Delay-Based User Association in Heterogeneous Networks with Backhaul

Wenchao Xia, Jun Zhang,, Shi Jin, Hongbo Zhu,＊

1 Jiangsu Key Laboratory of Wireless Communications, Nanjing University of Posts and Telecommunications, Nanjing 210003, China

2 National Mobile Communications Research Laboratory, Southeast University, Nanjing 210096, China

* The corresponding author, email: hbz@njupt.edu.cn

I. INTRODUCTION

With more and more devices, sensors, vehicles, and machines connected to the Internet,the Internet of things (IoT) comes into people’s lives and plays an important role [1].Many emerging IoT applications including autonomous driving, infrastructure monitoring, vehicular communication, tele-medicine,and smart grid improve the quality of people’s lives but also bring some new challenges to future communication networks [2]. For example, tele-medicine and infrastructure monitoring pose a demand for low-latency output.Large delay degrades the user experience and even causes economic losses, thus delay is a significant issue which must be paid more attention.

Besides, to fulfill the requirement of data rates, a growing number of small cells are embedded into conventional cellular networks forming heterogenous networks (HetNets).However, dense deployment of small cells makes the design of backhaul more difficult.For example, the locations of some smallcell base stations (SBSs) are hard to reach for conventional fiber links, such as street level or lamp posts, therefore the combination of different backhaul technologies, wired and wireless, is considered as a viable solution [3].Wired backhaul including fiber and xDSL can provide high capacity and high reliability with high deployment cost, and wireless backhaul including millimeter wave (mmWave) and sub-6G can provide cost-effective but capacity-limited alternatives [4]. By making full use of the advantages of both, heterogenous backhaul can also improve the economic benefits and energy efficiency of HetNets [5].

When IoT applications meet HetNets, some traditional problems, such as user association,resource allocation, and interference management, need rethinking, because delay issues emphasized by IoT applications and heterogeneity of backhaul in HetNets should be taken into account. For user association, a lot of schemes to solve user association problem have been investigated in previous papers [6-16]. The nearest base station (BS) association algorithm as a common baseline was used in[6]. Cell association based on signal-to-interference-plus-noise ratio (SINR) resulted in load imbalance [7]. To alleviate this problem,cell range extension of small cells via biasing method was used in [8]. [9] proposed a distributed algorithm with low complexity through dual decomposition, which converged to a near-optimal solution. Furthermore, a coupled association problem with resource allocation was considered in [10]. However, there are a few papers taking the delay issue into consideration to optimize user association problem.A novel backhaul-aware approach to interference management was proposed in [17], which enabled a non-cooperative game among users that optimized their delay-rate tradeoff by exploiting the presence of neighboring SBSs.[18] presented a distributed backhaul-aware load balance algorithm for user association in HetNets to maximize the network-wide achievable spectrum efficiency, while satisfying given delay and reliability constraints. In[3] bias value was optimized to minimize the network delay. Encouraged by this fact, we formulate a delay-addressed user association problem.

In this paper, we consider the user association problem where the delay issue is addressed in HetNets with different backhaul technologies. It’s assumed that the SBSs which are near to the macro-cell base station (MBS)are connected to the MBS with mmWave backhaul but the SBSs that are in the farther area choose fiber links as their backhaul. The packet delay concerned in this paper, from the MBS to the user terminals (UTs), includes the processing time in each node and the transmission time of each hop in case of retransmissions caused by decoded-and-forward scheme[3]. In general, the main contributions of this work include the following two aspects.

● Firstly, we propose a novel model where mmWave and fiber links cooperatively serve as backhaul in HetNets which can provide high-capacity and economic backhaul links for UTs and formulate the corresponding user association problem to minimize the total delay of all UTs.

● Secondly, user-association algorithms for active mode and mixed mode are designed respectively considering different operation modes of BSs. The total delay depending on the probability of successful transmission, the number of UTs, and the number of SBSs can be decreased significantly by the proposed algorithms according to the simulation results.

The remainder of this paper is organized as follows. In Section II, the system model is presented and the delay model including backhaul delay and radio access delay is provided in Section III. In Section IV, algorithms for active mode and mixed mode are proposed,whose performances are simulated and compared in Section V. Finally conclusions are drawn in VI.

We formulated the optimal problem aiming to minimize the total delay of all UTs and proposed mutual selection and multi-candidate-mutual-selection algorithms for active mode and mixed mode respectively.

II. SYSTEM MODEL

We consider a two-tier HetNet where an MBS is located at the centre of the macro tier with radius R and a large number of second-tier SBSs belonging to the set S=…{1,2,,}S are distributed uniformly within the radiated area of the MBS. We use index 0 to indicate the MBS and thus the set S0=S ∪{0} includes all BSs in the HetNet. Massive single-antenna UTs in the set K={1,2,…,K} are distributed uniformly over the coverage area of the MBS. All BSs in the HetNet are equipped with only one antenna, which does not lose generality and can be easily extend to the multiple-antenna scenarios [19]. We assume the SBSs are connected to the MBS via different backhaul links. More Specifically, if the distance between SBS i∈S and the MBS,denoted as ri, meets the constraint R1≤ri＜R2(0＜R1＜R2＜R), then SBS i is connected to the MBS via a mmWave link. But if R2＜ri＜R, it is connected to the MBS via a fiber link, shown as figure 1. It’s assumed that there is no SBS closer the MBS than R1.

Such deployment can provide high backhaul-capacity for UTs because mmWave links with highly directional antenna array can be modeled as pseudo-wired and noise-limited and mmWave spectrum have spacious bandwidth. However, high frequency in mmWave band leads to one hop transmission can reach out only 100-200 m [20]. Therefore, we use mmWave backhaul to replace fiber backhaul for those SBSs which are close to the MBS to improve economic efficiency without performance loss.

Fig. 1 A two-tier HetNet with different backhaul links

We denote the set of the SBSs connected to the MBS via wireless backhaul (i.e., mmWave links) as S1and the set of other SBSs which are connected via wired backhaul (i.e., fiber links) as S2, S1∪S2=S .

We introduce a binary variable xij∈{0,1}as an indicator of cell association status of UT j∈K with BS i∈S0, where xij=1 represents association. The set of UTs served by BS i is expressed as Kiwith cardinality ki=|Ki|. It is also assumed that each UT can be served by only one BS in S0at the same time,

Given that SBSs have active and sleep modes. Specifically, the RF equipment of an SBS radiates in the former mode causing interference to other SBSs, but it does not work in the latter mode. We also use a binary variable indicator aito represent the mode of SBS i∈S where ai=1 indicates the active mode and ai=0 represents the sleep mode. The MBS is always active to guarantee the ubiquitous coverage for UTs outside active small cells and provides backhaul links for active SBSs.

III. DELAY MODEL

We consider a downlink scenario where the packet delay stems from the process from the MBS to the UTs, generally composed of transmission delay, prorogation delay along links,and the processing delay at nodes (BSs in this work) [3,21].

In what follows packet delay is separated into two parts, backhaul delay (from the MBS to the SBSs) and radio access delay (from the SBSs to the UTs) for convenience of analysis.

3.1 Backhaul delay

Because of large capacity and high reliability, the prorogation and transmission delay of wired backhaul can be ignored, compared with the process time at the MBS. Thus only the processing delay is considered into wired backhaul. However, the decode-and-forward scheme leads to retransmission when the SINR is below the required value, which brings wireless backhaul transmission delay.

1)Wired Backhaul: As mentioned above,only processing delay at the MBS is considered. The delay in routers and switches has been investigated using different distributions,e.g., Gaussian, Gamma, Pareto, and Weibull distributions in previous papers [22-24]. In this work, we model the processing delay at the MBS as a Gamma distribution [3],Γ(cκ0,λ0+χ0u0), thus the mean packet delay at the MBS T0is given as

where t0=κ0(λ0+χ0u0), c is the number of active SBSs connected to the MBS, the constants κ0, λ0and u0are the parameters suggesting the processing capability of the MBS,and χ0is the packet size. Therefore, the wired backhaul delay of SBS i∈S2is denoted as

2)Wireless Backhaul: We assume that wireless transmission is time slotted and the transmission of one packet in each time slot succeeds if and only if the received SINR is beyond a pre-determined threshold θ [25].Due to highly directive narrow beamwidth,mmWave links are thought as pseudo-wired and noise-limited rather than interference-constrained [26]. We model the path loss in mmWave line-of-sight links like [20]

where ς～N(0,ν2) with ν2being the lognormal shadowing variance in dB and riis the distance between the MBS and SBS i. The transmission succeeds when the received signal-to-interference ratio meets the constraint

where PTis the transmit power in dB, WMrepresents the mmWave bandwidth, and σ2denotes noise power density.

The success probability of a transmission of mmWave backhaul is given as

The wireless backhaul delay of SBS i∈S1including the processing delay at the MBS and the transmission delay along the link between SBS i and the MBS is calculated by

where τMis the time slot length. For convenience of expression, we denote wired and wireless backhaul delay into a uniform form

where tiis given as

3.2 Radio access delay

The MBS and SBSs share the same radio access spectrum and UTs can associate with them depending on specific schemes.

where Psis the transmit power of BS s, hsjis the channel gain from BS s to UT j which follows an exponential distribution with unit mean, lsjis the distance from BS s to UT j,α＞2 is the path loss exponent and W is the access bandwidth.

1) MBS-association Delay: We first assume that UT j is associated with the MBS, i.e.,s=0. Without loss of generality, we assume the abilities of MBS processing backhaul data and access data are equivalent. Thus the time for processing UT j’s downlink data is

where k0is the number of UTs associated with the MBS.

Lemma 1. The total radio access delay for UT j that is associated with the MBS is

where τ0is the time slot length of MBS access links and

proof: With (9), we obtain the probability of a successful downlink transmission in the radio access network as

where the second equation holds because Isjis a function of random variables hij’s, and the third and last equations are computed using the fact hij～exp(1),∀i ∈S0. Typically when UT j is associated with the MBS, The corresponding success probability p0jcan be derived by setting s=0 in (13). Therefore, the average number of transmissions of a packet from the MBS to UT j is 1/p0j.

Given the number of UTs associated with the MBS k0and the length of time slot τ0, in order to avoid intra-cell interference, the UTs associated with the same BS are served in turn, consequently the average number of time slots needed to transmit a packet successfully is

which multiplied by τ0, leads to the transmission delay τ0N. Finally, the MBS-association delay is a sum of the processing delay and the transmission delay.

2) SBS-association Delay: Then, UT j is assumed to select SBS s∈S as its serving BS.The processing delay at the SBS s is

Lemma 2. The total radio access delay for UT j that is associated with SBS s is

where τ1is the time slot length of SBS access links and psjis given as （13）.

proof: Similar to the proof of Lemma 1.

For ease of notation, we rewrite radio access delay of MBS-association and SBS-association into a unified form

Based on the aforementioned results, the total downlink delay of UT j is obtained as

IV. ASSOCIATION ALGORITHM

In this section, we first formulate the UT association problem and then propose algorithms to solve it in different cases.

The association problem aiming to find the optimal set of xij’swhich minimizes the total delay of the downlink network is formulated as

where the first constraint in (20) means any UT can associate with one and only one active BS. Because of the high capacity of fiber and mmWave links, we assume that the backhaul links can transmit all traffic from the SBSs to the MBS without capacity constraint. We also assume the UTs (e.g., sensors in IoT applications) are not sensitive to transmission rate.Although we do not take the rate constraint for the UTs into account, the achievable rates of the UTs have an implicit relation with the delay we aim to minimize because the larger probability of downlink (backhaul) transmission, brings the smaller access (backhaul)delay, and also results in the larger achievable access (backhaul) rate on average.

The optimization problem in (20) is a nonlinear integer programming whose optimal solutions are hard to find. Therefore, two heuristic algorithms are designed in this paper to find sub-optimal solutions to minimize the total delay.

We consider the aforementioned association problem in two different cases: 1) All SBSs work in active mode, regardless of whether they are serving UTs; 2) only if an SBS has one or more associated UTs, it operates in active mode, otherwise in sleep mode. We refer to such two cases as active mode and mixed mode. Note that the MBS always keeps radiating over the coverage area in two modes.

4.1 Algorithm for active mode

In active mode, all SBSs are in active mode,i.e., ai=1,∀i ∈S , then c=S. For convenient expression, we define

where the first part is a sum of the delay of all the UTs including UT j associated with BS i.∆ij,is the incremental portion when UT j acts as a candidate of Ki. The algorithm for active mode is shown as Algorithm 1.

In this algorithm, UT j selects BS i which makes the incremental portion ∆i,jminimal as its candidate serving BS from S0, then BS i selects UT j′which makes the incremental portion ∆i,j′

minimal as its potential serving object from the unserved UT set K. If j′=j,we think UT j matches well with BS i and UT j is laid in the UT set Kiserved by BS i, otherwise such mutual-selection (MS) process is repeated until all UTs are served, i.e.,Note thatis updated at the end of each while loop. This algorithm aims to minimize the increased delay brought by a new access UT via MS procedure and thus we refer to it as MS algorithm.

4.2 Algorithms for mixed mode

In mixed mode, we assume an SBS works in active mode only when at least one UT is associated with it. Such constraint is expressed in mathematical terms:

1) Distance-based Algorithm for Mixed Mode: For comparison, we first propose a baseline algorithm based on distance for mixed mode, shown as Algorithm 2. In step 1, each UT is associated with its nearest BS respectively and those SBSs that have no UT to serve are turned into sleep mode. And then in step 2, the SBSs serving less than KCUTs,regarded as “inefficient” SBSs, are checked and determined whether or not to turn them into sleep mode and transfer their UTs to other SBSs as [28]. More specifically, after step 1 where each UT is associated with their nearest BS leading to the total delay D, the SBS which has the least number of UTs is assumed to be turned into sleep mode and its UTs are assumed to be re-associated to their nearest BSs. Next, we re-calculate the total delay denoted asand compare it with D. IfD＜D,we make the aforementioned assumption a reality and update relevant sets, otherwise the above process is repeated until all “inefficient”SBSs are checked. We describe this algorithm as distance-based (DB) algorithm.

The most important improvement of system performance via DB algorithm results from the fact that turning interfering SBSs into sleep mode reduces interference to the serving SBSs especially when many free SBSs (i.e.,SBSs which have no UT to serve) and a few busy SBSs (i.e., SBSs which have at least one UTs to serve) coexist. In addition, step 2 in DB algorithm can further reduce the total delay. However, limited to step 1 where each UT is simply connected to its closest BS, there are still potential for reducing the system delay.Therefore, we subsequently propose another algorithm for mixed mode.

2) MS-based Algorithm for Mixed Mode:Next, we propose a multi-candidate-mutual-selection (MCMS) algorithm for mixed mode, shown as Algorithm 3, based on the MS algorithm introducing sleep mode for SBSs.

In step 1, we find candidate BSs for each UT according to large-scale fading coefficients and map the relation to the matrix B.On specifics, ifwhere lijis the distance between UT j and its nearest BS i and ξ∈[0,1] is a predefined constant, BSwould be a candidate serving BS of UT j and such relation would be recorded in the binary matrix. In other word, the element B(i′,j)=1 represents BSis the candidate BS of UT j.

Then in step 2, global candidate BSs for the whole network are found out and composes a set. According to their weighting factorsthe SBS with high weighting factor is reserved and keep into the setS.Such process is repeated until each UT has at least one candidate BS in the set S and then turn those SBSs out of S into sleep mode.

Algorithm 1 is applied to the set of global candidate BSs S and the set of UTs K in step 3, to find the serving BSs for each UT. Finally in step 4, we find and check the “inefficient”SBSs, which is the same as step 2 in Algo-rithm 2.

Note that the predefined threshold ξ introduced in step 1 triggers a non-trivial tradeoff:1) The smaller ξ is, the more BSs are in candidate BS set; typically when ξ=0, all BSs are candidate BSs of each UT, thus a UT is likely to select a far BS as its serving BS and the system performance is degraded; 2)but when ξ is too large, typically ξ=1, the MCMS algorithm is degenerated into DB algorithm because only the nearest BS is in the candidate BS set. In this paper, we setas [28] where ξ0is the predefined minimum value of ξ which can avoid the far SBSs being selected and lijis the distance between UT j and its nearest BS i.

V. SIMULATION RESULTS

In this section, we examine the performance of proposed association algorithms for the downlink scenario in a two-tier HetNet. We assume S SBSs and K UTs are independently distributed within the coverage of the MBS with R=500 m. There is no UT is closer to the MBS than 50 m and there is no SBS is closer to the MBS than R1=100 m. Considering one hop of mmWave links being about 100-200 m, we let R2=200 m. The length of the time slot and the bandwidth of mmWave backhaul are τM=5 us and WM=200 MHz respectively. The parameters of power consumption are given as PT=30 dBm, P0=47 dBm, and Pi=30 dBm, ∀∈iS, and the noise power spectral density is σ2=−174 dBm/Hz. It is assumed that the path loss exponent is α=3.5 and the standard deviation of shadow fading ν=5. The time slot and bandwidth for radio access network are τ0=τ1=5 us, and W=20 MHz respectively. The SINR threshold is set as θ=2.

The parameters of processing delay are given as λ0=λ1=10 us, u0=u1=0.01 us/bit,κ0=10, and κ1=1. Furthermore, we assume that

which ensures different backhaul technologieshave the same bits in a packet [3]. Finally we set

Algorithm 3 MCMS algorithm for mixed mode.

For comparison, we also introduce a baseline scheme called nearest-BS association(NA) for active mode, where each UT is associated with its nearest BS.

Fig. 2 Total delay versus the number of UTs with S1=8 and S2=16

Fig. 3 Total delay versus the number of SBSs with K = 10

Figure 2 shows the sum of all UTs’ delay obtained by the proposed algorithms and NA algorithm versus the number of UTs with the condition that S1=8 and S2=16. It is suggested that the total delay of all UTs increases with different rates as the number of UTs rises. The performance of MCMS algorithm is the best and that of NA algorithm is the worst.It’s interesting to find that the total delay of MS algorithm is even smaller than that of DB algorithm in large K range, because more UTs need more SBSs in active mode, less SBSs can be turned into sleep mode in DB algorithm. In general, algorithms based on the MS scheme between BSs and UTs (i.e., MS and MCMS)are better than those based on distance (i.e.,NA and DB). And algorithms for mixed mode(i.e., DB and MCMS) are better than those for active mode (i.e., NA and MS) when the number of UTs is in small K range.

In figure 3, we present the total delay of all UTs versus the number of SBSs S with the assumption that S2=2S1and K=10 in four cases. It is observed that the total delay of algorithms for active mode (i.e., NA and MS)increases with the growth of S due to more interference caused by more SBSs to UTs.However, the total delay of algorithms for mixed mode (i.e., DB and MCMS) decreases with the growth of S because more available SBSs bring more choices. Therefore, when S is large enough, algorithms for mixed mode show better performance than those for active mode, which is consistent with the conclusion drawn from figure 2. Also, algorithms based on MS scheme leads to less delay than those based on distance.

As observed from figure 2 and 3, MS and MCMS algorithms improve the system performance, but the complexity of computation is aggravated typically when and are large. To alleviate the complexity, we can divide the UTs and BSs into subsets respectively, and then we can apply the proposed algorithms in subsets to find sub-optimal solutions.

Finally, given the total number of the SBSs S=12, we change the ratio of S1and S2and investigate the effect of it in figure 4, which suggests that the delay of NA and DB algorithms increases with the growth of the ratio of S1and S2because more SBSs with wireless backhaul cause more backhaul delay. However, such an obvious effect is alleviated in MS and MCMS algorithms mainly due to MS process.

VI. CONCLUSION

In this paper, we have studied the user association problem from the view of delay in a two-tier HetNet where the small cells overlapped the macro cell. MmWave links were used to provide high-capacity backhaul for SBSs in the area near to the MBS due to its short distance of one hop transmission, while fiber links were responsible for transmitting the data from SBSs which were far from the MBS, to the core network. We formulated the optimal problem aiming to minimize the total delay of all UTs and proposed MS and MCMS algorithms (DB algorithm was a baseline for MCMS algorithm) for active mode and mixed mode respectively. Simulation results suggested that compared with distance-based algorithms, algorithms based on MS scheme between BSs and UTs had less delay. It was also observed that algorithms for mixed mode showed better performance than those for active mode when the number of BSs is large enough with respect to the number of UTs.

ACKNOWLEDGMENT

This work of W. Xia, J. Zhang, and H. Zhu was supported by the National Natural Science Foundation of China (NSFC) under Grants 61427801 and 61671251, the Natural Science Foundation Program through Jiangsu Province of China under Grant BK20150852,the open research fund of National Mobile Communications Research Laboratory, Southeast University under Grant 2017D05, China Postdoctoral Science Foundation under Grant 2016M590481, and Jiangsu Planned Projects for Postdoctoral Research Funds under Grant 1501018A. The work of S. Jin was supported by NSFC under Grants 61531011 and 61625106.

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