Enhancing Multi-User Detection in Multicarrier 5G and Beyond: A Space-Time Spreading Approach with Parallel Interference Cancellation

Multi-Carrier Code Division Multiple Access (MC-CDMA) [1-3], a prominent transmission technique that amalgamates Direct Sequence CDMA (DS-CDMA) and Orthogonal Frequency Division Multiplexing (OFDM) [4-7], is presently incorporated in Non-Orthogonal Multiple Access (NOMA) systems [8]. In the quest for delivering high-speed multimedia services and wireless Internet, broadband mobile wireless systems are expected to provide high data rates. However, numerous factors impede system capacity and data rate, necessitating strategies such as Space-Time Spreading (STS) to mitigate the effects of fading [3]. It has been demonstrated that STS can achieve a substantial diversity gain, thereby enhancing system throughput.

In this work, a novel STS-assisted multi-carrier direct sequence code division multiple access system is proposed, designed to support a wide range of bit rates. The study examines the concept of Single-User Detection (SUD) where, amid simultaneous communication of multiple users, only the signal of the user of interest is treated as useful information while the remaining users' data is considered noise. Conversely, Multi-User Detection (MUD) considers the data of other users as useful information [9-11]. Various MUD schemes have been proposed, including a Maximum Likelihood (ML) MUD for MC-CDMA [12] and an Interference Cancellation (IC) based MUD.

A physical perspective reveals that the Minimum Mean Square Error (MMSE) detector strikes a balance between the need to eliminate Multiple Access Interference (MAI) and the necessity to avoid enhancing background noise [13-15]. Despite the MMSE detector's superior performance over the Decorrelating detector, its complexity remains an issue [16]. Therefore, this study investigates the Parallel Interference Canceller (PIC), which promises to mitigate noise enhancement and complexity in 5G networks. Owing to its parallel nature, it proves equally effective in Orthogonal Multiple Access systems (OMA) and NOMA [17-20]. This proposed scheme serves as a receiver optimization approach when the number of users is excessive.

While traditional multiuser detection and interference cancellation schemes exist, computational intelligence techniques proposed in the last decade promise improved detection efficiency [21-25]. These techniques employ meta-heuristic and stochastic algorithms to reduce the multiuser search space, utilizing Genetic Algorithms (GA), Particle Swarm Optimization (PSO), Artificial Bee Colony (ABC), Chaotic Firefly Algorithm (CFA), and Ant Colony Optimization (ACO), among others.

In addition to space-time transmit-receive antenna topology and diversity, adaptive communication is a leading technique in modern communication systems, including 5G and beyond, facilitating both OMA and NOMA systems [26-30]. This approach adapts transmission parameters, such as the modulation symbol, code rate, and transmit power, in response to the ever-changing and hostile Channel State Information (CSI). At the same time, optimizing system throughput while fulfilling Signal-to-Noise Ratio (SNR) constraints as widely used in serval studies in the literature for various OFDM based adaptive communication systems [31-40].

A thorough review of the literature reveals a scarcity of studies that explore the role of the PIC detector over other counterparts in an STS-based MC-CDMA system. While research exists comparing various detectors in a multiuser environment, they do not operate under STS or within an MC-CDMA environment. Likewise, studies investigating STS and MC-CDMA seldom feature PIC detectors or contrast them with other detectors. Consequently, this research emphasizes the role of PIC for varying numbers of users in STS-based MC-CDMA systems, conducting multiple experiments to investigate the impact of transmitting/receiving antennas under various conditions. The proposed study aims to examine the effectiveness of PIC in the current settings, compared to other detectors like SIC and DD, which exhibit relatively more complexity. The proposed scheme is a receiver optimization scheme with reduced complexity and better bit error rate.

The remainder of the paper is structured as follows: Section 2 provides a background; Section 3 details the proposed scheme. Simulation results are discussed in Section 4, and Section 5 offers a conclusion.

This section introduces the transmitter and receiver models assumed for the study.

3.1 Transmitter

We consider an orthogonal bit-synchronous MC DS-CDMA system illustrated in Figure 1.

3.png

Figure 3. A (2,1) STS scheme

In the system model, we are using single receiving antenna, T_x number of transmitting antennas and V*S number of frequency subcarriers. K user signals are transmitted synchronously in this MC DS-CDMA scheme. Per the Figure 1, we are investigating the kth user where real-valued data symbol using binary phase shift keying (BPSK) modulation and real-valued spreading is considered. A block of V.L_x data bits each having a bit duration of T_b is serial to parallel converted to $V$ parallel subblocks. Each parallel sub-blocks have L_x data bits which are space-time spread using the scheme described in Figure 3. With the aid of M_x number of orthogonal spreading codes e.g.,

Walsh codes = $\left\{c_{k, 1}(t), c_{k, 2}(t), \ldots, c_{k, M_x}(t)\right\}, 1 \leq k \leq K$  

Subsequently, it is represented on set of aforementioned transmitting antennas. The interval of the symbol used as the STS signal can be calculated as:

$\frac{U L_x T_b}{T_c}=U L_x N$ as $\frac{T_b}{T_c}=N$

Here T_c correspond to the chip interval of the Walsh spreading codes in our case. Now it can be shown from Figure 1 that the output coming out from the STS blocks is then mapped on the T_x transmit antennas. These V STS signals that are frequency domain spread can be expressed as:

$\left\{c^{I I}{ }_k[0], c^{I I}{ }_k[1], c^{I I}{ }_k[2], \ldots \ldots \ldots \ldots, c^{I I}{ }_k[S-1]\right\}$         (7)

Consequently, each signal spread over the space-time is communicated over the mentioned subcarriers. The main idea of spreading the signal in the frequency domain is to achieve maximum frequency spacing to avoid potential fading. Inverse fast Fourier transform (IFFT) is then applied on the STS and F-domain spread signals to carry out multicarrier modulation. The IFFT block output is then transmitted using one of the transmitter antennas. The composite transmitted signal over all the transmitters can be represented as:

$s(t)=\sum_k s_k(t)$           (8)

$s_k(t)=\operatorname{Re}\left\{\sqrt{\frac{2 E_b}{V T_b S M_x T_x}}\left[C_k B_k\right]^T G w * \exp \left(j 2 \pi f_c(t)\right)\right\}$          (9)

where, $\frac{E_b}{V T_b}$  is the transmitted power per sub-carrier. Here G in Eq. (3) represents V×VS dimensional frequency domain spreading matrix:

$G=\left[C_K{ }^{I I}[0], C_K{ }^{I I}[1], C_K{ }^{I I}[2], \ldots \ldots, C_K{ }^{I I}[S-1]\right]$           (10)

Here,

$C_k{ }^{I I}[s]$, where $s=0,1, \ldots \ldots, S-1$

It is the set of rank V matrices and can be further be represented as:

$C_k^{I I}[s]=\operatorname{diag}\left\{c_k{ }^{I I}[s], c_k{ }^{I I}[s], c_k{ }^{I I}[s], \ldots \ldots, c_k{ }^{I I}[s]\right\}$           (11)

The expanded form of the equivalent transposed matrix can be expressed as diagonal matrix of dimension V×VM_x:

$C_k{ }^T=\left(\begin{array}{ccccc}c_{k, 1}(t) & 0 & \cdots & \cdots & 0 \\ c_{k, 2}(t) & 0 & \cdots & \cdots & 0 \\ \vdots & \vdots & \ddots & \ddots & \vdots \\ c_{k, M_x}(t) & 0 & \cdots & \cdots & 0 \\ 0 & c_{k, 1}(t) & 0 & \cdots & 0 \\ 0 & c_{k, 2}(t) & 0 & \cdots & 0 \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ 0 & c_{k, M_x}(t) & 0 & \cdots & 0 \\ \vdots & \vdots & \ddots & \ddots & \vdots \\ 0 & 0 & \cdots & \cdots & c_{k, 1}(t) \\ 0 & 0 & \vdots & \vdots & c_{k, 2}(t) \\ \vdots & \vdots & \ddots & \ddots & \vdots \\ 0 & 0 & \cdots & \cdots & c_{k, M_x}(t)\end{array}\right)$

B_k is a VM_x×T_x is dimensional matrix mapping the data of V sub-blocks to T_x antennas. This is done according to the requirements space-time spreading described earlier. The matrix B_k can be expressed as:

$B_k=\left[B_{k 1}{ }^T, B_{k 2}{ }^T, \ldots \ldots \ldots, B_{k V}{ }^T\right]^T$               (12)

where, B_ku, u=1, 2, ..., V are M_x×T_x dimensional matrices. The matrix structure of this matrix is as follows:

$\left(\begin{array}{cccc}a_{11} b_{k, 11}^{\prime} & a_{12} b_{k, 12}^{\prime} & \cdots & a_{1 L_x} b_{k, 1 T_x}^l \\ a_{21} b_{k, 21}^{\prime} & a_{22} b_{k, 22}^{\prime} & \cdots & a_{2 L_x} b_{k, 2 T_x}^{\prime} \\ \vdots & \vdots & \ddots & \vdots \\ a_{M_x 1} b_{k, M_x 1}^{\prime} & a_{M_x 2} b_{k, M_x 2}^{\prime} & \cdots & a_{M_x L_x} b_{k, M_x T_x}^{\prime}\end{array}\right)$               (13)

In the above-given matrix a_ij is the sign of the element in the i^th row and j^th which is determined by the STS design rule.

Here in the currently setting, the variable w in equation represents the IFFT multi-carrier modulated vector of length VS and it can be written as:

$w=\left[\exp \left(j 2 \Pi f_1 t\right), \exp \left(j 2 \Pi f_2 t\right), \ldots \ldots \ldots, \exp \left(j 2 \Pi f_{S V} t\right)\right]^T$              (14)

Eq. (3) shows the general form of the transmitted signal regardless of the values L_x, M_x, T_x. The study of space time spreading shows that L_x=M_x=T_x gives the best results as this combination provides maximum transmit diversity utilizing a common set of codes.

Hence no extra set of codes is required. Now talking about the number of users supported by this broadband multicarrier direct sequence code division multiple access system using space time and frequency domain spreading the analysis is given as follows. The total number of orthogonal codes used by the space time spreading VL_xN with the overall quantity of users accommodated by the system are:

$K \max =\frac{V L_x N}{M_x}$

As compared to this the number of orthogonal codes used by frequency domain spreading is S. This shows that the S number of signals can share a common set of space time spreading codes. These S users are distinctly separable with the help of S number of frequency domain codes. It means that the total number of users supported by this multicarrier direct sequence code division multiple access system using space time spreading and frequency domain spreading are:

$S K \max =\frac{V S L_x N}{M_x}$

Now the orthogonal code assignment can be done as follows: If the total numbers of users are in the range of maximum user limit, they will be assigned the same number of orthogonal space time spreading codes and the same S number of frequency domain spreading codes. However, if the number of users increased sufficiently that is if they are in the range $s K(s+1)_{\max } \max$. 

Consequently, these s(s+1) users are assigned the same set of space time spreading codes but the s+1 users are assigned different frequency domain codes. In doing so multi-user interference is introduced which affects the overall bit error rate performance of the system.

Nonetheless, this where the receiver’s optimization plays its role in reducing the multiuser interference by employing the proposed parallel inference cancelation assisted multiuser detection scheme. It will combat with the induced interference by adequately mitigating it with a relatively lower imposed computational complexity compared to the other state of the art detectors.

3.2 Channel

The channel assumed in this context is a slowly varying frequency non-selective Rayleigh flat fading channel. Each sub-carrier signal will experience flat fading. Now let us assume that $0 \leq K^{\prime} \leq S$ corresponds to the count of users communicating with the same group of space time spreading codes. Here it can also be stated that the number of space time spreading codes are shared among same set of users as mentioned above.

The moment these mentioned set of signals are transmitted over a frequency nonselective Rayleigh flat fading channel as utilized in several studies in the literature for similar type of the assumed OFDM systems [41-48], the received equivalent low pass signal can be written as:

$R(t)=\sum_{k=1}^{K^{\prime} K_{\max }} \sum_{i=1}^{T_x} \sqrt{\frac{2 E_b}{V T_b S M_x T_x}}\left(\left[C_k B_k\right]^T G\right)_i H w+N(t)$            (15)

where, N(t) represents additive white Gaussian noise (AWGN) having a double-sided spectral density of N₀ and single sided spectral density of N₀/2.

The idea of assuming this channel is to assure that the simulation environment is aligned to the fifth-generation systems as previously investigated in the studies [49-51].

3.3 Receiver

A comprehensive schematic of the receiver of the proposed scheme is shown in Figure 4. The sequence of the steps taken by the receivers are successive as well as parallel in nature depending on the respective block. The blocks employed are frequency demodulation block, followed by space time de-spreading block and finally the detectors are employed.

4.png

Figure 4. Receiver of the proposed 5G system

On the receiver side, the inverse operations are being carried out. As can be seen in the Figure 4 the received signal is first down converted using demodulation in the FFT multi-carrier block. Consequently, we received equivalent parallel outputs to be fetched to the subsequently blocks.

After performing the de-spreading operation in space time a outcome argument is obtained against each transferred bit of data after performing de spreading in the frequency domain as well. It is worth mentioning that we are assuming the transmitter and receiver diversity with two, four and eight antennas, respectively.

Hence the output of the overall system can be readily expressed as:

$z_{u 1}=\left[Z_{u, 1}, Z_{(V+u), 1\quad}, \ldots \ldots \ldots \ldots, Z_{(S-1) V+u, 1\quad}\right]^{\mathrm{T}}$             (16)

The intermediate operations are expressed by means of segregating different components as given in Eq. (17) with all the effects and then combining them in the form of Eq. (18).

$\begin{gathered}A=\operatorname{diag}\left\{\sum_{L=1}^{T_x} h_{u L,}^2 \sum_{L=1}^{T_x} h_{(V+u) L,}^2, \ldots \ldots ., \sum_{L=1}^{T_x} h_{((S-1) V+u) L,\quad}^2\right\} \\ Q=\left(\begin{array}{cccc}q_1^{I I}[0] & q_2^{I I}[0] & \cdots & q_K^{I I}[S-1] \\ q_1^{I I}[1] & q_2^{I I}[1] & \cdots & q_K^{I I}[S-1] \\ \vdots & \vdots & \ddots & \vdots \\ q_1^{I I}[S-1] & q_2^{I I}[S-1] & \cdots & q_K^{I I}[S-1]\end{array}\right) \\ b=\left[\begin{array}{lll}b_{1, u 1}, b_{2, u 1}, \ldots \ldots \ldots \ldots \ldots, b_K /, u 1 & ]^T\end{array}\right. \\ n=\operatorname{Re}\left[N_{u, 1}^{\prime}, N_{(V+u), 1}^{\prime}, \ldots \ldots \ldots \ldots \ldots, N_{((S-1) V+u), 1\quad}^{\prime}\right]\end{gathered}$             (17)

By considering all the parameters given in the equations, now the decision variable can be expressed as:

$z=\sqrt{\frac{2 V E_b T_b}{S}} A Q B+n^{\mathrm{T}}$             (18)

3.4 Detection with parallel interference canceller

In the detection of Space-Time Spreading STS-based MC DS-CDMA signals, we investigate correlation-based single-user detector, de-correlation-based multi-user detector, and parallel interference canceller. The decision statistics are obtained after both STS and F-domain dispreading. In contrast to the SIC-based multi-user detector, the parallel interference cancellation (PIC) aided detector estimates and subtracts the MAI imposed by all interfering users from the signal of the desired user in parallel. Based on the discussion we can express as:

$Z=\left[z_{u 1}, z_{u 2}, z_{u 3}, \ldots \ldots, z_{u K^{\prime}}\right]^T \mathrm{~T}$             (19)

We can define this z_u,k as:

$z_{u k}=\sqrt{\frac{2 V E_b T_b}{S}} A Q b+n^{\mathrm{T}}$             (20)

$z_{u k}=A_{u, k} b_{u, k}+\sum_{\substack{j=1 \\ j \neq k}}^{K^{\prime}} A_{u, j} b_{u, j} \rho_{u j, k}+n^{\mathrm{T}}$             (21)

So, for the conventional PIC we can write:

$\hat{b}_{u k}=\operatorname{sgn}\left[z_{u k}-\sqrt{\frac{2 V E_b T_b}{s}} \sum_{\substack{j=1 \\ j \neq k}}^{K^{\prime}} A_j b_j \rho_{j, k}\right] \mathrm{T}$             (22)

We can see that there is parallel cancellation of interference. This is the required proposed scheme for PIC. The signum (sign) function represents the sign of the detected bit as the originally transmitted binary phase shift keying (BPSK) signal from the user.

The paper presents a novel approach to multiuser detection in multicarrier 5G systems with a parallel interference cancellation-based receiver. From the comparative study of different MUD schemes, following is concluded. The PIC-assisted MUD outperforms the De-correlating detector and correlator with hard decision; the comparison is more significant for higher SNR values. With an increase in the number of users, the performance is reduced due to MUI, but PIC-based MUD gives still a reasonable comparison; further, this issue can be overcome by an increase in the number of transmit antennas (transmit diversity). So, a greater number of users can be entertained by using PIC-assisted MUD, changing the length of frequency domain spreading codes, increase in SNR, or increasing the number of transmit antennas for more power propagation and good signal recognition, and relatively lesser BER. In the future, this scheme can be investigated with different detectors like multiple interference canceller, successive interference canceller assisted MUDs. Moreover, receiver diversity can also be investigated. Channel coding can be used to entertain a greater number of users with low BER and relatively easy decoding. Also, different channel models can be investigated with various other parameters to fine-tune. Moreover, artificial intelligence, machine, and deep learning-based approaches such as transfer learning etc. as already utilized in several studies in the literature [52-60]. Moreover, these schemes are quite promising in terms of addressing the similar type of engineering problems, can be investigated for performance improvement in terms of channel capacity enhancement mitigating bit error rate.