On the Performance Evaluation of 5G MIMO Networks employing NOMA via System-Link Level Simulations

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INTRODUCTION
Broadband wireless access networks have become a reality for the vast majority of mobile users. In this context, bandwidth demanding applications (i.e., live video streaming) define the transmission framework as well as related technologies that have to be adopted. To this end, the existing fourth generation (4G) wireless cellular networks can already deliver peak data rates up to 100 Mbps to mobile stations (MSs) [1]. This is achieved when transmission takes place over multiple assigned subcarriers per MS (or groups of subcarriers, also known as physical resource blocks -PRBs), using the orthogonal frequency division multiple access (OFDMA) physical layer protocol [2]. In addition, the use of multiple antennas at both transmission ends of a wireless configuration (multiple input multiple output -MIMO) can increase the overall system-wide capacity without additional spectrum requirements [3].
However, the ever-increasing demand for higher data rates in zero latency applications in combination with the already crowded spectrum, drive the technological evolutions towards the design and implementation of new transmission and multiple access schemes. Over the last years, scientific research has primarily focused on deployment aspects for fifth generation (5G) wireless cellular networks [4], [5]. In this framework, millimeter wave (mmWave) transmission along with massive MIMO architecture have been established as the best candidate enabling technologies for 5G network implementation [6] - [8].
Subsequently, carrier frequencies ranging from 30 GHz up to 300 GHz (with equivalent wavelengths from 10 mm to 1 mm) are adopted, thus leading to large bandwidth channels (i.e., of 2 GHz, 4 GHz, 10 GHz, or even 100 GHz).
In addition, non-orthogonal multiple access (NOMA) can further improve the total network capacity without requiring additional spectrum resources [9] - [11]. In this principle, a higher number of users than the number of orthogonal resource slots can be supported, with the aid of nonorthogonal resource allocation. This may be realized by employing sophisticated inter-user interference cancellation schemes at the cost of an increased receiver complexity. The prominent NOMA schemes are principally divided into two categories, namely, power-domain (PD) and code-domain (CD) NOMA. In the first case, PD NOMA can serve multiple users in the same time slot, OFDMA subcarrier, or spreading code, and multiple access is realized by allocating different power levels to different users [12]. In the second case (CD-NOMA), multiple access schemes rely on low-density spreading (LDS) and sparse code multiple access (SCMA) [13].
A challenging research field towards NOMA implementation is user pairing, a term that includes all policies and conditions under which two independent users can share the same resource block. In this context, a joint user pairing and power allocation problem is considered in [14] to optimize the achievable sum rate with minimum rate constraint for each user. In [15], the impact of user pairing on the performance of two NOMA systems, i.e., fixed power NOMA (F-NOMA) and cognitive radio NOMA, is outlined. According to the presented results, F-NOMA can offer a larger sum rate than orthogonal multiple access (OMA), and the performance gain of F-NOMA over conventional OMA can be further improved by selecting users whose channel conditions are more distinctive. Ιn [16], a low complexity user pairing approach is proposed and evaluated, based on principal component analysis (PCA) of the received data matrix. Moreover, the NOMA concept has been also extended to relay node selection, allowing for significant improvements in the capacity of 5G networks [17]. In [18], the authors propose a NOMA pairing scheme that includes a near user and a far user, whose signals are superposed at the transmitter side, and successive interference cancellation (SIC) is applied to the receiver side. Finally, in [19], the authors investigate the minimum pairing distance which separates the far and near users in order to promote massive connectivity. In this framework, an analytical expression of the pairing distance threshold assuming a fixed power allocation is derived. However, all the aforementioned studies, consider either limited number of active users or restricted network topologies. The goal of the work presented in this paper is to evaluate the performance of a user pairing approach (NOMA transmission) in 5G multicellular/multiuser wireless orientations, where PRB reuse is based on performance metrics related both to received signal quality of the potential MS as well as to the total amount of interference that causes to the rest co-channel MSs. For this purpose, a hybrid system link level simulator has been developed, which couples System Level (SL) and Link Level (LL) simulations in the same evaluation snapshot (Monte Carlo -MC simulation): MSs enter the network based on predefined SL criteria (e.g., maximum allowed transmission power, blocking rate, etc.) and then LL simulations take place for all active links. Hence, all related Key Performance Indicators (KPIs) can be directly extracted after a sufficient number of MC simulations.
The novelty of our work can be summarized as follows: a) Accurate evaluation of throughput and associated KPIs of 5G cellular networks, as derived by the developed system-link level simulator. In this context, recent works (e.g. [20]) focus on decoupled SL and LL simulations. In particular, in LL simulations, no spatial network geometry has been considered in order to determine the path loss, which has been set as an input parameter of the simulator. Likewise, the inputs to the SL simulator are defined after extensive LL simulations. b) Incorporation of the latest 3GPP channel model for 5G wireless environments in the proposed simulation framework and c) Evaluation of the capacity boundaries of NOMA transmission in realistic multicellular wireless orientations.
The rest of this paper is organized as follows. In Section II, channel modelling of 5G wireless cellular orientations according to 3GPP specifications is formulated. In Section III, transceiver procedures in the 5G air interface along with the derivation of output metrics are described. The simulation framework is analyzed in Section IV, where the developed simulator along with the proposed NOMA approach are described. Simulation results are presented in Section V, where the benefits of our proposed approach compared to OMA are highlighted. Finally, concluding remarks and proposals for future work are outlined in Section VI.
The following notation is used in the paper. An italic variable a or A denotes a scalar, whereas boldface lowercase and uppercase variables a and A denote vectors and matrices, respectively. Moreover, ||a||F stands for the Frobenius norm of vector a. A calligraphic variable  denotes a set. Finally, A T and A H denote the transpose and conjugate transpose of matrix A, respectively.

II. MIMO WIRELESS CHANNEL IN 5G NETWORKS
The extension of the widely used 3GPP 3D channel model with various additional modeling components can be found in [21]. To this end, the channel coefficient in a non-line of sight (NLOS) environment for the n th cluster (1≤n≤N) between an arbitrary pair of Tx,Rx (q,u) is modelled as a sum of individual channels from M subpaths: (1) Corresponding geometry (considering only the x-y plane) is depicted in Fig. 1, where ΩBS/ΩMS denote the orientation of base station (BS)/MS antenna array, respectively, defined as the difference between the broadside of the BS/MS array and the absolute North (N) reference direction. Moreover, θBS is the line of sight (LOS) AoD direction between the BS and MS (with respect to the broadside of the BS array), while θMS is the angle between the BS-MS LOS and the MS broadside. Finally, Δn,m,AoD is the angle offset of the m th subpath with respect to θn,m,AoD and Δn,m,AoA the corresponding offset with respect to θn,m,AoA.

III. MIMO-5G TRANSCEIVER CONFIGURATION
Considering an arbitrary MIMO configuration with Nt transmitting antennas and Nr receiving antennas (Nt × Nr system), then the transmitted Nt×1 signal for the k th MS (1≤k≤K, OFDMA transmission is assumed) is given by [22]: where Ssub are the available subcarriers, pk,s is the allocated power to the s th subcarrier for the considered MS, T is the duration of the OFDM symbol and xk(t), Xk,s,l are the transmitted vector signal in time domain and the symbol of the k th MS transmitted from the s th subcarrier at the l th symbol period, respectively. It is assumed that downlink transmission for the k th MS is performed using the subcarriers in set k  , with fs being the corresponding frequency for the s th subcarrier and tk,s the transmission precoding vector.
where Hk,sec(k),s is the equivalent channel matrix (Nr×Nt) of the k th MS relevant to its serving sector for the s th subcarrier (each entry is derived after the summation of all cluster components in (1) taking into consideration the corresponding time delays) and TL stands for the total losses (including shadowing and attenuation due to antenna radiation patterns). In particular, pathloss is calculated according to the urban macro-cellular (UMa) model [21]. Moreover, where Io is the thermal noise level. From (3), it follows that the ratio of the desired signal power of a particular MS to the total amount of interference that causes to the rest co-channel MSs (also referred as jamming) can be expressed by (Signal to Jamming Ratio -SJR): It is important to note at this point that SJR maximization ensures the maximization of the desired MS's signal strength and at the same time the minimization of the interference to the rest of co-channel MSs. Finally, in realistic wireless orientations subcarriers are grouped in PRBs [22], defined as 12 consecutive subcarriers. Therefore, the term PRB will be used throughout the rest of this paper to indicate the allocated resource block in frequency domain.

IV. SIMULATION FRAMEWORK
A. Simulation Setup A hybrid system-link level simulator has been developed, allowing the execution of independent MC simulations in order to evaluate the performance of 5G wireless orientations for various transmission techniques and radio resource management (RRM) strategies. In this framework, MSs enter the network sequentially in a 5G topology with up to two tiers of cells around the central cell. For every new MS in the network, pathloss calculation from all BSs is performed. Afterwards, equivalent channel matrices for all PRBs are generated, according to the channel model described in Section II. In the next step, PRB assignment takes place, based on the proposed approach that will be described in the following subsection. If during power allocation the requested transmission power for acceptable quality of service (QoS) exceeds a predefined threshold, the new (potential) MS is discarded from the network. Otherwise, an MS entry occurs and the simulation terminates when lack of either available power or PRBs is triggered in at least one of the active BSs. The positions of the MSs as well as channel matrices remain constant during an MC run (semistatic simulator). Once the entrance of MSs is finalized, link level simulations take place for a sufficient number of OFDM symbols.
In Fig. 2, a workflow of the simulation procedure is depicted, assuming that the potential MS is served by the b th BS (1≤b≤B). In this context, Pt,b denotes the total downlink transmission power of the b th BS and Pm/pm the maximum allowed transmission power per BS/MS, respectively. Moreover, b  denotes the set of available subcarriers of the b th BS, | k  | denotes the total number of elements in set k  and Rk the requested PRBs of the new MS. Simulation setup and parameter selection (tabulated in Table I) are aligned with the majority of related works described in [24], regarding system-and link-level simulations.

B. NOMA Grouping Algorithm
The proposed methodology is illustrated in Table II, represents the corresponding set of doubly allocated subcarriers. The latter implies that in this case MS grouping has been performed, whereas a specific subcarrier from this particular set is shared by two MSs. Moreover, Step 2, the set of available PRBs is defined as a union of the non-allocated PRBs and those which have been allocated only once (i.e., no NOMA transmission has taken place for the specific PRBs). Thereafter, in Step 3, PRB s is defined according to the maximization of the product of SINR and SJR for the k th MS. However, if a given PRB has already been assigned to another MS, then the selection criterion is updated accordingly. In this case, NOMA transmission takes place and the set (i.e., x(λm(A)) is the eigenvector of matrix A relative to its maximum eigenvalue). Furthermore, Step 5 involves the power allocation per PRB. In this case, the Channel Gain (CG) per MS and PRB is defined, according to the MSs' channel quality and related total losses (SNRth denotes the minimum Signal to Noise Ratio for acceptable QoS). Finally, in Step 6, simulation is finalized either when resource loading (RL, defined as the ratio of PRBs that have been assigned to two individual MSs within the same BS to the total available PRBs) exceeds a predefined threshold (denoted as RLF) or there is lack of available power in the b th BS.
In NOMA approach, as already mentioned and depicted in Fig. 3, a specific PRB can be shared by two MSs (denoted as k, k') that are associated with the same BS. In this scenario, the signal of the MS with the highest channel quality is decoded first (denoted as k), treating all other interfering signals as noise. However, for the second MS sharing the same PRB, SIC takes place, where the signal of the k th MS is decoded first and the result is subtracted from the total received signal of the k' th MS. The overall procedure is described in the final entries of Table II, where ζk',s is the received signal of the k' th MS at the s th PRB after MRC processing and Zk',s the corresponding decoded symbol, derived from a set of predefined constellation (denoted as C).
. This is rather expected, since MSs access the network as long as there is available power per BS. Hence, in the vast majority of MC runs, simulations come to an end when lack of available PRBs takes place. Therefore, the maximum number of accepted MSs is upper limited by the amount of available physical resources. However, the deployment of massive MIMO architecture at BSs results in total downlink transmission power reduction, as shown in Fig. 5. In particular, mean transmission power is 43.5/38.6/35.9/31.3/23 W for the 2×2, 4×4, 12×2, 24×2, 64×2 MIMO configurations, respectively. Therefore, although transmission gain is improved when considering higher order MIMO configurations, the corresponding improvement ratio is decreased, since theoretical improvement with the deployment of massive MIMO architecture is limited by multiple access interference.
In an effort to further increase system capacity (i.e., maximum number of accepted MSs) with minimum transmission overhead and transceiver complexity, the proposed NOMA approach is employed during transmission. To this end, in Figs. 6 -7 the total network throughput and transmission power are presented, respectively, resulting from the proposed NOMA grouping algorithm (mean values have been considered). In this case, a 2×2 MIMO configuration is assumed. All simulation results are depicted in contrast to the tolerable RLF that ranges from 10% to 50% (for ease of comparison, OMA transmission is depicted in all simulation scenarios). It is assumed that MSs are assigned with either 5 or 15 PRBs (i.e., corresponding transmission rates are 7.2/21.6 Mbps, respectively).
As it can be observed, even for low RLF values, a significant throughput gain can be achieved compared to OMA transmission. The throughput gain is more evident for the case of 15 PRBs per MS. In particular, in the OMA case, total throughput is 1573 Mbps. For RLF equal to 10%, corresponding value in the NOMA case is 1737 Mbps. Hence, an equivalent throughput gain of almost 11% can be achieved. For RLF equal to 20%, the corresponding throughput value is 2131 Mbps, with an equivalent gain of 35% with respect to the OMA case. Moreover, it should be noted that in the first case (i.e., RLF equal to 10%), throughput improvement is derived with minimum transmission overhead. In particular, as readily observed in Fig. 7, transmission power in the NOMA/OMA case is 28/26.5 W, respectively. Hence, transmission burden is limited to 5%, i.e., half of the throughput gain.
Finally, in Fig. 8 mean BER is illustrated in logarithmic scale considering 15 PRBs per MS and three transceiver scenarios: OMA and NOMA with/without SIC at the receiver. It should be mentioned that BER is maintained at the corresponding OMA values without employing SIC at the receiver, even for RLF equal to 20%. Importantly, these results are particularly promising to drive the design and implementation of realistic 5G networks since simplified transceiver configurations can be employed towards achieving latency-critical applications.

VI. CONCLUSIONS
The performance of a proposed user pairing algorithm in NOMA transmission has been evaluated in the context of 5G networks. To this end, a hybrid system -link level simulator was developed, supporting the performance evaluation of multicellular/multiuser network orientations. According to the presented results, a significant throughput gain can be achieved when NOMA is employed, without any BER deterioration. Notably, the developed simulator made the performance evaluation of massive MIMO configurations feasible, thus allowing for future coupling of NOMA transmission in massive or distributed MIMO systems with realistic channel modelling.
ACKNOWLEDGMENT This work has been partially supported by the Affordable5G project, funded by the European Commission under Grant Agreement H2020-ICT-2020-1, number 957317 through the Horizon 2020 and 5G-PPP programs (www.affordable5g.eu/).