-word), n is the length of codeword 'encoder output'(number of bits in the codeword)and t refers to the number of correctable error bits which are can be corrected by this code, for example Hamming code (7, 4, 1). On the other hand, the convolutional codes can be represented by "Convolutional code (n, k, K), where, K is the number of shift register in the encoder + 1. It is known as the constraint length, which is the number of inputs 'processed' controls the encoder outputs. The complexity of the bloc and convolutional coding schemes depends on the k, n, t, K and Ω(ɛ) according to the type of this encoder. The computational complexity of various error control schemes depends on some parameters. In general, the complexity of all error control techniques is related to the length of input and output of the encoders. The convolutional codes have complexity higher than the block codes. On the other hand, complexity of the fountain codes depends on its message length and the degree of the distribution [18].
The complexity of the convolutional coding and Turbo coding can be calculated by the formula as given in Eq. ( 12).

Encoder input length length
Encoder input Memory length In Eq. (12), the symbol () Γ refers to the memory length (K-1),The input of encoder is represented by () Φ symbol and the () Ψ is the amount of processed data.
While the complexity of Reed-Solomon coding can be calculated by the mathematical formula in Eq. (13):- In Eq. (13), k symbol refers to the source message symbols and n represents the output of the encoder length.
In Eq. (14), the complexity of Raptor code is given:- The Raptor code complexity is gien in Eq. (14), It gives the needs average number of the operations for decoding k source blocks, while the formula ( [log (1 ] O ε ) gives required process for encoding k [18].

Promising Technologies and Challenges of Next Mobile Generation
As mentioned about the Bluetooth technology in [19], "Bluetooth is considered the engine of the personal wireless communications", the engine of developing the wireless networks to reach the expected vision of 6G is the artificial intelligent and the nano-science and nanotechnology. The promising technologies and the challenges of the next mobile wireless networks are discussed in the following sub-sections.

The promising Technologies of 6G Mobile Wireless Networks
In this section, the different promising technologies for the 5G and 6G mobile wireless are presented with focusing on the error protection scenarios. The advanced digital fountain codes are one of these technologies due to its features compared to the fixed code rate schemes. Also, these rate-less codes have number of advantages such as it is applied within the real-time applications, where it is generated on-line. Also, the truncation of the rate-less codes mechanism can be applied in wireless network. Also, the fountain codes can be suitable for the 5G, 5G beyond and 6G next mobile wireless networks, these networks require high data rate, the rate-less codes reduce the latency due to decreasing the retransmission processes [18]. the 5 G is the next mobile cellular generation networks, the advanced technologies will be utilized for the 5G and the beyond. In [19],  are proposed for 5G mobile wireless network generation, it is utilized for M-MIMO wireless system over the noisy/lossy wireless communications channel [20].
The block codes schemes with the rate-less coding are employed for M-MIMO wireless system, also, concepts of the fixed and rate-less coding techniques are discussed.
The channel path losses/pilot contamination cause data lost, the M-MIMO is proposed for the next mobile/cellular wireless generation, where its spectrum and energy are high efficient. The RSTBC scheme is combined with the M-MIMO for enhancing the reliability of the data transmission over the noisy/mobile channel. the results of the simulation experiments proved that the M-MIMO-RSTBC based system is suitable for the next mobile 5G networks [21].
The Internet of Things (IOT) and Internet of Nano-Things (IONT) can be considered one of the promising technologies for the beyond 5G and 6G fixed/mobile wireless networks also, the rate-less coding schemes are considered one of these promising technologies. In [22], the Analog Fountain Code (AFC) is proposed for encoding the small packets transmission. The optimized parameters of the AFC are determined by analyzing the probability density function (PDF) of the data between the variable Node (VN) and Check Nodes (CN) for the fountain code with respect to the BER according to the SNR of the communication channel [22].
The complexity of the rate-les codes is mainly characterized by the weight set, the source message length and degree distribution function as cleared in Eq. (14). The AFC has linear-complexity encoding and decoding processes in terms of the block length. The code is rate-less in nature and can generate a potentially limitless number of coded symbols; thus, achieving any desired rate on the-fly. The coding and decoding of rate-less code are explained for the Raptor code rate-less scheme which is considered the widely fountain code technique [23].

The promising Technologies of 6G Mobile Wireless Networks
Due to the experts and researchers visions toward the beyond 5G and 6G specifications and capabilities, there are several challenges restricts this vision and requirements. Although, the big difference between 2G mobile/cellular network and the present 4G&4G+ mobile/cellular network, the variation between the next mobile generation (6G) and the present network is not expected, where "the end of cellular starts with the beginning of 6G establishing". On the other hand, the developing of mobile wireless networks will jumping several jumps, every jump represents step and wall in the 6G world.
Really, based on the vision and promising and the expected capabilities of 6G system, it will be considered the new "6G world".
In this section, some of the expected challenges of 6G vision are mentioned, as in the following:--Security:-The back bone of the 6G will be the open environment, with this transmission media and the advances in the DSP and software the security risks and threats will be increased. Hence, the security tools must be developed to be more effective and efficient. The AI is the main key in the data analysis for discovering the original and false data. Also, the AI can be employed to generate smart data can resist and detect any attacker by intelligent encryption technique not the traditional encryption tools.

Rate-less Fountain Code based M-MIMO System
In this section, the expected technology which is recommended for the 5G and beyond 5G

The Proposed Model Description
The model starts with the original signal preparation step and generating the binary version. the second step is data packetizing and segmenting. After the CRC encoding, the convolutional encoding with the various constraint length (K= shift registers in the encoder+1) is performing on the input packet-by packet. The next step is executing the Raptor code mechanism by the LT code. The packet randomizing process is performed by the different techniques, no-int., block int., zigzag int. and chaotic int. The interleaved encoded packets and its images are modulated by QPSK modulation. The modulatedinterleaved encoded packets are transformed form serial top parallel (S/P) for performing the IFFT transforming. After the transforming, the output is equalized by Zero Forcing Equalizer (ZFE) or MMSE Equalizer. the parallel to serial (P/S) process is performed and followed by the D/A conversion. The wireless communications channel is utilized for transmitting the data is simulated by Jake's model.

Description of M-MIMO System
In this section, the M-MIMO system contents and its constructions have been discussed, also, the setting of the MIMO which is utilized in the computer simulation is presented. In Figure 6, the M-MIMO and the expected promising LIS technology are given.
In Figure 8, the simple block diagram of the M-MIMO contents are given, as shown in this figure, the number of antennas at the transmitting side is denoted by (Nt), it can be expressed as a matrix contains one column as in Eq. (15). In the other side the number of antennas at the receiver are represented by (Nr) and expressed as a matrix contains one column [30].
The SNR of the MIMO channel is expressed as given in Eq. (18), hence the capacity of the system (C) can be calculated by the formula in Eq. (19) [31].
The M-MIMO system capacity (C) is used as metric for evaluating the proposed rate-

Spatial Diversity and Multiplexing
The spatial diversity and spatial multiplexing are considered in this section. These Hence, suppose, MIMO system have (Nt) and (Nr), the system capacity increases with min (Nt, Nr) [33].

Simulation Experiments and Results
In  interleaving is applied in the system. Using the same simulation parameters described in Table I.  It is clear that the proposed system has a BER reduction using QPSK modulation. The simulations also evaluate the Throughput Vs SNR & FD for Raptor with QPSK for different interleaving techniques. This experiment is repeated also over AWGN and different fading channels. The proposed system is able to receive any changes occur in the channel.   5, 8.25, 9, 9.75 dB respectively for FD=0 Hz. Figure 9, also, shows the results of the first experiment with the FD=100 Hz, the MMSE with and without diversity are almost congruent to give BER = 1e-5 at SNR=7. 5

Conclusions
The promising technologies of 5G and 6G mobile wireless networks are discussed in this paper with focusing on the advanced error protection techniques. Signals transmission over various environments is the main challenge in the 6G generation, due to the 6G will integrate the terrestrial, space, underwater and mountains environments. In this research paper, the flexible adaptive interleaved rate-less coding technique based on the channel conditions is proposed for the beyond 5G and 6 G wireless networks generations. The M-MIMo Raptor code based system is presented for improving the error performance and throughput enhancing utilizing the interleaving techniques. The proposed system improves the BER and the throughput. The performance of the proposed Raptor code based M-MIMO system with the convolutional codes (1, 2, 6) and the chaotic interleaving over a multipath fading channel is better than the traditional system with respect to the MMSE equalization.
The experiments prove the superiority of the presented wireless rate-less system compared to the fixed rate wireless system due to the improved results of BER and the throughput values which are utilized as a performance evaluating metrics. Theoretical analysis of the M-MIMO throughput proves the enhancing of M-MIMO utilizing the rate-less Raptor code and its applicability for the next mobile wireless networks generations.
-No conflict of interest exists.
Authors wish to confirm that there are no known conflicts of interest associated with this publication and there has been no significant financial support for this work that could have influenced its outcome.
Also, they confirm that there is no funding was received for this work.
-Data Availability: The data associated with a paper and support the findings of research work are available from the corresponding author upon reasonable request. Figure 1 Channel coding techniques categories with respect to the code rate.  Steps of the Raptor codes Decoding process.

Figure 4
Raptor code block diagram for estimating the symbols with MMSE. Adaptive rate-less Raptor codes for 6G wireless mobile networks, a-Adaptive Pre-code based on channel conditions, b-Adaptive Interleaved Pre-code based on the wireless link. Figure 6 Promising 6G technologies, a-Simple M-MIMO example , b-The LIS system for smart wireless environment.