(PDF) Fronthaul-Aware Software-Defined Joint Resource Allocation and User Scheduling for 5G Networks

Fronthaul-Aware Software-Defined Joint Resource Allocation and User Scheduling for 5G Networks Chen-Feng Liu, Sumudu Samarakoon, and Mehdi Bennis Centre for Wireless Communications, University of Oulu, Finland E-mail: {cliu, sumudu, bennis}@ee.oulu.fi Abstract—Software-defined networking (SDN) is the concept fronthaul which negatively impacts the network performance. of decoupling the control and data planes to create a flexible Hence, the impact of fronthaul capacity and latency on the and agile network, assisted by a central controller. However, the network performance cannot be ignored, especially in highly- performance of SDN highly depends on the limitations in the fronthaul which are inadequately discussed in the existing litera- centralized SDN architectures. ture. In this paper, a fronthaul-aware software-defined resource The main contribution of this paper is to propose a allocation mechanism is proposed for 5G wireless networks fronthaul-aware SDN architecture for a network consisting with in-band wireless fronthaul constraints. Considering the of locally coupled small cell BSs. These BSs compete over fronthaul capacity, the controller maximizes the time-averaged limited resources to maximize their own throughputs while network throughput by enforcing a coarse correlated equilibrium (CCE) and incentivizing base stations (BSs) to locally optimize ensuring mobile users’ (MUs) quality-of-service (QoS) re- their decisions to ensure mobile users’ (MUs) quality-of-service quirements. Due to the time-varying environment and mutual (QoS) requirements. By marrying tools from Lyapunov stochastic interference coupling among BSs, the throughput maximiza- optimization and game theory, we propose a two-timescale tion problem is modeled as a stochastic game. In the SDN approach where the controller gives recommendations, i.e., sub- architecture, the central controller optimizes the weighted sum- carriers with low interference, in a long-timescale whereas BSs schedule their own MUs and allocate the available resources in log utility subject to a game theoretic equilibrium known every time slot. Numerical results show considerable throughput as coarse correlated equilibrium (CCE), and provides recom- enhancements and delay reductions over a non-SDN network mendations for BSs via an in-band wireless fronthaul. The baseline. reliability of the fronthaul is measured in terms of the signal- to-noise ratio (SNR) between the BS and the controller while I. I NTRODUCTION the cost of fronthaul is modeled in terms of a time penalty To satisfy the ever-increasing traffic demands in wireless as a function of the number of BSs and MUs. To reduce networks, small cell base stations (BSs) are deployed to the overhead in the fronthaul, we propose a two-timescale boost network capacity. However, due to frequency reuse in decomposition: optimization at the central controller in a long adjacent cells, signals from neighboring BSs result in severe timescale and decision making at BSs during a short timescale. co-channel interference. Although coupled BSs can coordinate Using tools from Lyapunov optimization, a low-complexity their transmissions by exchanging information [1], it incurs resource allocation and MU scheduling scheme is employed at high overhead in terms of latency, power cost, and allocated each BS. In the numerical results, we evaluate the performance bandwidth. In order to reduce the overhead of coordination, of the proposed SDN-aware resource allocation solution by the concept of software-defined networking (SDN) which comparing it to a non-SDN architecture. Furthermore, the decouples the control and data plane of networks has been impact of fronthaul reliability on the performance is studied considered [2]–[4]. Under current wireless SDN architectures, with the aid of the simulations. a central controller, having the global view of the network at the top of the hierarchy, makes control decisions and issues II. S YSTEM M ODEL recommendations to BSs at the lower-level of the hierarchy. We consider a downlink (DL) wireless network consisting of Thus, BSs are allowed to locally optimize their transmissions a set of locally coupled small cell BSs ℬ with frequency reuse following the controller’s recommendations without further factor 1. In this network, BS 𝑏 serves a set of MUs ℳ𝑏 , and coordination among neighboring BSs. In [5], Fu et al. consider each MU is associated with one BS only. A central controller a scenario in which wireless service providers (WSPs) bid coordinates these locally coupled BSs and communicates with for resources via a central controller on behalf of the sub- BSs via an in-band wireless fronthaul. We assume that all scribed users. The resource management is analyzed through network entities are equipped with single antenna and share a an auction process. In [6], a central controller schedules set of sub-carriers 𝒮 in the DL. Additionally, the considered users based on the WSP’s value function which relies on network operates in slotted time indexed by 𝑡 ∈ ℤ+ , and each other competitors’ private information. Additionally, the flow time slot is unit time for simplicity. In this regard, we refer to programmability of SDN under dense mobile environments 𝑇0 slots as one time frame ℱ and index the time frame by 𝑎 ∈ is studied in [7]. However, the above studies do not address ℤ+ in which ℱ(𝑎) = [(𝑎 − 1)𝑇0 + 1, ⋅ ⋅ ⋅ , 𝑎𝑇0 ]. Furthermore, (𝑠) (𝑠) the overhead induced by using a capacity-limited shared ℎ𝑖𝑗 ∈ ℋ𝑖𝑗 denotes the channel gain (including path loss and channel fading) from transmitter 𝑖 to receiver 𝑗 over sub- time with the mean 𝜆𝑏𝑚 > 0 and bounded above by a finite (𝑠) carrier 𝑠 where ℋ𝑖𝑗 is a finite set. Note that all channels are value 𝐴max , i.e., 0 ≤ 𝐴𝑏𝑚 (𝑡) ≤ 𝐴max . Since it is infeasible to independent and experience block fading over time slots. store data indefinitely, BSs need to ensure that queue buffers At the beginning of frame 𝑎, BS 𝑏 uploads its local infor- are mean rate stable, i.e., lim 𝔼 [∣𝑄𝑏𝑚 (𝑡)∣]/𝑡 = 0 for all 𝑡→∞ mation to the controller via the fronthaul by equally allocating 𝑏 ∈ ℬ, 𝑚 ∈ ℳ𝑏 . Note that satisfying queue stability is equiva- the power budget ∣𝒮∣𝑃 𝑏 over all sub-carriers. For a given lent to ensuring that the average serving rate is larger than the target fronthaul rate 𝑅U , the required time 𝜏𝑏U (𝑎) to upload mean arrival [8]. Therefore, the stability ∑ ∑𝑇 ∑ [ (𝑠) condition ] becomes, the information at BS 𝑏 ∈ ℬ satisfies, ¯ (𝑠) 𝑠∈𝒮 𝑅𝑏𝑚 = 𝑇lim 𝑡=1 𝑠∈𝒮 𝔼 𝑅𝑏𝑚 (𝑡) /𝑇 ≥ 𝜆𝑏𝑚 . Thus, ∑ ( (𝑠) ) →∞ 𝑃 𝑏 ℎ𝑏C (𝑎) as BSs compete one another over the limited resources to 𝑅U = 𝑠∈𝒮 𝜏𝑏U (𝑎) log2 1 + ∑ (𝑠) , (1) 𝑁0 + 𝑏′ ∈ℬ∖𝑏 𝑃 𝑏′ ℎ𝑏′ C (𝑎) maximize the average DL rate, they need to satisfy, where subscript C refers to the controller, and 𝑁0 is the noise ∑ ¯ (𝑠) ≥ 𝜆𝑏 = ∑ 𝜆𝑏𝑚 , ∀ 𝑏 ∈ ℬ. 𝑅 𝑏𝑚 (5) variance. To gather information from all BSs, the controller 𝑚∈ℳ𝑏 ,𝑠∈𝒮 𝑚∈ℳ𝑏 requires max𝑏∈ℬ {𝜏𝑏U (𝑎)} time slots. After manipulating the III. S TOCHASTIC G AME AMONG BS S acquired local information, the controller sends back recom- The competition among BSs over resources to maximize mendations to every BS 𝑏 with a target rate 𝑅D . Thus, the their utilities (in terms of rates) under queue and chan- time required for feedback 𝜏𝑏D (𝑎) for all BSs 𝑏 ∈ ℬ satisfies, ∑ ( (𝑠) ) ( uncertainties is) modeled as a stochastic game 𝒢 := nel 𝑅D = 𝑠∈𝒮 𝜏𝑏D (𝑎) log2 1 + 𝑃 C ℎC𝑏 (𝑎) (𝑠) . (2) ℬ, 𝒲, 𝒫, {𝑢𝑏 }𝑏∈ℬ among ∣ℬ∣ players/BSs. Here, 𝒲 and ∣ℬ∣𝑁0 +(∣ℬ∣−1)𝑃 C ℎC𝑏 (𝑎) 𝒫 are the state and action spaces of all players, while In (2), the controller equally allocates the available power 𝑢𝑏 : 𝒲 × 𝒫 → ℝ+ ∪ {0} denotes player 𝑏’s utility. In ∣𝒮∣𝑃 C to all BSs over all sub-carriers. Finally, aided by each time slot 𝑡, BS 𝑏 observes a random state realization (𝑠) the controller’s suggestions, BS 𝑏 serves its associated MUs 𝝎 𝑏 (𝑡) := (𝜏 (𝑎), ℎ𝑏𝑚 (𝑡), 𝑚 ∈ ℳ𝑏 , 𝑠 ∈ 𝒮) from the state in the remaining slots of frame 𝑎. It is assumed that sub- space 𝒲𝑏 .( Then, BS 𝑏 chooses a )transmit power vector, (𝑠) carriers are shared in both DL and fronthaul. To avoid P𝑏 (𝑡) := 𝑃𝑏𝑚 (𝑡), 𝑚 ∈ ℳ𝑏 , 𝑠 ∈ 𝒮 ∈ 𝒫𝑏 from its action { (𝑠) ∑ { (𝑠) } interference between the DL and fronthaul, BSs wait for space 𝒫𝑏 := P𝑏 𝑃𝑏𝑚 ∈ ℒ, 𝑚∈ℳ𝑏 𝕀 𝑃𝑏𝑚 > 0 ≤ 𝜏 (𝑎) = max𝑏∈ℬ {𝜏𝑏U (𝑎)} + max𝑏∈ℬ {𝜏𝑏D (𝑎)} time slots, i.e., ∑ (𝑠) } 1, 𝑚∈ℳ𝑏 ,𝑠∈𝒮 𝑃𝑏𝑚 ≤ ∣𝒮∣𝑃 𝑏 to serve its MUs. Here, 𝕀{⋅} is round trip time for the controller’s recommendations. Thus, the the indicator function. We define BS 𝑏’s utility 𝑢𝑏 (𝝎(𝑡), P(𝑡)) overhead of the fronthaul is 𝜏 (𝑎) which belongs to the finite as the expected DL rate with respect to the interference set 𝒯 , and 𝑇0 − 𝜏 (𝑎) time slots are left for DL transmission channels at the associated MUs which is given by, within frame 𝑎. It is assumed that the knowledge of 𝜏 and the ∑ [ (𝑠) ] perfect channel information of the signaling links are available 𝑢𝑏 (𝝎(𝑡), P(𝑡)) := 𝔼𝜾𝑏 𝑅𝑏𝑚 (𝑡) , (6) 𝑚∈ℳ𝑏 ,𝑠∈𝒮 at both the central controller and BSs. Moreover, BSs have full (𝑠) information of the direct links to the associated MUs. (𝑠) where 𝜾𝑏 := {ℎ𝑏′ 𝑚 , 𝑏′ ∈ ℬ∖𝑏, 𝑚 ∈ ℳ𝑏 , 𝑠 ∈ 𝒮} is In the DL transmission, BS 𝑏 serves MU 𝑚 with power 𝑃𝑏𝑚 the set of interference channel gains of ℳ𝑏 . Additionally, (𝑠) over sub-carrier 𝑠 in which 𝑃𝑏𝑚 ∈ ℒ = {0, 𝑃 𝑏 , ⋅ ⋅ ⋅ , ∣𝒮∣𝑃 𝑏 } 𝝎 := [𝝎 1 , ⋅ ⋅ ⋅ , 𝝎 ∣ℬ∣ ] ∈ 𝒲 is the global random state with ∑ (𝑠) and 𝑚∈ℳ𝑏 ,𝑠∈𝒮 𝑃𝑏𝑚 ≤ ∣𝒮∣𝑃 𝑏 . Each sub-carrier is used by 𝒲 := 𝒲1 × ⋅ ⋅ ⋅ × 𝒲∣ℬ∣ , and P := [P1 , ⋅ ⋅ ⋅ , P∣ℬ∣ ] ∈ 𝒫 is the the BS to serve one MU, but can be reused in other cells global control action with 𝒫 := 𝒫1 × ⋅ ⋅ ⋅ × 𝒫∣ℬ∣ . Furthermore, resulting in inter-cell interference. Considering the available Pr(P(𝑡)∣𝝎(𝑡)) is the mixed strategy of the stochastic game, time in the DL, i.e., 𝑇0 − 𝜏 (𝑎), the effective DL rate of MU and we focus on the mixed stationary and Markovian strategy 𝑚 served by BS 𝑏 over sub-carrier 𝑠 and time period 𝑡 ∈ ℱ(𝑎) Pr(P∣𝝎) in this work. Thus, the long-term time average is given by, expected utility of BS 𝑏 is given by, ( ) ∑ (𝑠) (𝑠) (𝑠) 𝑃𝑏𝑚 (𝑡)ℎ𝑏𝑚 (𝑡) ¯𝑏 = 𝑢 Pr(𝝎) Pr(P∣𝝎)𝑢𝑏 (𝝎, P). (7) 𝑅𝑏𝑚 (𝑡) = 𝑇0 −𝜏𝑇0 (𝑎) log 2 1+ ∑ (𝑠) (𝑠) . (3) 𝝎∈𝒲,P∈𝒫 𝑁0 + 𝑃𝑏′ 𝑚′ (𝑡)ℎ𝑏′ 𝑚 (𝑡) 𝑏′ ∈ℬ∖𝑏 For the purpose of allocating resources among BSs, the 𝑚′ ∈ℳ ′ 𝑏 controller acts as a game coordinator. According to BSs’ re- (𝑠) It can be noted that 𝑅𝑏𝑚 is bounded above by a maximal rate quirements (5), the controller provides suggestions for BSs. In 𝑅max due to the fact that the channel gains and transmit power order to incentivize BSs to follow the controller’s suggestions, are upper bounded. Moreover, each BS has queue buffers to the controller finds the strategy satisfying the CCE constraints. store the traffic arrivals for MUs from the core network. Let In this regard, we consider a more general case, i.e., the 𝜖- 𝑄𝑏𝑚 (𝑡) denote the data queue at the beginning of slot 𝑡 for coarse correlated equilibrium (𝜖-CCE) [9]. MU 𝑚 ∈ ℳ𝑏 which evolves as follows: { } Definition 1. The probability distribution Pr(P∣𝝎) is an 𝜖- ∑ (𝑠) 𝑄𝑏𝑚 (𝑡+1) = max 𝑄𝑏𝑚 (𝑡)− 𝑅𝑏𝑚 (𝑡), 0 +𝐴𝑏𝑚 (𝑡). (4) CCE if it satisfies, for some 𝜖 ≥ 0, 𝑠∈𝒮 ˜ 𝑏 , P̃𝑏 ) ≤ Pr(𝝎 ¯ 𝑏 (𝝎 𝑢 ˜ 𝑏 )𝜃𝑏 (𝝎 ˜ 𝑏 ), ∀ 𝑏 ∈ ℬ, 𝝎 ˜ 𝑏 ∈ 𝒲𝑏 , P̃𝑏 ∈ 𝒫𝑏 , (8) Here, 𝐴𝑏𝑚 (𝑡) is the data arrival for MU 𝑚 ∈ ℳ𝑏 during time ∑ slot 𝑡 which is independent and identically distributed over 𝑢 ¯𝑏 ≥ 𝝎𝑏 ∈𝒲𝑏 Pr(𝝎 𝑏 )𝜃𝑏 (𝝎 𝑏 ) − 𝜖, ∀ 𝑏 ∈ ℬ, (9) ∑ where 𝑢 ˜ 𝑏 , P̃𝑏 ) = ¯ 𝑏 (𝝎 𝝎∈𝒲,P∈𝒫∣𝝎 𝑏 =𝝎 ˜ 𝑏 Pr(𝝎) Pr(P∣𝝎) × information sent via fronthaul. Thus, the controller solves the 𝑢𝑏 (𝝎, P̃𝑏 , P−𝑏 ) is the conditional expected utility on the state modified problem of OP given by, ˜ 𝑏 . Here, 𝜃𝑏 (𝝎 𝑏 ) is the maximal utility BS 𝑏 can achieve at 𝝎 RP: ∑ ˆ ( ) state 𝝎 𝑏 when deviating from the strategy Pr(P∣𝝎). maximize 𝑏 𝜆𝑏 ln 1 + 𝑣 ˆ𝑏 P̂r𝑣 (P∣𝝎),𝜃ˆ𝑏 (𝝎 𝑏 ) IV. C ONTROLLER - ASSISTED R ESOURCE A LLOCATION subject to ˆ𝑏, 𝑣ˆ𝑏 ≥ 𝜆 ∀ 𝑏, AND U SER S CHEDULING 𝑣¯𝑏 (𝝎 ˜ 𝑏 )𝜃ˆ𝑏 (𝝎 ˜ 𝑏 , P̃𝑏 ) ≤ P̂r(𝝎 ˜ 𝑏 ), ˜ 𝑏 , P̃𝑏 , ∀ 𝑏, 𝝎 To ensure an 𝜖-CCE for the stochastic game among BSs, ∑ ˆ 𝑣ˆ𝑏 ≥ 𝝎𝑏 P̂r(𝝎 𝑏 )𝜃𝑏 (𝝎 𝑏 ), ∀ 𝑏, the controller solves the network utility maximization problem ∑ which is given by, P P̂r𝑣 (P∣𝝎) = 1, ∀ 𝝎, P̂r𝑣 (P∣𝝎) ≥ 0, ∀ 𝝎, P, OP: maximize 𝜙(¯ 𝑢1 , ⋅ ⋅ ⋅ , 𝑢 ¯∣ℬ∣ ) Pr(P∣𝝎),𝜃𝑏 (𝝎 𝑏 ) where P̂r𝑣 (P∣𝝎) is the strategy related to the auxil- subject to QoS requirement (5), iary utility 𝑣𝑏 and the estimated statistics P̂r(𝝎) = ∏ (𝑠) 𝜖-CCE constraints (8) and (9), P̂r(𝜏 ) 𝑏∈ℬ,𝑚∈ℳ𝑏 ,𝑠∈𝒮 P̂r(ℎ𝑏𝑚 ). Accordingly, we have 𝑣ˆ𝑏 = ∑ ∑ P∈𝒫 Pr(P∣𝝎) = 1, ∀ 𝝎 ∈ 𝒲, 𝝎∈𝒲,P∈𝒫 P̂r(𝝎)P̂r𝑣 (P∣𝝎)𝑣𝑏 (𝝎, P). Pr(P∣𝝎) ≥ 0, ∀ 𝝎 ∈ 𝒲, P ∈ 𝒫, Due to the fact that the objective and all the constraints ∑ ( ) in RP are concave and affine functions, respectively, RP where 𝜙(¯ 𝑢1 , ⋅ ⋅ ⋅ , 𝑢 ¯∣ℬ∣ ) = 𝑏∈ℬ 𝜆𝑏 ln 1 + 𝑢¯𝑏 is the network is a convex optimization problem. Owing to the fact that (𝑠) utility. In OP, 𝑢𝑏 and 𝑅𝑏𝑚 depend on the statistics of 𝜾𝑏 , i.e., analytically solving RP is not tractable, we resort to CVX, distributions of all interference channels, as per (3), (6), and a package for specifying and solving convex programs [10], ∗ (7). Since the MU has only the knowledge of the aggregate by numerically finding the optimal strategy P̂r𝑣 (P∣𝝎) of ∗ interference, estimating the distribution for each individual RP. Based on the strategy P̂r𝑣 (P∣𝝎), for each global state interference channel is impractical. To cope with this, an 𝝎 ∈ 𝒲, the controller generates 𝑇0 global action realizations auxiliary utility 𝑣𝑏 (𝝎, P) for BS 𝑏 is introduced as follows: P̌((𝑎 − 1)𝑇0 + 1), ⋅ ⋅ ⋅ , P̌(𝑎𝑇0 ). From all global states and ∑ 𝑇0 −𝜏 (𝑎) the corresponding global action realizations P̌(𝑡) for time slot 𝑣𝑏 (𝝎(𝑡), P(𝑡)) := 𝑇0 𝑡, there exists a mapping rule Ψ∗ (𝑡) : 𝒲 → 𝒫 describing 𝑚∈ℳ𝑏 ,𝑠∈𝒮 ( (𝑠) (𝑠) ) the above state-to-action relation, i.e., Ψ∗ (𝝎; 𝑡) = P̌(𝑡). × log2 1 + 𝑃 (𝑡)ℎ𝑏𝑚 (𝑡) ∑ 𝑏𝑚 (𝑠) (𝑠) , (10) Afterwards, the controller feeds {Ψ∗ (𝑡), 𝑡 ∈ ℱ(𝑎)} back to 𝑁0 + 𝑃𝑏′ 𝑚′ (𝑡)[ℋ𝑏′ 𝑚 ]max 𝑏′ ∈ℬ∖𝑏,𝑚′ ∈ℳ BSs. 𝑏′ With the knowledge of Ψ∗ (𝑡) and the observed 𝝎 𝑏 (𝑡), (𝑠) (𝑠) where [ℋ𝑏′ 𝑚 ]max is the maximal element in ℋ𝑏′ 𝑚 . BS 𝑏 obtains the suggested transmit action P̌𝑏 (𝑡) [11]. Al- Proposition 1. Let 𝑣¯𝑏 be the average auxiliary utility of BS 𝑏. though following the suggested P̌𝑏 (𝑡) assures data throughput Then, the mean rate stability in (5) is assured if 𝑣¯𝑏 ≥ 𝜆𝑏 , ∀ 𝑏 ∈ higher than the mean data arrival, it may suggest to schedule ℬ, is held. MUs considering only the channel quality neglecting their queues. Therefore, this transmission suggestion may result in Proof: Please refer to Appendix A. high latency. To remedy to this issue, instead of following Proposition 2. The CCE strategy with respect to 𝑣𝑏 (𝝎, P) is the suggested action, BS 𝑏 optimizes the transmit power an 𝜖-CCE with respect to 𝑢𝑏 (𝝎, P). over the recommended set of sub-carriers 𝒳𝑏 (𝑡) = {𝑠 ∈ ∑ 𝒮∣ 𝑚∈ℳ𝑏 𝑃ˇ𝑏𝑚 (𝑡) > 0} and schedules its MUs. Thus, uti- (𝑠) Proof: Please refer to Appendix B. lizing the available sub-carriers, BS 𝑏 maximizes the average Since 𝑣𝑏 is the lower bound of 𝑢𝑏 as in (16), Proposi- DL rate by scheduling the MUs ensuring their queue stability tions 1 and 2 state that finding a CCE with respect to 𝑣𝑏 in the remaining time slots of frame 𝑎. This is modeled as the maximizes the lower bound of the optimal solution of OP. following sub-problem: However, to solve OP, each BS requires the knowledge of the ∑ other BSs’ actions (i.e., P−𝑏 ) and their impact on 𝑣𝑏 (𝝎, P). SP: maximize 𝑅¯ (𝑠) 𝑏𝑚 P𝑏 (𝑡)∈𝒫𝑏 𝑚∈ℳ,𝑠∈𝒮 Since the MU has the ability to measure only the aggregate interference, estimating the impact of P−𝑏 on 𝑣𝑏 (𝝎, P) is subject to lim 𝔼[∣𝑄𝑏𝑚 𝑡 (𝑡)∣] → 0, ∀ 𝑚 ∈ ℳ𝑏 , 𝑡→∞ also impractical. To address this, we assume that the mapping (𝑠) 𝑃𝑏𝑚 (𝑡) = 0, ∀ 𝑡, 𝑚 ∈ ℳ𝑏 , 𝑠 ∈ / 𝒳𝑏 (𝑡), 𝑣𝑏 : 𝒲 × 𝒫 → ℝ+ ∪ {0}, ∀ 𝑏 ∈ ℬ, is known at the controller in advance. Additionally, to ensure 𝑣¯𝑏 ≥ 𝜆𝑏 , ∀ 𝑏 ∈ ℬ, and the which can be solved using dynamic programming. How- CCE, the controller needs Pr(𝝎) and all 𝜆𝑏 which in practice ever, dynamic programming suffers from high computational are unknown even at the BSs. Nevertheless, as time evolves, complexity. To cope with this complexity issue, we resort all the statistics can be empirically estimated by BSs. For to the tools in the Lyapunov optimization framework. Let notational simplicity, we denote the estimated state distribution Ξ𝑏 (𝑡) := {𝑄𝑏𝑚 (𝑡), 𝑚 ∈ ℳ𝑏 } be the combined queue at BS 𝑏. and mean data arrival as P̂r(𝝎) and 𝜆ˆ 𝑏 which are the uploaded The conditional Lyapunov drift-plus-penalty for slot 𝑡 is given by, Controller’s BS’s operation [ ∑ ] operation ˆ𝑏 , (𝑠) Initialize P̂r(𝝎 𝑏 ), 𝜆 𝔼 𝐿(Ξ𝑏 (𝑡+1))−𝐿(Ξ𝑏 (𝑡))− 𝑉 𝑅𝑏𝑚 (𝑡)Ξ(𝑡) (11) {𝑄𝑏𝑚 }, and {P̂r(𝐼𝑏𝑚 )} (𝑠) 𝑚∈ℳ𝑏 ,𝑠∈𝒮 for 𝑡 = 1 with a parameter 𝑉 ≥ 0 which decides the trade-off Upload P̂r(𝝎 𝑏 ) )2and queue stability, and 𝐿(Ξ𝑏 (𝑡)) = Yes between optimality ( ˆ𝑏 𝑡−1 ∈ ℕ? 1 ∑ Solve RP and 𝜆 Is 𝑇0 𝑚∈ℳ𝑏 𝑄𝑏𝑚 (𝑡) is the Lyapunov function. Using to the controller 2 No max{𝑥, 0} ≤ 𝑥2 , (11) can be simplified as follows, Send {Ψ∗ } Solve BP [ to BSs ∣ℳ𝑏 ∣∣𝒮∣2 𝑅max 2 ∣ℳ𝑏 ∣𝐴2max ∑ (11) ≤ 2 + 2 + 𝔼 𝑄𝑏𝑚 (𝑡) (𝑠) Update {𝑄𝑏𝑚 } and {P̂r(𝐼𝑏𝑚 )} 𝑚∈ℳ𝑏 ( ] ∑ (𝑠) ) ∑ (𝑠) × 𝐴𝑏𝑚 (𝑡) − 𝑅𝑏𝑚 (𝑡) − 𝑉 𝑅𝑏𝑚 (𝑡)Ξ(𝑡) . (12) Is 𝑡 ∈ ℕ? No 𝑡=𝑡+1 𝑇0 𝑠∈𝒮 𝑚∈ℳ𝑏 𝑠∈𝒮 Yes The solution to SP can be found by minimizing the upper ˆ𝑏 Update P̂r(𝝎 𝑏 ) and 𝜆 bound in (12) in every time slot [8]. Thus, relaxing the power constraint in SP, the MU scheduling problem during time slot Figure 1. Information flow digram of the two-timescale software-defined control approach. 𝑡 at BS 𝑏 becomes, ∑ if 𝝎 𝑏 (𝑡) = 𝝎˜ 𝑏 and 𝒳𝑏 (𝑡) = 𝒳˜𝑏 . Otherwise, BP: maximize (𝑄𝑏𝑚 + 𝑉 ) ( (𝑠) ) ( (𝑠) ) P̂r 𝐼˜ ; 𝑡 + 1∣𝝎˜ 𝑏 , 𝒳˜𝑏 = P̂r 𝐼˜ ; 𝑡∣𝝎 ˜ 𝑏 , 𝒳˜𝑏 . (𝑠) 𝑃𝑏𝑚 𝑚∈ℳ𝑏 ,𝑠∈𝒮 [ ( ) ] 𝑏𝑚 𝑏𝑚 (15) (𝑠) (𝑠) 𝑃 ℎ ×𝔼𝐼 (𝑠) ln 1 + 𝑏𝑚 𝑏𝑚 𝝎 , 𝒳 𝑁0 +𝐼𝑏𝑚 (𝑠) 𝑏 𝑏 Furthermore, the BS empirically updates the estimated state 𝑏𝑚 ∑ (𝑠) (𝑠) distributions of ℎ𝑏𝑚 and 𝜏 , and the mean arrival 𝜆𝑏 for the subject to 𝑃𝑏𝑚 ≤ ∣𝒮∣𝑃 𝑏 , 𝑚∈ℳ𝑏 ,𝑠∈𝒮 purpose of upload to the controller during frame (𝑎 + 1). (𝑠) The overheads in fronthaul depend on the amount of infor- 𝑃𝑏𝑚 ≥ 0, ∀ 𝑚 ∈ ℳ𝑏 , 𝑠 ∈ 𝒳𝑏 , (𝑠) mation which needs to be uploaded. Based on the cardinalities 𝑃𝑏𝑚 = 0, ∀ 𝑚 ∈ ℳ𝑏 , 𝑠 ∈ / 𝒳𝑏 . of sets of channels and waiting time along the mean arrivals, ∑ (𝑠) 𝑚∈ℳ𝑏 ,𝑠∈𝒮 ∣ℋ𝑏𝑚 ∣ + ∣𝒯 ∣ + 1 amount of Here, the expectation is over the conditional distribution of each BS uploads the( estimated aggregate ) interference in slot 𝑡, denoted by statistical values via the fronthaul. Thus, 𝑅U in (1) becomes (𝑠) ∑ (𝑠) P̂r 𝐼𝑏𝑚 ; 𝑡∣𝝎 𝑏 , 𝒳𝑏 . For simplicity, the time index 𝑡 is omitted ( 𝑚∈ℳ𝑏 ,𝑠∈𝒮 ∣ℋ𝑏𝑚 ∣ + ∣𝒯 ∣ + 1)𝑅unit , where 𝑅unit is the (𝑠) ∑ (𝑠) (𝑠) in the interference term 𝐼𝑏𝑚 = 𝑏′ ∈ℬ∖𝑏,𝑚′ ∈ℳ𝑏′ 𝑃𝑏′ 𝑚′ ℎ𝑏′ 𝑚 . required transmission rate to upload a single statistical value. Applying the KKT conditions, the feasible power allocation Moreover, assuming that all possible mapping rules Ψ are (𝑠)∗ 𝑃𝑏𝑚 , ∀ 𝑠 ∈ 𝒳𝑏 , is found by available at both the controller and BSs, the controller sends [ ( ) (𝑠) ] 𝑇0 real values representing the mappings {Ψ∗ (𝑡), 𝑡 ∈ ℱ(𝑎)}. 𝑄𝑏𝑚 + 𝑉 ℎ𝑏𝑚 𝔼𝐼 (𝑠) 𝝎 , 𝒳𝑏 = 𝛾𝑏 (13) Thus, 𝑅D in (2) becomes 𝑇0 𝑅unit . (𝑠) (𝑠)∗ (𝑠) 𝑏 𝑏𝑚 𝑁0 + 𝐼𝑏𝑚 + 𝑃𝑏𝑚 ℎ𝑏𝑚 Remark 2. The proposed software-defined approach operates [ (𝑠) ] (𝑄𝑏𝑚 +𝑉 )ℎ𝑏𝑚 (𝑠)∗ in two timescales. In the long timescale, BS 𝑏 uploads P̂r(𝝎 𝑏 ) if 𝔼𝐼 (𝑠) 𝝎 𝑏 , 𝒳𝑏 > 𝛾𝑏 , and 𝑃𝑏𝑚 = 0 otherwise. 𝑏𝑚 (𝑠) 𝑁0 +𝐼𝑏𝑚 ∑ and 𝜆 ˆ 𝑏 at each time frame. Based on the uploaded information, (𝑠)∗ Here, 𝛾𝑏 is chosen to satisfy 𝑚∈ℳ𝑏 ,𝑠∈𝒮 𝑃𝑏𝑚 = ∣𝒮∣𝑃 𝑏 . Fi- the controller finds the set of optimal CCE mapping rules nally, we search for the nearest (with respect to the Euclidean {Ψ∗ (𝑡)} and feeds them back to the BSs. In the short timescale, distance) P∗𝑏 in 𝒫𝑏 as the transmit power. i.e., at every time slot, BS 𝑏 schedules its MUs by solving BP. Remark 1. From (13), it can be observed that for small 𝑉 , BS The information flow diagram of the two-timescale 𝑏 has high priority to serve MU 𝑚 with a large queue 𝑄𝑏𝑚 . software-defined control approach is shown in Fig. 1. Analogously, for large 𝑉 , the BS allocates higher power to the MUs with better links. As such, the BS maximizes its DL V. N UMERICAL R ESULTS rate while allowing the queues of the MUs with worse links In this section, we validate the proposed solution for a to grow. network composed of two small cell BSs and two MUs per cell. For notation clarity, we refer to the BS and the two By the end of DL transmission in time slot 𝑡, MUs send MUs in the first cell as BS 1, MU 1, and MU 2 while for feedback of the aggregate interference to the BS. Then, the the second cell, BS 2, MU 3, and MU 4, respectively. We BS updates 𝑄𝑏𝑚 (𝑡 + 1) according to (4) and the estimated consider an indoor communication environment with the path interference statistics as follows: ∑𝑡 loss model 30 log 𝑑 + 20 log 2.4 + 46, where 𝑑 in meters is the ( (𝑠) ) 𝜉=1 𝕀{𝝎 𝑏 (𝜉)=𝝎 ˜ 𝑏 ,𝒳𝑏 (𝜉)=𝒳˜𝑏 } P̂r 𝐼˜𝑏𝑚 ; 𝑡 + 1∣𝝎˜ 𝑏 , 𝒳˜𝑏 = 1+∑ 𝑡 𝕀{𝝎 (𝜉)= ˜ 𝑏 ,𝒳𝑏 (𝜉)=𝒳˜𝑏 } 𝝎 distance between the transmitter and receiver [12]. At MUs 𝑏 𝜉=1 { (𝑠) } 1 and 3, the distances to the associated and interfering BSs ( (𝑠) ) 𝕀 𝐼 (𝑡)=𝐼 ˜(𝑠) × P̂r 𝐼˜𝑏𝑚 ; 𝑡∣𝝎˜ 𝑏 , 𝒳˜𝑏 + 1+∑𝑡 𝕀{𝝎𝑏𝑚(𝜉)=𝝎˜ 𝑏𝑚 ,𝒳 (𝜉)=𝒳˜ } (14) are 10 m and 40 m while at MUs 2 and 4, they are 20 m and 𝜉=1 𝑏 𝑏 𝑏 𝑏 30 m, respectively. Further, all wireless channels experience 3 7 2.9 6.5 6 2.8 5.5 2.7 5 Average rate (bit/s/Hz) Average queue (Mbit) 2.6 4.5 2.5 4 2.4 3.5 3 2.3 2.5 2.2 2 BS1, w/ SDN BS1, w/ SDN 2.1 BS2, w/ SDN BS2, w/ SDN 1.5 BS1, w/o SDN BS1, w/o SDN BS2, w/o SDN BS2, w/o SDN 2 1 0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100 Trade-off parameter V in the Lyapunov optimization Trade-off parameter V in the Lyapunov optimization Figure 2. BS’s average DL rate as 𝑉 varies. Figure 3. BS’s average queue as 𝑉 varies. Rayleigh fading with unit variance, and channel gains are 6 quantized into two levels. The time cost 𝜏 is quantized into w/ SDN w/o SDN two levels with 𝒯 = {0.25, 0.5}. Additionally, we assume 5.8 that the fronthaul SNR measured at the controller is 20 dB. V = 100 Time-averaged network sum rate (bit/s/Hz) 5.6 V = 50 Coherence time and the bandwidth in each sub-channel are V = 30 5.4 100 ms and 10 MHz, respectively. We consider Poisson data V = 20 arrival processes with mean values 𝜆11 = 𝜆12 = 8 Mbps 5.2 V = 10 and 𝜆23 = 𝜆24 = 5 Mbps. Moreover, 𝑃 1 = 𝑃 2 = 20 dBm, 𝑃 C = 25 dBm, 𝑁0 = −85 dBm, ∣𝒮∣ = 2, 𝑇0 = 10, and 5 𝑅unit = 0.25 log2 1.05 (bit/s/Hz). For performance compar- 4.8 ison, we consider a non-SDN scheme without the central 4.6 controller, and BSs do not communicate with each other. In this baseline, the BS solves BP without the available sub- V =0 4.4 carrier constraint, i.e., 𝒳𝑏 (𝑡) = 𝒮, ∀ 𝑡, 𝑏 ∈ ℬ, and 𝜏 = 0. 4.2 The impact of the trade-off parameter 𝑉 on the BS’s average DL rate and queue length for the proposed and baseline 4 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 schemes is illustrated in Fig. 2 and Fig. 3, respectively. Note Time-averaged network sum queue (Mbit) that the average queue length is proportional to the average Figure 4. Trade-off between the time-averaged sum rate and queue size. waiting time of a packet in the queue (i.e., 𝑄/𝜆) ¯ and thus, represents the average delay/latency. For small 𝑉 , Lyapunov Fig. 4 shows that increasing 𝑉 improves the rates with a price optimization aims at minimizing the average queues while of the latency which grows as 𝑉 increases. Therefore, 𝑉 = 50 for large 𝑉 , the focus is on maximizing the average rates. can be selected as the preferred trade-off parameter due to the Thus, the lowest queues can be observed at 𝑉 = 0 while fact that the cost of latency dominates the gains in rates for the highest rates can be seen at 𝑉 = 100 for both SDN values of 𝑉 > 50, for both schemes. For the choice of 𝑉 = 50, and non-SDN schemes. Furthermore, Fig. 2 illustrates that the the proposed SDN scheme yields about 8% gains in rates and proposed approach is aware of the traffic demands in which 19% reductions in latency over the non-SDN scheme. higher rates are ensured for BS 1 over BS 2 while the non- Finally, the impact of the fronthaul SNR on the throughput SDN scheme provides equal rates for both BSs. According to and latency on the proposed two-timescale SDN approach is Fig. 3, it can be noted that the SDN scheme maintains a lower shown in Fig. 5. Note that the non-SDN scheme has no impact queue length for the BS with high demands (BS 1) over the from the reliability of the fronthaul. For a low-quality fron- non-SDN scheme, i.e. a significant delay reduction for high thaul, the round trip time for the controller’s recommendations, traffic demands is ensured. Although there is no improvement 𝜏 , is larger than [𝒯 ]max , i.e., the maximum element in 𝒯 . in the latency of BS 2, the proposed scheme provides higher Therefore, BSs do not receive any recommendation even after rates compared to the non-SDN scheme. waiting [𝒯 ]max time slots and thus, cannot utilize their DL The trade-off between the time-averaged network sum rate transmission resulting lower rates and higher delay compared and the aggregate queue is illustrated in Fig. 4. It can be noted to the non-SDN scheme. As the fronthaul becomes reliable, that for a given target rate, the proposed SDN approach yields BSs obtain the recommendations with 𝜏 ≤ [𝒯 ]max . Thus, lower latency compared to the non-SDN scheme. Moreover, a significant improvement in throughputs can be observed. 6 12 A PPENDIX B Time-averaged network sum rate R̄ (bit/s/Hz) 5.8 11.6 P ROOF OF P ROPOSITION 2 Time-averaged network sum queue Q̄ (Mbit) 5.6 11.2 Let Pr𝑣 (P∣𝝎) be the CCE with respect to 𝑣𝑏 . Thus, from (8) and (9), it satisfies, 5.4 10.8 ˜ 𝑏 , P̃𝑏 ) ≤ Pr(𝝎 𝑣¯𝑏 (𝝎 ˜ 𝑏 )𝜃𝑏 (𝝎 ˜ 𝑏 ), (17) 5.2 10.4 ∑ 𝑣¯𝑏 ≥ 𝝎𝑏 Pr(𝝎 𝑏 )𝜃𝑏 (𝝎 𝑏 ). (18) 5 10 Furthermore, (16) can be rewritten as follows: 4.8 9.6 𝑢𝑏 (𝝎, P) = 𝑣𝑏 (𝝎, P) + 𝛿𝑏 (𝝎, P), (19) 4.6 9.2 with 𝛿𝑏 (𝝎, P) ≥ 0. Applying (19) to (17), it holds that, 4.4 R̄ w/ SDN 8.8 ∑ ∑ R̄ w/o SDN Pr(𝝎) Pr𝑣 (P∣𝝎)𝑢𝑏 (𝝎, P̃𝑏 , P−𝑏 ), 4.2 8.4 Q̄ w/ SDN ˜ 𝑏 P∈𝒫 𝝎∈𝒲∣𝝎 𝑏 =𝝎 Q̄ w/o SDN ( ) 4 8 ˜ 𝑏 ) 𝜃 𝑏 (𝝎 ≤ Pr(𝝎 ˜ 𝑏 ) + 𝜖 𝑏 (𝝎 ˜ 𝑏 ) = Pr(𝝎 ˜ 𝑏 )𝜂𝑏 (𝝎 ˜ 𝑏 ), (20) -10 -5 0 5 10 15 20 SNR (dB) where Figure 5. Time-averaged sum rate and queue size as the fronthaul SNR { { ∑ ∑ varies, 𝑉 = 100. ˜ 𝑏 ) = max 0, max − 𝜃𝑏 (𝝎 𝜖𝑏 (𝝎 ˜ 𝑏) + P̃𝑏 ∈𝒫 ˜ 𝑏 P∈𝒫 𝝎∈𝒲∣𝝎 𝑏 =𝝎 These gains in rates dominate the overhead in fronthaul and Pr(𝝎)Pr𝑣 (P∣𝝎) ( )}} thus, improve the overall latency. ˜ 𝑏) Pr(𝝎 𝑣𝑏 (𝝎, P̃𝑏 , P−𝑏 ) + 𝛿𝑏 (𝝎, P̃𝑏 , P−𝑏 ) , VI. C ONCLUSIONS ˜ 𝑏 ) = 𝜃 𝑏 (𝝎 and 𝜂𝑏 (𝝎 ˜ 𝑏 ) + 𝜖 𝑏 (𝝎 ˜ 𝑏 ) is an auxiliary variable. By In this paper, we propose a software-defined control mech- applying (16) and (20) to (18), anism for wireless networks with an in-band fronthaul. Here, ∑ ¯𝑏 ≥ 𝝎𝑏 ∈𝒲𝑏 Pr(𝝎 𝑏 )𝜂𝑏 (𝝎 𝑏 ) − 𝜖, 𝑢 (21) BSs compete over the wireless resources in both the DL and {∑ } fronthaul to maximize their utilities in terms of the average where 𝜖 = max𝑏∈ℬ 𝝎 𝑏 ∈𝒲𝑏 Pr(𝝎 𝑏 )𝜖𝑏 (𝝎 𝑏 ) . From (20) and DL rates under the uncertainties of queues and channel states. (21), we note that Pr𝑣 (P∣𝝎) is an 𝜖-CCE of 𝑢𝑏 (𝝎, P). Thus, the utility maximization problem is cast as a dynamic R EFERENCES stochastic game among BSs where a central controller with a [1] T. Chen, H. Zhang, X. Chen, and O. Tirkkonen, “SoftMobile: Control global view coordinates BSs via the fronthaul. Leveraging the evolution for future heterogeneous mobile networks,” IEEE Wireless timescale separation among the central controller and BSs, Commun., vol. 21, no. 6, pp. 70–78, Dec. 2014. the controller ensures a CCE in the network by providing [2] I. F. Akyildiz, P. Wang, and S.-C. Lin, “SoftAir: A software defined net- working architecture for 5G wireless systems,” Comput. Netw., vol. 85, recommendations for BSs in the long timescale while BSs no. C, pp. 1–18, Jul. 2015. serve MUs in the short timescale. The tools of Lyapunov [3] A. Gudipati, D. Perry, L. E. Li, and S. Katti, “SoftRAN: Software optimization are invoked to provide a low-complexity traffic- defined radio access network,” in Proc. ACM SIGCOMM Workshop on Hot Topics in Software Defined Networking, Aug. 2013, pp. 25–30. aware user scheduling algorithm at each BS. Simulation results [4] L. B. Le, V. Lau, E. Jorswieck, N.-D. Dao, A. Haghighat, D. I. Kim, yield throughput and latency enhancements over a non-SDN and T. Le-Ngoc, “Enabling 5G mobile wireless technologies,” EURASIP scheme. Furthermore, it is noted that the cost of overhead J. Wireless Commun. Netw., vol. 2015, no. 1, pp. 1–14, 2015. [5] F. Fu and U. Kozat, “Stochastic game for wireless network virtualiza- in fronthaul becomes negligible compared to the gains in tion,” IEEE/ACM Trans. Netw., vol. 21, no. 1, pp. 84–97, Feb. 2013. throughput and latency as the reliability of the fronthaul [6] X. Chen, Z. Han, H. Zhang, M. Bennis, and T. Chen, “Foresighted improves. resource scheduling in software-defined radio access networks,” in Proc. IEEE Global Conf. Signal Inf. Process., Dec. 2015, pp. 128–132. ACKNOWLEDGMENTS [7] I. Gasparis, U. C. Kozat, and M. O. Sunay, “Programming flows in dense mobile environments: A multi-user diversity perspective,” CoRR, This research was supported by TEKES grant 2364/31/2014 vol. abs/1506.07816, 2015. [8] M. J. Neely, Stochastic Network Optimization with Application to Com- and the Academy of Finland project CARMA. munication and Queueing Systems. Morgan and Claypool Publishers, Jun. 2010. A PPENDIX A [9] S. Perlaza and S. Lasaulce, “Game-theoretic solution concepts and P ROOF OF P ROPOSITION 1 learning algorithms,” in Mechanisms and Games for Dynamic Spectrum Allocation, T. Alpcan, H. Boche, M. L. Honig, and H. V. Poor, Eds. As the aggregate interference in 𝑣𝑏 is modeled by the Cambridge University Press, 2013, pp. 185–226. (𝑠) maximal interference channel gain [ℋ𝑏′ 𝑚 ]max , 𝑢𝑏 is lower [10] M. Grant and S. Boyd, “CVX: Matlab software for disciplined convex programming, version 2.1,” http://cvxr.com/cvx, Mar. 2014. bounded by 𝑣𝑏 , i.e., [11] M. J. Neely, “A Lyapunov optimization approach to repeated stochastic games,” CoRR, vol. abs/1310.2648, 2013. 𝑢𝑏 (𝝎, P) ≥ 𝑣𝑏 (𝝎, P), ∀ 𝝎 ∈ 𝒲, P ∈ 𝒫. (16) [12] R. C. S. of ITU, “P.1238-8: Propagation data and prediction methods for the planning of indoor radiocommunication systems and radio local Taking the expectation of (16) with respect to Pr(𝝎) Pr(P∣𝝎) area networks in the frequency range 300 MHz to 100 GHz,” ITU-R, ∑ ¯ (𝑠) ≥ 𝜆𝑏 . and applying 𝑣¯𝑏 ≥ 𝜆𝑏 , we obtain 𝑚∈ℳ𝑏 ,𝑠∈𝒮 𝑅 𝑏𝑚 Tech. Rep., Jul. 2015.