Evaluating the Efficiency of Non-Orthogonal MU-MIMO Methods in Smart Cities Technologies & 5G Communication

Abstract

Many cutting-edge technologies, such as MIMO, cognitive radio, multi-carrier modulation, and network coding, have been proposed for wireless communication to satisfy needs for a higher data rate in the upcoming time, leading to improved quality of service (QoS) regardless of the weather. Orthogonal and non-orthogonal multiple access techniques are two categories into which multiple access technologies can be subdivided. Large networking with effective implementation of wireless devices is supported by non-orthogonal multiple access techniques. Massive NOMA has been implemented to advance access efficiency by permitting several users to share a similar spectrum. Because of the robust co-channel interference between mobile users presented by NOMA, it offers important tasks for system model and resources management. In this study, two additional sets of demanding codes are explored. Multi-user shared access methods and expanded multi-user shared access (EMUSA) methods are both employed. In the MUSA technique, an algorithm is used for the allocation of resources to achieve minimum intercorrelation to the maximum extent in 5G networks. A novel idea proposed in this paper is to create complex codes starting from PN codes (i.e., ePN), thereby achieving promising results in the overall system performance. The first part of this paper describes the fundamental principles of MUSA, and in the next part the main idea of the proposed technique will be studied in detail. Using Monte-Carlo MATLAB simulation, the performance of the suggested approach is assessed in terms of BER vs. SNR. The efficiency of the proposed approach is evaluated in various settings, and the outcomes are contrasted with those of the traditional CDMA technique, using parameters, such as the number of active users and antennas at the receiver.

1. Introduction

The major challenge of future communication networks is to handle the gigantic data traffic that is expected in near future and very low latencies of the order of ns [1,2]. This is due to both the fast-expanding user base that contributes to data traffic and the ongoing development of multimedia online apps. One more important parameter of any communication network is to maintain a very good quality of service (QoS) flexibility to future requirements. To meet the above-mentioned requirements along with higher spectral efficiency, NOMA is a promising technique in future communication networks, and this is also one of the new 5G standards [3,4]. As mentioned earlier, there are two types of multiple access techniques: (1) OMA and (2) NOMA.

An orthogonal multiple access technique presupposes that all of the signals arriving from various users are orthogonal to one another in terms of both time and frequency as well as code. In comparison to orthogonal multiple access, which utilizes the frequency or time domains, non-orthogonal multiple access employs the code or power domain. WCDMA, TDMA, and FDMA are the other categories into which multiple access technologies can be subdivided. This leads to a perfect receiver where all the unwanted noise signals are separated from the desired signals [5]. The orthogonality is more effective when the communication network is under load, i.e., more block resources are available than there are active users [6]. OFDMA, CDMA, FDMA, and TDMA are a few of the OMA techniques that are frequently employed in communication networks. In OMA techniques single users can be accommodated using the same time or frequency response to reduce inter-user interface (IUI). Moreover, OMA techniques offer satisfactory levels of IUI under normal standards [7].

By multiplexing all the codes or domains to reduce IUI, NOMA, in contrast to OMA, permits several users within the identical cell, within the identical time or frequency response block. The multiplexing in the code domain that is unique to each user is made possible by the spreading sequence employed in code domain NOMA techniques [8]. Some of the code domain NOMA techniques are my IDMA, sequence-based CDMA, and low-density signature (LDS). Some other techniques are diligently linked to NOMA are pattern division multiple access (PDMA), RSMA, MUSA SCMA, and LPMA.

Using the simple design of the receiver orthogonal multiplexing offers moderate performance in terms of throughputs in packet-based networks. To achieve better efficiency, more capacity improvement in future network design is required using non-orthogonal multiplexing. Furthermore, it should be emphasized NOMA composed with OMA achieves more capacity, but NOMA offers a better trade-off between system capacity and IUI which are important communication network parameters [9,10,11].

In this paper, the study of uplink performance is carried out which uses the NOMA technique along with MIMO Technology. In the uplink of the MUSA technique, the complex spreading sequence is used to spread the symbol of each user before transmission. For each sent symbol, a spreading sequence will be chosen at random by all users from a pool of spreading sequences. When utilized in conjunction with SIC at the receiver to attain low cross connection, the spread sequences are of a short length and more effective. In [12], the comparison of two NOMA techniques viz. SCMA and PDMA are presented in terms of SNR and BER. It can be concluded at this point that, the SCMA performs well than MUSA & PDMA due to the optimal design of code blocks [13]. In [14], when QPSK modulation and coding rates are utilized at the receiver, it is analyzed how spreading codes with pseudo-random noise (PN) codes function over time. Further, when LTE’s block error rate (BLER) is compared with that of one of the NOMA techniques, MUSA, it is discovered that there is no performance degradation. On the transmitting end, simple antennas, and on the receiving end numerous antennas are considered for this proposed work, which results in MIMO technology [15,16]. Instead of direct communication from source to destination, a relay is introduced between source and destination, i.e., decode-and-forward (DF) method for better coverage in a shared environment of the communication network. Two new sets of complex spread codes are introduced with an algorithm that reduces the interconnection as much as possible. A novel approach to creating complex codes starts from PN codes proposed in this paper and it is also proven that the results are promising. The performance of this novel approach is evaluated in terms of SNR and BER using Monte Carlo MATLAB simulations. It is discovered that there is no performance degradation when comparing the block error rate (BER) of one NOMA approach, MUSA, with LTE.

Two further sets of difficult codes are investigated in this paper. Both enlarged multi-user shared access techniques and multi-user shared access (EMUSA) methods are used. In the MUSA approach, a resource allocation process is employed to achieve the smallest possible intercorrelation in 5G networks. The creation of complex codes starting from PN codes (i.e., ePN) is a unique notion put forward in this study, and it has the potential to provide positive outcomes in terms of system performance. The basic concepts of MUSA are described in the first section of this essay, and the core notion of the suggested approach will be thoroughly examined in the section that follows. The effectiveness of the recommended technique is evaluated using Monte-Carlo MATLAB simulations in terms of BER vs. SNR.

2. Schematic Model of Novel Approach

In this part, we will describe and explain the proposed schematic model of the novel approach briefly.

Take into account a single-cell communication network with a K number of users, one relay, and a single BTS. All the K users are multiplexed using different codes, the number of antennas equipped by K users is denoted Nr, the number of antennas at BTS is given by Nt, and the relay is prepared with Nrr antennas at the receiver along with Ntr antennas at the transmitter [5,17,18,19]. At the relay, the delay and forward (DF) protocol will be used. Additionally, it is assumed that each channel is a Rayleigh fading channel that is identically independent and distributed (i.i.d). Figure 1 below displays the schematic flowchart of the novel method.

The binary data input sequence is passed into LDPC coding at the transmitter before being modulated using BPSK or QPSK methods. The input is then switched from series to parallel before being sent to the IFFT block, parallel to series, and cyclic prefix. Additionally, exact reverse operations are carried out at the receiver to produce the output of the sum-product algorithm (SPA).

2.1. Coding and Decoding Algorithm Using LDPC

In this section, LDPC codes and simplified SPA algorithms are studied which will be used for LDPC decoders.

(a)

LDPC codes

The input sequence of length ‘K’ is converted to a code word of length ‘n’ using some rules in channel codes at channel coding. The code word is a block code with ‘n’ symbols. It is derived from the channel encoder with a block code (n,k) by adding (n-k) redundant algebraically with ‘K’ symbols [6,20,21,22]. The block codes are linear in general and hence reduced complexity in encoding and also have systematic structure. The message symbol ‘K’ remains unchanged in the encoding process and redundant parity check symbols (n-k) are added to message symbols.

The generator matrix G of (k × n) dimension associated with linear block codes is given by

$$G=\left[\begin{array}{c}{g}_0\\ g1\\ g_{k-1}\end{array}\right]$$

(1)

To conclude the encoding procedure, it will be multiplied by the message vector “m”. The message vector is provided by

$$m=\left[m_{0, }{m}_{1, }\dots m_{k-1,}\right]$$

(2)

Then, the code word can be written as

$$c=mG$$

(3)

Therefore, the code word is k base vectors combined linearly in this way gi, i = 0,1,2…, k − 1 and a block code G(n × k), it is given by

$$G=\left[I_k|P_{}\right]$$

(4)

$$c=\left[m|b\right]=m\left[I_k|P_{}\right]$$

(5)

Since an extremely sparse parity check matrix defines LDPC codes, they are linear block codes (i.e., only a small number of ones in respective rows and columns). LDPC codes used in this study have a set number of ones in each row and column. A signal constellation marked by the letters “M” and “vectors” is used to map the code word obtained after LDPC coding.

This study employs binary phase shift keying as

M = (−1, 1)

(6)

Quadrature phase shift keying

M = (1 + I, 1 − I, −1 + I, −1 − i)

(7)

signals are implemented.

(b)

Decoders

The soft decision algorithm used by the decoder is simply SPA, and it takes the probability of each received bit as input. This algorithm changes data iteratively amongst the checking node ‘m’ and varying node ‘n’ using a parity check matrix. The SPA algorithm uses an iteration process, and it is given below.

• Initialize variable notes
• Evaluate variable node ‘n’ and update all incoming messages.
• Variable node updation
• Decision-making from Step 2

The hyperbolic tangent and hyperbolic arc tangent functions are the foundation of the SPA method with good BER performance to estimate the check node update. As a result, out of the four phases in the LDPC decoding technique, the check node update has the highest computing complexity.

This SPA algorithm needs more computations because of the maximum number of multiplications and divisions and hence it is more complex. Therefore, this SPA algorithm is replaced by the simple version of SPA which uses additions and subtractions. This simplified SPA algorithm is used in this paper to decode the data at the receiver.

2.2. OFDM Method

The orthogonal frequency division multiplexing (OFDM) technique is used to transmit the large number of high data rate subcarriers which are closely spaced and also orthogonal with all parallelly. The schematic illustration of the OFDM method is as already displayed in Figure 1.

The input data symbols are complex in nature and represent modulation constellation points. The input symbols are coded using LDPC coding and modulated using QPSK/BPSK. After that, it is converted to parallel data and the IFFT algorithm is applied, which converts from the frequency domain to the time domain.

The OFDM complex signal can be written in the time domain as

$$s_{bb}\left(t\right)={\sum }_{l=0}^{L-1}{s}_l\left(t\right)e^{jl{w}_l}$$

(8)

$${\mathsf{\omega }}_{\mathrm{l}}=2\mathsf{\pi }{f}_l=\frac{2\mathsf{\pi }}{ T_{OFDM}}$$

(9)

f_l = f₀ + Δω

(10)

where f₀ is carrier frequency and Δω sub-carrier spacing.

The shortest subcarrier spacing can be expressed as

$$\omega l+1-\omega l=\Delta \omega =\frac{2\mathsf{\pi }}{ T_{OFDM}}$$

(11)

To avoid the possibility of inter-symbol interference (ISI), a guard interval is appended at the beginning of each OFDM symbol, which is known as a cyclic prefix. The OFDM symbol is filled with a null signal to create a guard interval [23,24,25]. While maintaining the orthogonality of the subcarriers, the length of the symbol is enhanced with T_cp; (i.e., T_OFDM + T_cp).

The output symbol of the OFDM transmitter after transmitting the OFDM symbol on a carrier with frequency f₀ can be expressed as

$$s_{cp}\left(t\right)= \mathrm{Re}\left\{\mathrm{sbb}\left(\mathrm{t}\right)e^{j2\pi f_0}\right\}$$

(12)

At the OFDM receiver, the exact reverse operation is performed, removing the guard interval and switching from serial to parallel, respectively [26]. This stream is used by the FFT technique to convert the signal’s time domain into its frequency domain [27]. The original data symbol is retrieved after using a parallel-to-serial converter.

Multiple Access Technology:

Multiple access approaches are utilized to increase the user’s number at any given time interval while keeping acceptable SINR restrictions.

In order to reduce multi-user interference, perfectly orthogonal signals must be transmitted by all the different users [28,29,30]. Numerous multiple access techniques are used based on their performance in terms of low cross-correlation minimum code length, spectrum spreading efficiency, and system complexity.

Among the best, perfectly orthogonal codes is zero-related Walsh codes, which can be generated easily at higher rates, thereby being best suitable for communication networks with more users [31]. However, the drawback of Walsh codes is they are limited and hence the number of users also will be limited. Another drawback of the Walsh code is non-uniform spectrum spreading.

On the other hand, despite the PN codes’ imperfect orthogonality, they can achieve low intercorrelation with other codes when used with the appropriate latency. The PN codes have the best uniform spreading properties within channel bandwidth (BW). Both Walsh and PN codes are best suitable to achieve better performance in multiple access techniques, but computational complexity is greater at the receiver [32,33,34]. For higher data rate users, channel distortion and fading lead to increased complexity, and to minimize fading and channel distortion, equalization techniques must be used at the receiver, which again leads to higher complexity and cost along with high power consumption [35].

To overcome these drawbacks, CDMA techniques are used. Multiuser shared access (MUSA), one of them, utilises compact spreading codes for complicated values. Cross-correlation is lesser as compared to PN codes with the capacity of supporting more users because of its imaginary component. The MUSA symbols are non-binary and facilitate robust SIC.

Complex spreading codes, such as binary codes, are made up of several different components. L stands for spreading code length, and a maximum of 4L power codes can be produced [36]. For instance, there are 256 potential codes for a length of 4, which is insufficient for large-capacity networks. Therefore, to expand the set, instead of (−1,1), elements of complex spreading codes (1 + i, 1 − i, −1 + i, −1 − i) have been utilized [37,38,39]. That means a total of 9L codes are possible and best suitable for networks with a high number of users. Each component of the sophisticated spreading code is present in this collection and can be used instead of {1, 0, 1}, {2, 1, 0, 1, 2} in situations when there are a lot of users.

In this study, the following codes consider are (−1, −1 − i, −1 + i, −i, 0, i, 1, 1 − i, 1 + i) for implementation.

As illustrated in (13) and (14), one can obtain groups of three orthogonal codes for length 4 and a minimum of 16 spreading codes having low correlation. As illustrated in (15) and (16), respectively, if the length is raised to 8, 7 orthogonal and 32 low correlated codes can be obtained [40].

$$\left[ \begin{array}{ccc}-i& -i& -1+i\\ -i& i& 1-i\\ i& -1+i& -1\\ i& 1-i& 1\end{array}\right]$$

(13)

$$\left[\begin{array}{cccccccccccccccc}-i& -i& -i& -i& -i& -i& -i& -i& -i& -i& i& -i& i& i& i& i\\ -i& -i& i& i& -1+i& -1+i& -1+i& 0& -1-i& -1-i& i& 1+i& 0& -1+i& -1+i& -1+i\\ -i& i& -i& i& 0& 1+i& i& -1+i& -i& -i& -1+i& -1+i& 1-i& i& i& i\\ i& 0& 0& 0& 0& 0& 0& i& -1+i& 1+i& -i& 0& 0& -i& 1-i& -1-i\end{array}\right]$$

(14)

$$\left[\begin{array}{ccccccc}-i& -i& -i& -i& -i& -i& -i\\ -i& -i& -i& i& i& i& i\\ i& -i& i& -i& -i& i& i\\ -i& i& i& -i& i& -i& i\\ -i& i& i& i& -i& i& -i\\ i& -i& i& i& i& -i& -i\\ i& i& -i& -i& i& i& -i\\ i& i& -i& i& -i& -i& i\end{array}\right]$$

(15)

A Novel algorithm for generating Complex spreading codes is shown below.

$$\left[\begin{array}{ccccccccccccccccccccccccc}1& 1& \cdots & 1& 1& 1& 1& 1& 1& 1& 1& 1& 1& 1& 1& i& i& i& 1& 1& 1& 1& 1& 1& 1\\ ⋮& 1& \ddots & ⋮& 1& 1& 1& 1& 1& 1& 1& 1& 1& -i& -i& -i& -i& i& 1& 1& 1& 1& 1& 1& 1\\ 1& 1& \cdots & 1& 1& 1& 1& 1& 1& 1& 1& -i& -i& 1& -i& i& i& i& -i& -i& -i& -i& -i& -i& -i\\ 1& 1& 1& 1& 1& 1& 1& 1& 1& 1& \dots & \dots & i& 1& -i& i& i& i& 1& 1& 1& 1& 1& -i& -i\\ 1& 1& 1& 1& -i& 1& -i& -i& i& i& i& \dots & 1& 1& -i& i& i& i& 1& -i& -i& -i& i& 1& 1\\ 1& 1& -i& -i& 1& i& 1& i& 1& 1& -i& \dots & -i& 1& -i& i& i& -i& i& 1& -i& i& 1& 1& i\\ -i& i& 1& i& 1& 1& i& 1& 1& i& 1& \dots & 1& 1& -i& i& i& -i& -i& -i& -i& -i& 1& 1& 1\\ i& -i& 1& -i& 1& 1& -i& 1& 1& -i& 1& \dots & 1& 1& -i& i& i& 1& i& -i& -i& -i& 1& 1& 1\end{array}\right]$$

(16)

• Decide the length of spread codes based on no. of users
• Define the values set (−1, 0, 1)
• Generate Matrix
• Find out inter-correlation
• Identify zero values
• Generate Matrix which includes all zero correlation
• Finish the matrix using (6)
• Assign codes to different users

The next algorithm for generating pseudo-noise (PN) codes is shown below.

• Decide the degree of polynomial based on users
• Find out the length of polynomial
• Select the generating polynomial
• Establish a matrix that generates PN code
• Create a collection of intricate PN codes with actual and fictitious parts.
• Cross verify inter-correlation
• Assign codes to users.

2.3. Transmission Using Relay

The following Figure 2 shows the proposed relay transmission network. The relay is used to minimize interference among active users by treating them as separate connections. There are two paths if you use a relay, one of the paths is the direct propagation path and the other is the indirect propagation path depending on the relays [41]. The noise present in the channel is thought to be AWGN [42,43,44].

The signal received by the relay path can be written as

$$y_{SR,k}=\sqrt{P}{J}_k{s}_k+n_{SR,k} k=1,2, \dots , K$$

(17)

Then, the receiver signal is given by

$$y_{SD,k={\sum }_{k=1}^{k=K}\surd \mathrm{P}{H}_{k }{S}_k+n_{SD,k} }$$

(18)

where P—transmitted signal power

s_k—spread MUSA signal

n_SD,—gaussian noise vector

H_k—channel matrix

The received signal from the relay station computed as,

$$y_{RD=}{\sum }_{k=1}^K\surd {\tilde{P}}_r{F}_k y_{SR,k} +n_{RD,k}$$

(19)

P + Pr = 1

(20)

where P_r—transmitted power from relay

F_k—channel matrix

n_RD,—gaussian noise vector

At the BTS, to recover the original signal from two synchronous signals, the maximum ratio combining is used. Then, the output of MRC is given by

$$\mathrm{y} ={ \mathsf{\alpha }}_1{y}_{SD}+{\mathsf{\alpha }}_2{y}_{RD}$$

(21)

The channel coefficients α1 and α2 are given by

$${\mathsf{\alpha }}_1=\frac{\sqrt{P{H}_k^{*}}}{{\mathsf{\sigma }}_{SD,k}}$$

(22)

$${\mathsf{\alpha }}_2=\frac{\sqrt{P_r{F}_k^{*}}}{{\mathsf{\sigma }}_{SD,k}^2}$$

(23)

3. Simulation Outputs

In this part, the performance results achieved by the proposed novel technology are discussed in detail. To obtain a higher degree of confidence in the simulation outputs, extensive simulations have been carried out using MATLAB along with Monte Carlo simulations.

Table 1. Simulation Parameters.

Parameter	Technique	Value
Channel Coding	LDPC	1/2
Modulation	QPSK	-
Channel	Rayleigh	-
FFT size	-	64
Number of Data Subcarriers	-	52
	Walsh	64 Length
Multiple Access	PN	64 Length
	MUSA	8 Length
Signal to Noise Ratio	-	1–20 dB
Number of Users	-	12,16
User Overload	-	150%,200%
MIMO configurations	-	(1 × 6 × 30)
(Nt × N rr × Nr)	-	(1 × 30 × 30)
Detectors	MMSE	-

provides an overview of the simulation parameters.

The performance of massive MIMO networks in uplink using Walsh codes, PSN codes, and also with Complex spreading codes [45]. The performance of MIMO networks of configuration (1 × 26 × 30) (1 × 30 × 30) at relay using QPSK modulation technique in a channel with Rayleigh fading and Walsh codes of length 64 is shown in Figure 3.

From Figure 3, it is evident that BER is decreased when the users are fewer because of the sharing of resources. Moreover, the performance of the memo networks is enhanced by the special diversity for reliable communication [46].

The simulation results of MIMO networks when the PN codes of length 63 are used are shown in Figure 4. It can be observed the performance is degraded when pin codes are used because they are not perfectly orthogonal. However, PN codes can offer superior spectrum spreading [47]. Therefore, the optimal decision should be taken taking BER values and receiver complexity into account.

Table 2. BER vs SNR for Walsh and PN spreading codes for SNR = 12 dB.

	(1 × 26 × 30) K = 12	(1 × 30 × 30) K = 12	(1 × 26 × 30) K = 16	(1 × 30 × 30) K = 16
Walsh	0.0006593	0.0001083	0.004657	0.001864
PN	0.001593	0.0005998	0.006406	0.00559

presents simulation results when Walsh codes and PN codes are used in MIMO networks for SNR = 12 dB.

In the simulation of MUSA technology, the considered code length is 8 and there are 32 codes with low correlation parameters from Equation (16). The MUSA set and 25 codes in ascending order from the matrix provided by (16) with low correlation are selected from the set. The remaining seven codes are replaced by zero cross-correlation codes.

It is possible to demonstrate the EMUSA sets, as predicted, had a lesser BER than the MUSA set at the identical SNR, with the improvements becoming further pronounced as the SNR rose. As opposed to that, the system rate improved fourfold, resulting in higher spectrum occupancy and more receiver complexity. Therefore, a trade-off between processing complexity and necessary performance levels must be negotiated, based on the application.

It can be observed that BER values decrease with SNR and low BER values, i.e., best performance results are obtained using MUSA technology.

We attempted to compare our findings with the equivalent model in the published literature in order to assess the effectiveness of the current strategy. Therefore, at the receiver, utilizing an MMSE-SIC detector and distinct quantities of antennas at the receiver and transmitter, the authors of [48] acquired numerous outcomes in somewhat equivalent circumstances to our approach, but with our configuration, we achieved BER less than 103 in all configurations. In contrast, the authors’ setup achieved an estimated rate for BER of 5102 for SNR, for 12 dB. The findings were somewhat superior to MUSA but inferior to MUSA0 in [45], where the authors estimated the value of BER to be 104 at an SNR of 12 dB.

4. Conclusions and Future Scope

The performance of large MIMO is examined in this research. Networks in the uplink direction along with the relay are studied when LDPC coding and complex spreading codes of MUSA, MUSA0, EMUSA, and EMUSA0 are used.

Hence, 32 codes with low correlation are chosen for the MUSA collection. Additionally, for MUSA0, seven‘ codes with zero cross-correlation and the top 25 codes are chosen in increasing order of their intercorrelation. The results are noted when QPSK modulation and Rayleigh fading channel are used for a MIMO network with a configuration (1 × 26 × 30) and (1 × 30 × 30) and 26, 30 antennas at the relay [49].

Walsh and PN codes that are more traditional are contrasted with the performance outcomes of the MUSA approach. The number of antennas to be employed at the relay and the receiver at the destination is also studied. Out of the available options, the best choice is selected considering BER, spectral behavior, and receiver complexity.

The study also includes complex spreading codes (ePN), which are produced from PN spreading codes. Promising results are achieved in terms of very low BER values, lower number of antennas, as well as reduced overall system cost. In the future, the implementation of more relays in massive MIMO networks between source and destination should be investigated when DF and amplify and forward (AF) protocols are used.