Co-Channel Interference Cancellation for 5G Cellular Networks Deploying Radio-over-Fiber and Massive MIMO Beamforming

Abstract

In future fifth-generation (5G) cellular networks, distributed multiple-input multiple-output (MIMO) technology will be applied such that much more challenges on efficient resource allocation to user equipment (UE) of high access density are raised in order to support their high mobility among different micro-/pico-cells. In this chapter, we propose a framework to enable an optical back-haul cooperation among different optical network units (ONUs) with distributed MIMO technology in wireless front-haul for next-generation optical-wireless cellular networks. Specifically, our proposal is featured by a downlink resource multi-cell sharing scheme for OFDMA-based passive optical network (PON) supporting radio-over-fiber (RoF). We first consider system architecture with the investigation of related works, and then we propose a co-channel interference mitigation and delay-aware sharing scheme for real-time services allowing each subcarrier to be multi-cell shared by different ONUs corresponding to different micro-/pico-cells. Furthermore, a heuristic algorithm to mitigate co-channel interference, maximize sharing capacity, and minimize network latency is given by employing the graph theory to solve such sharing problems for future 5G. Moreover, simulations are performed to evaluate our proposal.

1. Introduction

The increasing demand of real-time services (e.g., VoIP, the video telephony, and streaming) poses high requirements on communication quality (e.g., interference mitigation and delay constraint) and bandwidth increase in the network for the future era of big data [1]. Nowadays, the OFDMA-based passive optical network (PON) has been applied to provide such a large-capacity and also a high-flexibility solution for wireless cellular networks with radio-over-fiber (RoF) technology [2, 3]. Figure 1 describes a RoF-based optical-wireless system adopting OFDMA-PON, while one of prominent challenges in such networks for future 5G communications is the algorithm for effective resource allocation. In the related works, a dynamic bandwidth allocation (DBA) in OFDMA-PON has been implemented in [4] with fixed subcarriers for data scheduling, which adopts a traditional grant/report polling scheme. Moreover, dedicated resource allocation (DRA) and shared resource allocation (SRA) as two DBA methods were proposed in [5]. The DBA protocol in OFDM-PON therefore has been proposed in [6], where protocols are summarized in two schemes: the fixed burst transmission (FBT) and the dynamic circuit transmission (DCT). FBT employs a round-robin, IPACT algorithm [5] while DCT adopts bandwidth estimation. Furthermore, a power-efficient DBA scheme of OFDM-PON has also been given in [7] for the purpose of minimizing the optical network units (ONUs) transmitting power. In addition, a lot of works such as for attaining a low power consumption with OFDM-PON have been finished on a system hardware level. Specifically, a 36.86-Gb/s optical wavelength conveying six 100-MHz-bandwidth LTE-A signals has been proposed in [8]. The system supports five-carrier aggregation, 2 × 2 MIMO, and three sectors, over a 40-km SSMF front-haul adopting a single 1550-nm directly modulated laser. In addition, the system [2] adopts a fixed RF channel on subcarrier; however, it will become inflexible to satisfy DBA when high mobility of large number of user equipment (UE) occurs in the wireless front-haul. The structure [2, 3] deploys an optical distribution network (ODN), which is different with [4, 5], but the DBA problem is still the same.

Figure 1.

Network architecture of RoF-OFDM-PON based on 5G [9].

However, considering a very high density of UEs and their high mobility in future 5G cellular networks, a prominent problem waiting to be solved is the co-channel interference jointly employing radio-over-fiber, massive multiple-input and multiple-output (MIMO), and beamforming [9] technologies. For example, in optical-wireless networks, when the same wireless frequency resources carried by different optical wavelengths overlaps in the same beam direction and are received by different UEs, these UEs which emerge in this beam direction under their mobility will suffer high interference. Typically, in the case of distributed massive MIMO, numbers of UEs move frequently among a few of micro-/pico-cells in any time; wireless data carried over the wavelength are shared by all UEs in the pico-cell and adjacent cells. The minimizing of co-channel interference as mentioned will become much more imperative. Hence, it is expected to seek a scheduling optimization of wireless resources to each micro-cell mitigating the interference due to high UE mobility. Furthermore, we consider a given limited number of optical subcarriers, when an ONU needs additional resources, and in order to support the bandwidth demand for the rest of ONUs, optical subcarriers will not be reallocated in congestion cases, the problem herein is also to find ways to share optical subcarrier among local different cells by ONUs. However, it brings the additional delay problem and also configuration and control problem for selecting ONUs because of resource sharing and transmission. To achieve these targets, we propose and observe an interference mitigation and delay-aware sharing scheme for real-time services allowing that each subcarrier of RoF-OFDM-PON [2] can be multi-cell shared by UEs accessed from different micro-cells. Namely, each UE is arranged to receive multiple data streams demodulated from different ONUs simultaneously.

In this chapter, we address the aforementioned problems in the system, which have not been studied in other works before. The proposed method in this chapter can be employed by a future 5G operator to run an radio-over-fiber based optical OFDM (OOFDM) [3] network with multiple micro-/pico-cells as shown in Figure 1 ; it could be used as a method on network design to reduce resource waste and improve the performance of network.

The rest of this chapter is organized as follows. Section 2 presents our system architecture and resource allocation model. Section 3 introduces our resource sharing proposal. A heuristic algorithm guaranteeing minimum co-channel interference, maximum sharing capacity, and minimum delay time is presented in Sections 4 and 5 which provides evaluation results with simulations. Finally, the chapter is concluded in Section 6.

2. RoF-OFDM-PON system

2.1. Link architecture in RoF-OFDM-PON networks

Figure 2 illustrates an experimental link architecture for signal processing in RoF-OFDM-PON [10] to support our proposal and to be employed as a physical fundamental for one data stream in system. From the transmitter side, this implementation firstly modulates experimental data through an OFDM processing with performing of the PRBS, NRZ pulse, and QAM sequence generation (e.g., 4-QAM) in advance [10]. After that, a RF-IQ mixer is used to deal with the OFDM signal to analog RF with a proper quadrature modulation. The output signal then experiences an optical OFDM (OOFDM) modulation with a 193.1 THz CW laser by LiNbO3 mach-zehnder modulator (MZM) [10, 11] and then is sent into fiber through EDFA to amplify the signal.

Figure 2.

The downlink signal processing of RoF-OFDM-PON.

On each receiver of ONU side, signals from fiber are received by photo-detector (PD) [10, 11] and are executed with a RF de-multiplexing and OFDM demodulation followed by QAM sequence generator and NRZ pulse generator in order to recovery the experimental data [10]. It is important to note that one set of optical OFDM subcarrier on fiber could be modulated to accommodate different UEs belonging to two or more receivers/ONUs in cellular networks, and the wireless data allocated to UEs belonging to any micro-cell could be transmitted by the broadcasting of multiple sharing streams from other ONUs with antennas in other micro-cells nearby (e.g., by a distributed massive MIMO [9]). In this chapter, our work thus mainly consider these resource allocation problems, while detailed physical discussions on the control and configuration issues (e.g., protocol specification) for dynamic transmission from multiple ONUs for resource sharing are out of the scope of this chapter.

2.2. Optical subcarrier allocation model

Employing the downlink signal processing mentioned in Section 2, the current OFDM-PON access networks flexibly allocate the time/frequency blocks in OFDM frame logically as shown in Figure 3 under a mixed access rate. Figure 3 describes an example about resource allocation of optical time/frequency block distributed to three different ONUs under different time slots and optical subcarriers. In this case, multiple wireless UE data are modulated onto each time/frequency block, and each block could be allocated to a single ONU, while each ONU could receive several such time/frequency blocks in the same time slot [12, 13]. Each optical subcarrier of time/frequency block in Figure 3 could be addressed by a RoF modulation with radio frequency in the same or different wireless radio frequency spectra (e.g., a LTE radio frame frequency spectrum from 2110 to 2170 MHz) [14]. Moreover, according to a bandwidth capacity of single optical carrier, multiple radio frame could be conveyed on a single carrier (e.g., as reported in [8], six 100 MHz LTE-A signals are conveyed on a 36.86 Gb/s optical carrier).

Figure 3.

Optical OFDMA frame with time/frequency block allocation to different ONUs in RoF-OFDM-PON system [12].

Adopting this subcarrier allocation method, different UEs are fed by its ONU within its cell, and the subcarrier number allocating to each ONU could be appended according to the increase of traffic in this cell. However, the very high UE mobility in future 5G pico-cells [9] results that a few idle resource appears on a signal optical time/frequency block so that much more wasted resource is produced during resource allocation. In order to rationally allocate these idle resources (e.g., the remnant resource in Figure 4 during slot t ₂), it should be noted that the physical optical modulation process in Figure 2 can be easily controlled to make UE data belonging to different ONUs modulate onto the same optical time/frequency block with radio-over-fiber, as shown in Figure 4 . For instance, in Figure 4 , ONU 3 has idle resources in time slot t ₁; however, its data requirement exceeds the allocated amount from time slot t ₃ on. With our proposal, it will receive remnant resources of ONU 1 in time slot t ₃ by a real-time resource sharing for its additional requirement.

Figure 4.

Multi-cell sharing of wireless resources on optical time/frequency blocks allocated to different ONUs corresponding to different wireless cells.

2.3. Radio frame model on optical subcarrier

The wireless spectrum resource can be illustrated by Figure 5(a) . In contrast to the single-layer radio frame which is illustrated in Figure 5(a) , by allocating more subcarriers, multiple radio frames can be delivered on fiber to each ONU, forming the multi-layer radio frames which are shown in Figure 5(b) for each ONU. Note that Figure 5(b) describes multiple wireless frames carried by a single optical subcarrier λ_i . Therefore, the time slot in Figure 5 is different from that in Figures 3 and 4 , for example, optical scheduling time slot t ₁ in Figure 4 contains several consecutive time slots in Figure 5 which is named as transmission time interval (TTI) [15].

Figure 5.

Wireless resource sharing logically on optical time/frequency blocks by different ONUs.

Note that the smallest optical resource unit in Figures 3 and 4 is named as time/frequency block, while the smallest radio resource unit in Figure 5 is named as resource block (RB). There are different concepts in this chapter. Each component carrier (CC) contains several RBs [14, 15]. One UE can receive several CCs in a certain time slot simultaneously.

3. Mathematical optimization

3.1. Assumptions of the model

Assumption 1: There are total Nⁱ _sub-c optical subcarriers allocated to ONU i, and l is the indicator of optical subcarrier. For each l-th optical subcarrier, it contains C_l layers of frames, as shown in Figure 6(b) . p is the indicator of frame on optical subcarrier. The concept of multi-layer frames will be adopted in the following problem description and resource sharing algorithm.

Assumption 2: Denote R_k,t as the minimum capacity requirement for user k in slot t. The UE set {1, 2,…, $\tilde{k}$ ,…, $\tilde{K}$ } is served by ONU i, while UE set {1, 2,…, k,…, K} is served by ONU j. Denote N _sub-c as the consecutive subcarrier number on frequency of each RB and N _sym as OFDM symbol [14] number on time domain of each RB. In addition, denote N _sc ^(d) _s as the subcarrier number for date transmission in the s-th OFDM symbol, and N _sc ^(d) _s  < N _sub-c, because of the existence of subcarriers used in control signals in each RB.

Assumption 3: There are J numbers of modulation and coding scheme (MCS) for each RB to choose, and R_o ^(c) is code rate in a dedicated MCS, o∈{1, 2,…., J}. M_o describes the constellation size of MCS [14]. In each TTI of scheduling, the capacity r^(o) _RB for one RB under MCS o is then given by Eq. (1):

$$r_{\mathrm{RB}}^{\left(o\right)}=R_o^{\left(\mathrm{c}\right)}{\text{log}}_2\left(M_o\right)\sum _{s=1}^{N_{\mathrm{sym}}}{N_{\mathrm{sc}}^{\left(d\right)}}_s$$ E1

Assumption 4: Suppose that g_k,l,p,n indicates the wireless channel quality indicator (CQI) [14] of the n-th RB in each CC carried on the p-th optical subcarrier dedicated to UE k. The CQI of RB in each CC carried on the p-th frame on l-th optical subcarrier can be given by g_k,l,p = [g_k,l,p,1, g_k,l,p,2,…, g _{k,l,p,N RB} ]^T. Each UE can employ at most z CCs to receive data in each slot $.$ Each UE can only adopt one MCS for its assigned RB of CCs.

Assumption 5: We consider beam-forming [7] for wireless signal propagation. In terms of beam direction of the i-th ONU/antenna pair, two categories of UEs’ conflict relationship according to any two UEs’ locations (from the view point of the i-th ONU/antenna pair) are (1) same angle UEs and (2) different angle UEs. Define a matrix $\mathit{\chi }$ _i  = [χ_i (1, 2),…, χ_i (k, k′),…, χ_i (K-1, K)]. The value of χ_i (k, k′) is then defined in the Eq. (2).

$${\chi }_i\left(k,k^{\prime }\right)=\left\{\begin{array}{l}0;\text{different angle}\mathrm{UEs}\\ 1;\text{the same angle}\mathrm{UEs}\end{array}\right.$$ E2

Figure 6.

The illustration of multi-cell RoF-OFDM-PON scenarios with distributed massive MIMO deployment. (Each cross represents an ONU/antenna location, while the red circle represents the UE. Six red crosses in different cells highlight that one UE receives multiple data streams in the subcarrier sharing scenario).

Naturally, different beam directions can mitigate interference. For any two UEs, from a view point of the ONU/antenna pair, the first category (i.e., c_i (k, k′) = 1) is that two UEs locate at the same angle of beam direction. The second category (i.e., c_i (k, k′) = 0) is that two UEs locate at different beam directions. Hence, the co-interference of second category UEs will be mitigated, even if these UEs employ the same RB of CCs on different radio frames which are carried by different optical subcarriers. However, for the first category UEs, interference still occurs if the UEs employ the same RB of CCs on different radio frames.

Therefore, γ^(n,y,t) _{k, k′} is also defined as a binary variable. As shown in Eq. (3), γ^(n,y,t) _{k, k′}  = 1 indicates that the same RB n of the y-th CC is allocated to UE k and k′ in slot t at different frames. The same RB of CCs here means the RB on component carriers in the same frequency and also the same time slot carried by different frames:

$${\gamma }_{k,k^{\prime }}^{\left(n,y,t\right)}=\left\{\begin{array}{l}1;\mathrm{UE}k\text{and}{k}^{\prime }\mathrm{are}\text{allocated with the same}\mathrm{RB}\text{of}\mathrm{CC}\\ 0;\text{otherwise}\end{array}\right.$$ E3

Definition 1: The UE set {1, 2,…, $\tilde{k}$ ,…, $\tilde{K}$ } is located outside the cell ξ and served by ONU i, while UE set {1, 2,…, k,…, K} is in the cell ξ and served by ONU j.

Definition 2: For any two UEs, from the viewpoint of the MIMO antenna, we define that the same angle UEs in Eq. (2) are two UEs located at the same angle of beam direction. The angle space depends on the coverage of a beam released by antennas (e.g., 30° or the case of narrow beam in 5G). Otherwise, they are different angle UEs which locates at different beam directions (base station MIMO antenna arrays in the cell are in the same place and treated as one point).

3.2. Modeling of resource sharing proposal

The optimization model we proposed is more applicable for the small coverage cell deployment with a high UE mobility scenario, so that the sharing capacity can be maximized and the delay time from the OLT to each UE could be minimized by the model. In the system, we suppose a remnant resource of bandwidth of each ONU after its inter-cell allocation can be delivered to the UEs in different cells for resource sharing by the broadcasting of distributed antennas. It is assumed that the antenna transmission for wireless signals in each cell could well reach the UEs in several adjacent cells. We also suppose that each ONU is attached by one antenna element in its location by default. In this chapter, for simplicity, we directly denote i or j as an ONU/antenna pair, that is, the ONU i means the ONU in i-th ONU/antenna pair, and the ONU j means the ONU in j-th ONU/antenna pair. Especially, in terms of UE k which located in cell ξ, we define ONU i for the ONU placed outside cell ξ and ONU j for the ONU placed in cell ξ. The UE set {1, 2,…, $\tilde{k}$ ,…, $\tilde{K}$ } is located outside the cell ξ and served by ONU i, while UE set {1, 2,…, k,…, K} is in the cell ξ and served by ONU j. The classification of different UE sets and different ONU/antenna pairs is to clearly describe the optimization problem of subcarrier multi-cell sharing.

Consider the single UE k which is accommodated by ONU j, and UE k receives data from ONU j and a shared ONU i. For the data stream from ONU i to UE k, we define d ^k _i,t as its delay of sharing data for UE k in time slot t by ONU i from optical back-haul in OLT to the UE.

We consider the case that multiple ONUs share their data for a single UE k. As the system model depicted in Figure 6 , we define a set $\mathcal{M}$  = {i|i = 1, 2,…, b,…, m} which represents the set of ONUs outside the cell where UE k is located for bandwidth sharing to UE k.

On the other hand, we define $\mathcal{P}$  = {j|j = 1, 2,…, b,…, n} representing the set of ONUs inside the cell where UE k belongs and $\mathcal{N}$  = {i|i = 1, 2,…, b,…, n} representing the set of total ONUs in a local network, respectively. Here, m is less than n and $\mathcal{M}$ U $\mathcal{P}\subseteq \mathcal{N}$ . For the parameter b, note that the delay time d^k _b,t is the maximum delay in sharing links among all the links through the selected ONUs to the UE k satisfying

$$b=\underset{i\in \mathcal{M}}{\text{arg}\text{max}}{d}_{i,t}^k$$ E4

We could enrich our model to the real-time scenario for multiple UEs. The joint objective to (i) maximize sharing capacity and (ii) to minimize delay in a time duration T can be formulated by Eq. (5) in detail.

Objective:

$$\begin{array}{l}\text{max}\{{\displaystyle \sum _{t=1}^T}{\displaystyle \sum _{k=1}^K}\left({\displaystyle \sum _{i=1,i\ne j}^m}{w}_{i,t}^k\cdot c_{i,t}^k-{\displaystyle \sum _{i=1,i\ne j}^m}{q}_{i,t}^k\cdot d_{i,t}^k\right)-\hfill \\ {\displaystyle \sum _{i=1,i\ne j}^m}{\displaystyle \sum _{t=1}^T}{\displaystyle \sum _{y=1}^{N_{CC}}}{\displaystyle \sum _{n=1}^{N_{RB}}}\left({\displaystyle \sum _{C_i\left(k\text{,}{k}^{\prime }\right)=1}}{\gamma }_{k.k^{\prime }}^{\left(n\text{,}y\text{,}t\right)}+{\displaystyle \sum _{C_i\left(k\text{,}\tilde{k}\right)=1}}{\gamma }_{k.\tilde{k}}^{\left(n\text{,}y\text{,}t\right)}\right)\}\hfill \end{array}$$ E5

where w^k _i,t and q^k _i,t can be further described in Eqs. (6) and (7), respectively:

$$w_{i,t}^k={\beta }_{i,t}^k\cdot G_{i,t}^k\cdot \text{min}\left\{h_{i,t-1}^k,h_{i,t-2}^k,\dots ,h_{i,1}^k\right\}$$ E6

$$q_{i,t}^k={\beta }_{i,t}^k\cdot D_{i,t}^k\cdot \text{max}\left\{U_{i,t-1}^k,U_{i,t-2}^k,\dots ,U_{i,1}^k\right\}$$ E7

Here, β^k _j,t represents a binary indicator that UE k is served or not by ONU i in slot t. Deferring to c^k _i,t which is a current capacity which could be provided to UE k in slot t, while G^k _i,t is a current capacity which is obtained by UE k in the end in slot t. Moreover, h^k _i,t-1 is a historical capacity obtained by UE k in slot t-1. It should be noted that c^k _i,t is a shared capacity available for UE k from ONU i. Meanwhile, in Eq. (7), D^k _i,t and U^k _i,t-1 are current delay constraint of UE k in slot t and historical delay record of UE k in slot t-1, respectively.

The optimization objective in Eq. (5) may be seemed indeed as an interference mitigation problem of finding c^k _i,t subjected to the delay requirement from a set of $\mathcal{M}$  = {i|i = 1, 2,…, b,…, m} for UE k severed by ONU j. This will be solved in more details in our heuristic algorithms later. Firstly, we discuss all the constraints of objective as follows;

1) Capacity constraints for UE k:

$$\sum _{i\in \mathcal{M},i\ne j}{c}_{i,t}^k\ge A_t^k-\sum _{j\in \mathcal{P}}{F}_{j,t}^k$$ E8

Equation (8) describes the total sharing capacity should not be less than the capacity requirement for each UE k in each time slot t. A^k _t is total data capacity demand of UE k and F ^k _j,t is data capacity provided by ONU j to UE k.

2) Delay constraints for UE k:

$$d_{b,t}^k\le D_{i,t}^k$$ E9

The delay constraint in Eq. (9) in each slot t means that the delay time spent on the path from the source of OLT and the destination of UE should not exceed the maximum tolerable transmission delay time (TDT) of UE k in a real-time service.

3) Capacity constraint for ONU i

Considering the 5G communication with carrier aggregation from [14, 16], we may further discuss the constraint of c^k _i,t :

$$\sum _{k=1}^K{c}_{i,t}^k\le E_{i,t}$$ E10

Denote E_i,t as the total remaining capacity of ONU i after the allocation for its UEs accommodated. Equation (10) describes that the total amount of sharing capacity of UEs should be less than E_i,t .

With respect to our resource allocation model for optical time/frequency blocks with RoF and downlink signal processing in Section 2, we formulate E_i,t approximately with the aforementioned assumptions which are detailed in the aspect on resource allocation.

The remaining capacity E_i,t of ONU i in time slot t is then given as Eq. (11) approximately:

$$E_{i,t}=\sum _{l=1}^{N_{\mathrm{sub}‐\mathrm{c}}^i}{C}_l\left(\frac{1}{Q}{N}_{\mathrm{cc}}{N}_{\mathrm{RB}}\sum _{o=1}^Q{r}_{\mathrm{RB}}^{\left(o\right)}\right)-\sum _{l=1}^{N_{\mathrm{sub}‐\mathrm{c}}^i}\sum _{p=1}^{C_l}\sum _{\tilde{k}=1}^{\tilde{K}}\sum _{y=1}^{N_{\mathrm{cc}}}\sum _{n=1}^{N_{\mathrm{RB}}}{\sigma }_{\tilde{k},l,p}^{\left(n,y,t\right)}\sum _{o=1}^Q{\mu }_{\tilde{k},o}\cdot r_{\mathrm{RB}}^{\left(o\right)}$$ E11

Especially, σ ^(n,y,t) _k,l,p is a binary variable to define whether or not the n-th RB of the y-th CC is assigned to the k-th UE on the p-th frame on the l-th optical sub-carrier in slot t, and σ ^(n,y,t) _k,l,p  = 1 expresses that allocating the n-th RB of the y-th CC to the k-th UE in slot t. Here, we define a binary variable μ_k,o  = 1 to express that the k-th UE employs the o-th MCS. Q in Eq. (13) describes the highest MCS employed by the k-th UE corresponding to a CQI of RB “max(g_k,l,p,δ* )” in each CC on p-th frame on l-th optical subcarrier. Here:

$${\delta }^{\ast }=\underset{n\in \left\{1,2,\dots ,N_{\mathrm{RB}}\right\}}{\text{arg}\text{max}}\left(g_{k,l,p,n}\right)$$ E12

$$Q_{k,l,p,\text{max}\left(g_{k,p,{\delta }^{\ast }}\right)}=\underset{j\in \left\{1,2,\dots ,J\right\}}{\text{arg}\text{max}}\left(R_j^{\left(c\right)}{\text{log}}_2\left(M_j\right)\left|g_{k,l,p,{\delta }^{\ast }}\right.\right)$$ E13

In Eq. (11), Nⁱ _sub-c, N _cc, and N _RB are the number of optical subcarrier allocated to ONU i by OFDM-PON, the total number of wireless component carriers (CC) [15, 16] modulated onto a single optical subcarrier, and total number of wireless resource blocks (RB) carried by a single wireless component carrier (CC), respectively. The second term of polynomial in Eq. (11) should be larger than the summation of total UE minimum capacity requirement. Hence, a constraint of c^k _i,t can be further formulated as in Eq. (14),

$$\sum _{k=1}^K{c}_{i,t}^k\le E_{i,t}\le \sum _{l=1}^{N_{\mathrm{sub}‐\mathrm{c}}^i}{C}_l\left(\frac{1}{Q}{N}_{\mathrm{cc}}{N}_{\mathrm{RB}}\sum _{o=1}^Q{r}_{\mathrm{RB}}^{\left(o\right)}\right)-\sum _{\tilde{k}=1}^{\tilde{K}}{R}_{\tilde{k}}$$ E14

In the following allocation algorithm, we will satisfy all the constraints above to find a sharing capacity c^k _i,t for UE k from ONU i.

4) Interference constraint for UEs

In terms of the i-th the ONU/antenna pair, the constraint of γ^(n,y,t) _k, ${}_{\tilde{k}}$ is described in Eq. (15). It means that the number of same RB of CC allocated to different UEs on all the frames on the optical subcarriers has an upper limitation. Since γ^(n,y,t) _k, ${}_{\tilde{k}}$ is a binary indicator, Eq. (15) could be treated as two cases. First, when γ^(n,y,t) _k, ${}_{\tilde{k}}$  = 1, the same RB n of the y-th CC is allocated to UE k, and $\tilde{k}$ in slot t at different frames, the product of all the numbers of these RBs allocated to UE k and all the number of same RBs allocated to UE $\tilde{k}$ must be not larger than their arithmetic mean square, while the upper limitation of their arithmetic mean equals half of the number of total frames. Second, when γ^(n,y,t) _k, ${}_{\tilde{k}}$  = 0, any RB n of the y-th CC is not allocated to both UE k and $\tilde{k}$ in slot t at different frames; therefore, for all the number of RBs allocated to UE k and $\tilde{k}$ , their product must equal to 0 (i.e., without RB overlapping on the same time/frequency domain) as described in Eq. (15):

$$\begin{array}{l}\begin{array}{l}\begin{array}{l}\begin{array}{l}{\displaystyle \sum _{l=1}^{N_{Sub‐\text{c}}^i}}{\displaystyle \sum _{p=1}^{C_l}}{\sigma }_{k,l,p}^{\left(n\text{,}y\text{,}t\right)}\cdot {\displaystyle \sum _{l=1}^{N_{Sub‐\text{c}}^i}}{\displaystyle \sum _{p=1}^{C_l}}{\sigma }_{\tilde{k},l,p}^{\left(n\text{,}y\text{,}t\right)}\le {\gamma }_{k,\tilde{k}}^{\left(n\text{,}y\text{,}t\right)}\hfill \end{array}[\frac{1}{2}({\displaystyle \sum _{l=1}^{N_{Sub‐\text{c}}^i}}{\displaystyle \sum _{p=1}^{C_l}}{\sigma }_{k,l,p}^{\left(n\text{,}y\text{,}t\right)}+\hfill \end{array}\hfill \end{array}\hfill \\ {{\displaystyle \sum _{l=1}^{N_{Sub‐\text{c}}^i}}{\displaystyle \sum _{p=1}^{C_l}}{\sigma }_{\tilde{k},l,p}^{\left(n\text{,}y\text{,}t\right)})]}^2\le {\gamma }_{k,\tilde{k}}^{\left(n\text{,}y\text{,}t\right)}{\left[\frac{1}{2}\left({\displaystyle \sum _{l=1}^{N_{Sub‐\text{c}}^i}}{C}_l\right)\right]}^2,\forall k,\tilde{k},\forall y,\forall n,\forall t\hfill \end{array}$$ E15

Similarly, we hereby obtain the following constraint of γ^(n,y,t) _k,k′ as described in Eq. (16):

$$\begin{array}{l}\begin{array}{l}{\displaystyle \sum _{l=1}^{N_{Sub‐\text{c}}^i}}{\displaystyle \sum _{p=1}^{C_l}}{\sigma }_{k,l,p}^{\left(n\text{,}y\text{,}t\right)}\cdot {\displaystyle \sum _{l=1}^{N_{Sub‐\text{c}}^i}}{\displaystyle \sum _{p=1}^{C_l}}{\sigma }_{k^{\prime },l,p}^{\left(n\text{,}y\text{,}t\right)}\le {\gamma }_{k,k^{\prime }}^{\left(n\text{,}y\text{,}t\right)}\hfill \end{array}[\frac{1}{2}({\displaystyle \sum _{l=1}^{N_{Sub‐\text{c}}^i}}{\displaystyle \sum _{p=1}^{C_l}}{\sigma }_{k,l,p}^{\left(n\text{,}y\text{,}t\right)}+\hfill \\ {{\displaystyle \sum _{l=1}^{N_{Sub‐\text{c}}^i}}{\displaystyle \sum _{p=1}^{C_l}}{\sigma }_{k^{\prime },l,p}^{\left(n\text{,}y\text{,}t\right)})]}^2\le {\gamma }_{k,k^{\prime }}^{\left(n\text{,}y\text{,}t\right)}{\left[\frac{1}{2}\left({\displaystyle \sum _{l=1}^{N_{Sub‐\text{c}}^i}}{C}_l\right)\right]}^2,\forall k,k^{\prime },\forall y,\forall n,\forall t\hfill \end{array}$$ E16

4. Proposed resource sharing algorithm

In this section, we propose a heuristic algorithm for obtaining a sub-optimal solution because solving the objective in Section 3 is complex. A natural and simple approach to address the joint objectives of Eq. (5) is to treat it as a maximum flow and minimum cost problem about resource allocation (e.g., RB of CC) by assigning σ ^(n,y,t) _k,l,p , we defined for UE in each slot, approximately. We record and observe some historical information (e.g., h^k _j,t-1 and U ^k _j,t-1) as timely references and evaluations for finding a maximum flow (c^k _i,t ) subjected to the delay requirement (d ^k _i,t ) with minimum delay time from a set of $\mathcal{M}$  = {i|i = 1, 2,…, b,…, m} for UE k severed by ONU j. In the following sections, the sharing path assignment and resource allocation will be detailed in algorithm description by transferring the problem into graph theory.

4.1. Problem statement

• Given parameters:

  • G ( $\mathcal{V}$ , $\mathcal{E}$ ) where $\mathcal{V}$ is UE k and set of all ONUs and $\mathcal{E}$ is the set of resource sharing path through multiple ONUs to UE k

  • Matrix $\mathcal{C}$ _k,t  = [c^k _1,t ,…, c^k _i,t ,…, c^k _N,t ], ∀ k in $\mathcal{K}$ , c^k _i,t  > 0

  • Matrix $\mathcal{D}$ _k,t  = [d ^k _1,t ,…, d ^k _i,t ,…, d ^k _N,t ], ∀ i in $\mathcal{N}$ , ∀k in $\mathcal{K}$

  • Matrix $\mathcal{X}$ _i  = [χ_i (1,2),…, χ_i (k,k′),…, χ_i (K-1,K)]

  • Matrix $\mathcal{Y}$ _i  = [Y_i (k,1),…, Y_i (k, $\tilde{k}$ ),…, Y_i (k, $\tilde{K}$ )]

  • Set of UE in the cell: $\mathcal{K}$  = {k|k = 1, 2, $\dots$ , K}

  • Set of UE outside the cell: $\stackrel{=}{\mathit{K}}$  = { $\tilde{k}$ | $\tilde{k}$  = 1, 2, $\dots$ , $\tilde{K}$ }

  • Set of ONU: $\mathcal{N}$  = {i|i = 1, 2,…, b,…, N}

  • R_k,t : Minimum data capacity requirement for UE k

  • B_k,t : Allocated data capacity to UE k

Note that $\mathcal{X}$ _i and $\mathcal{Y}$ _i are two matrices which store UE conflict relationships.

• Objective:

  • Minimize the co-channel interference which is generated by sharing data received for the same angle UEs in their located cell and also in their adjacent cells.

  • Maximize the sharing capacity in terms of UEs.

  • Minimize the average delay of sharing data transmission by ONUs to satisfy UE requirement.

4.2. Algorithm description

The sharing algorithm tries to search the idle RBs over each optical subcarrier delivering to each cell and shares them to the UEs in the adjacent cells. From the sharing paths with minimum delay time, the algorithm selects the paths with maximum number of idle RBs for each UE so that it could maximize the sharing capacity for each UE. Consequently, the algorithm as a solution of optimization problem for our resource allocation model is suggested to be executed on the OLT side of optical back-haul. Considering the single UE k (k = 1, 2,…, K) which is accommodated by multiple sharing paths from different ONUs, UE k can receive the data from each sharing ONU i (i = 1, 2,…, N). The algorithm is divided into several steps as shown in Tables 1 , 2 , and 3 .

ALGORITHM 1 Real-time Sharing Algorithm (RTSA); <Note>:Algorithm 1 contains FUNCTION 1, 2 and 3

Input: Matrix $\mathcal{C}$ k,t = {c^k i,t |c^k 1,t ,…, c^k i,t ,…, c^k N,t ,∀ c^k i,t  > 0}; Matrix $\mathcal{D}$ k,t = {d^k 1,t ,…, d^k i,t ,…, d^k N,t }; Set of UE: $\mathcal{K}$  = {k|k = 1, 2, $\dots$ , K}; Set of ONU: $\mathcal{N}$  = {i|i = 1, 2,…, b,…, N}; Initialization: G k  = Ø for all k = 1, 2,…, K; G k : total RB set to UE k; While (Bk,t  < Rk,t ) do; STEP 1: Make a sharing graph G ( $\mathcal{V}$ , $\mathcal{E}$ ); $\mathcal{V}$  = {1,…, N}U{k} $,\mathcal{E}=$  {(i, k) | d^k i,t  ≤ Dk, }; Dk is a maximum tolerable delay(MTD).; STEP 2: Assign weights to $\mathcal{E}$ by matrix $\mathcal{D}$ k,t and sort the edges in $\mathcal{E}$ according to its weight in graph G ( $\mathcal{V}$ , $\mathcal{E}$ ) in an ascending order.; STEP 3: Find an edge (i, k) with minimum d^k i,t in the ascending order of; $\mathcal{E}$ as a current link (i, k) for resource sharing.; STEP 4: Bk,t  ← c^k i,t by allocating σ ^(n,y,t) k,l,p until Bk,t  ≥ Rk,t ,; otherwise, go to STEP 3; STEP 5: Traverse all UEs in set $\mathcal{K}$ to allocate resource satisfying,; i = argmin d^k i,t , Bk,t  ← c^k i,t , find c^k i,t employing; FUNCTION 1: form G k; End while; STEP 6: Traverse all ONUs in set $\mathcal{N}$ to allocate resources,; repeat STEPS 1–5.; STEP 7: Record historical information (e.g., h^k j,t and U^k j,t ) by FUNCTION 2; STEP 8: Update matrix $\mathcal{C}$ k,t , and matrix $\mathcal{D}$ k,t .; End; Out put: G k  = { C k (1), C k (2), C k (i), ……. , C k (N)}; End; FUNCTION 1: form G k, for any k; C k (i): a RB set from ONU i to UE k; Initialize G k  = { C k (1), C k (2), C k (i), ….. , C k (N)} = Ø, set Bk,t  ← 0.; 1: Find ONU i for current link(i, k), where i = argmin d ^k i,t , set p ← 1.; 2: Set l ← 1; l is layer (radio frame) indicator.; 3: Find the idle RB for any UE by FUNCTION 3,; where σ ^(n,y,t) k,l,p  = 0,∀k.; 4: Allocate a corresponding idle RB to UE k, put RB of σ ^(n,y,t) k,l,p  = 0 into set C k (i),; then for the UE k,σ ^(n,y,t) k,l,p  ← 1. Increase capacity Bk,t , where, $B_{k,t}=B_{k,t}+r_{\mathrm{RB}k,l,p}^{\left(n,y,t\right)}·$; 5: If Bk,t  ≥ Rk,t, break; r ^(n,y,t) RB k,l,p is the capacity of RB.; Else if ∀k,∀σ ^(n,y,t) k,l,p  = 1, i.e., the set of RBs on current layer have been occupied and cannot be scheduled to UE k for sharing, and if l ≤ L add l, go to STEP 3.; Else if p ≤ P max-sub, add p, go to STEP 2.; Else go to STEP 1.; End IF; 6: Output G k  = { C k (1), C k (2), C k (i), ……. , C k (N)}

Table 1.

Real-time sharing algorithm.

FUNCTION 2 Historical State Recording

1: Set ${h^k}_{i,t}=\sum _{p=1}^{N_{\mathrm{sub}‐\mathrm{c}}^i}\sum _{y=1}^{N_{\mathrm{cc}}}\sum _{n=1}^{N_{\mathrm{RB}}}{\sigma }_{k,p}^{\left(n,y,t\right)}\sum _{o=1}^Q{\mu }_{k,o}\cdot r_{\mathrm{RB}}^{\left(o\right)}$; 2: Set U^k i,t  = d ^k i,t; 3: For t from 1 to T, ∀k,i; 4: If h^k i,t  < h ^(min) k,t , then h ^(min) k,t  = h^k i,t; 5: If U^k i,t  > U ^(max) k,t , then U ^(max) k,t  = U^k i,t; End

Table 2.

Historical state recording function.

FUNCTION 3 Interference Mitigation; <Note>:This function addresses RB allocation according to UE conflict relationships

1: If χi (k, k′) = 0, ∀k, k′ and Yi (k, $\tilde{k}$ ) = 0, ∀k, $\tilde{k}$; Find any RB where σ ^(n,y,t) k,l,p  = 0, σ ^(n,y,t) k′,l,p  = 0, and σ ^(n,y,t) $\tilde{k}$ ,l,p  = 0 to allocate, for UE k; 2: Else if Yi (k, $\tilde{k}$ ) = 1, find RB where σ ^(n,y,t) k′ ,l,p  = 0 and σ ^(n,y,t) k,l,p  = 0 to allocate,; but refrain RBs where σ ^(n,y,t) $\tilde{k}$ ,l,p  = 1,∀l,p; 3:          Else if χi (k, k′) = 1, find RB where σ ^(n,y,t) $\tilde{k}$ ,l,p  = 0 and σ ^(n,y,t) k,l,p  = 0 to allocate,; but refrain RBs where σ ^(n,y,t) k′ ,l,p  = 1,∀l,p; End

Table 3.

Interference mitigation function.

In the first step, a dynamic sharing graph is generated, for instance, Figure 7(a) illustrates an example of a sharing tree that five ONUs share bandwidth resources to UE k. The rooted vertex represents UE k, and any leaf vertex i represents ONU i, respectively. Each edge represents a sharing path. In the second step, the weights of vertex and edge are assigned. For the data of UE k from ONU i, d^k _i,t denotes the overall delay on sharing path through ONU i to UE k in time slot t. c^k _i,t denotes the available sharing data capacity for UE k from ONU i in time slot t. For each time slot t, the weight of each leaf is h_i,kc^k _i,t . The weight of edge between the rooted vertex and any leaf vertex i is U_i,kd ^k _i,t , as shown in Figure 7(b) . Specifically, for t = 1, 2,…, T, we define h_i,k = min{hⁱ _k,t , h^k _j,t-1,…, h^k _j,1} and U_i,k = min{Uⁱ _k,t , U^k _j,t-1,…, U^k _j,1}, respectively.

Figure 7.

Wireless resource sharing logically on optical time/frequency blocks by different ONUs.

In the third step, the sharing path selection is performed by finding minimum delay time on each ONU. A sharing ONU combination could be found for UE k aiming to a minimum delay under its data rate demand.

In the fourth step, we allocate RB of CC to UEs in each ONU. Resource sharing for each UE (e.g., RB of CC) is executed by assigning σ ^(n,y,t) _k,l,p . Here, σ ^(n,y,t) _k,l,p is a binary variable to define whether or not the n-th RB of the y-th CC on the l-th radio frame on p-th optical subcarrier is assigned to the k-th UE in slot t for finding a proper c^k _i,t subjected to the minimum delay d ^k _i,t from a set of ONUs.

In the fifth step, the algorithm loops to another UE allocating RBs to it until all the UEs of current set have been finished. In the sixth step, the algorithm traverses all ONUs to finish the RB allocation. In the seventh step, we compute the capacity obtained by UE k by ONU i in slot t and its delay time. Then we compare them to the previous historical values and update the historical peak value in the case that the current one exceeds it. After executing these steps, the algorithm output the RB set allocated to UE k classifying into each subset of RB obtained by each sharing ONU individually.

To meet constrains of mathematical description in Section 3, we formulate three different functions in the heuristic algorithm herein as practical approaches to achieve the optimization. Function 1 is one solution to search idle RBs for resource sharing satisfying minimum optical wavelength cost. Function 2 addresses historical information recording and their updating. Function 3 finds idle RBs and allocates them according to different UE conflict relationships in order to mitigate co-channel interference, which will be focused to evaluate and discuss in the next section of this chapter.

5. Simulations and numerical results

5.1. Simulation parameters

In this section, we provide a deep evaluation for the proposed resource sharing approach on the performance of wireless UEs in the OFDM-PON system. The simulation and analytic evaluation mainly focus on the interference mitigation of mobile UEs in the cell under different mobility and times.

In the simulations, a RoF-OFDM-PON covering up to 256 cells assuming random UE mobility is deployed to evaluate our proposal as shown in Figures 8 and 9 . Optical subcarriers with per λ _i 10-Gb/s digital-equivalent data rate are adopted. LTE-like wireless resources carried on optical subcarriers are assigned to UEs corresponding to the scheduling solution in the well-known network simulator 3 (ns-3) [17], supporting the maximum five-carrier aggregation, simultaneously. MCS is assigned to UEs corresponding to Eqs. (12) and (13) by the scheduling in ns-3. The main simulation parameters are described in Table 4 .

Figure 8.

Scenarios of UEs and distributed antenna allocation in simulations with beamforming in the cluster of wireless cells.

Figure 9.

Scenarios of UE long-distance migration with position distribution for each UE by random model library (e.g., random waypoint) in simulations. (a) The aggregation of UEs at central cells. (b) The spreading of UEs to border cells.

Parameter	Value	Parameter	Value
LTE subcarrier; Resource block; RB carriers (N sub-c); RB OFDM symbols; UE received CCmax (z); Single CC length (m); BS TX power; Noise spectral density; Path loss (distance R), in dB	15 kHz; 180 kHz; 12; 7; 5; 100RB; 30 dBm; −174 dBm/Hz; 128.1 + 37.6lgR	Frame duration; TTI; UE date ratemin (Rk ); MCS(J); Bandwidth of CC; Testing MIMO per cell; Number of cell; Cell radius; SMF fiber distance	10 ms; 1 ms; 200 Mbps; 29; 20 MHz; 4 × 4; 256; 500 m; 20 km

Table 4.

Simulation parameters.

In the simulations, according to LTE-EPC model [18] in ns-3 simulator and with respect to its resource allocation models, we modify the scheduler significantly based on our proposed real-time sharing algorithm (RTSA). We evaluate the throughput performance of UEs by comparing RTSA with maximum throughput (MT) and proportional fair (PF) schemes [6, 19]. Note that for a fair comparison, we also modify the scheduler to serve multiple wavelength scheduling (i.e., multiple radio frames carried on one optical wavelength) since MT and PF themselves have no such functionality.

From the entire network perspective, the total UE number is set to 36,000 in simulations under different mobility ratios (a = number of mobile UEs/number of total UEs). We set a position for each UE with position allocator by model library of NS3 [17] (e.g., random waypoint). Meanwhile, we aim to simulate a difference specifically on UE mobility, for example, changing the residential position of UEs (e.g., migrate and recall UEs) within the scope of all cells regularly in different times. For instance, we define different mobility ratios of UEs equaling to 0.2 and 0.8, respectively.

5.2. Results and analysis on interference mitigation

Next, we observe the effect on interference mitigation under different UE mobility within different time slots by generating massive number of same angle UEs (the conflict UEs) in each beam direction. As an example, in Figure 10 we typically illustrate four windows of UE distribution states under random mobility in four different time slots, respectively. With the irregular movement of UEs, new UE conflict relationship will be generated randomly in terms of different antennas. For instance, in the time slot 1, UE k ₄ and k ₅ are located in different directions in terms of antenna 1. Simultaneously, UE k ₁ and k ₇ are located in the same direction for antenna 1 which have a conflict relationship with each other. However, in the time slot 2, a new UE conflict relationship is generated between UE k ₄ and k ₅, while UE k ₁ and k ₇ are located in different directions, and their conflict relationship disappears. Similarly, in a continuous time scope (e.g., 10 min) containing many more time slots, we then observe our proposed scheme in the aspect of interference reduction. We therefore evaluate the block error rate (BLER) of RTSA, PF, and MT under Gauss interference model in ns-3 model library so as to compare our proposed scheme with conventional schemes in terms of their effectiveness on interference mitigation. In simulations, BLER is observed under fair channel condition, for instance, the same level of signal power which is set by signal-to-noise ratio (SNR), and the SNR is obtained according to the parameters in Table 4 . In addition, we set random UE location and irregular mobility with the increase of time.

Figure 10.

A group of observations about interference with UE/antenna distribution under different time slots and UE movement when employing the proposed scheme. In (a)–(d), the dashed line represents the propagation scope of each antenna. The solid arrow line represents a link with a beam direction (the thick arrow line represents a link which has conflict UEs with the potential interference).

The change of BLER is observed under low mobility (a = 0.2) and high mobility (a = 0.8) cases, respectively. As shown in Figure 11 , RTSA has a lowest level of BLER than MT and PF, which also can be found in Figure 12 . This feature reflects that proposed RTSA has a benefit on BLER improvement. Compared with the results in Figures 11 and 12 , we could further observed that the level of BLER for a = 0.8 is larger than that in a = 0.2 and the fluctuation of BLER in different time is also obvious in terms of the case that a = 0.2. The reason for a higher level of BLER is that a higher mobility brings much more interference with the conflict UEs generated in each beam direction. Nevertheless, our proposed RTSA will still have a lowest BLER level even in the case of higher UE mobility.

Figure 11.

Comparisons of BLER under different time duration (mobility ratio 0.2).

Figure 12.

Comparisons of BLER under different time duration (mobility ratio 0.8).

6. Conclusions

This chapter investigates the resource sharing problems for future 5G cellular networks [20], which jointly employ distributed massive MIMO, beamforming, and OFDMA-based passive optical network supporting radio-over-fiber (RoF). We have shown the system and its physical transmission features to research reasonable solutions. With the assumptions based on physical features of system given in the chapter, we describe the problem with mathematical optimization for minimizing co-channel interference, etc. Since it is complex to get optimal results, then we heuristically formulate a real-time sharing algorithm as a practical solution. Simulation results also reveal that the proposed scheme is the most efficient at the interference mitigation compared to conventional schemes.