Practical Scheduling Algorithms with Contiguous Resource Allocation for Next-Generation Wireless Systems
11 Practical Scheduling Algorithms with ContiguousResource Allocation for Next-Generation WirelessSystems
Shu Sun and Sungho Moon
Abstract —This paper proposes three novel resource and userscheduling algorithms with contiguous frequency-domain re-source allocation (FDRA) for wireless communications systems.The first proposed algorithm jointly schedules users and re-sources selected adaptively from both ends of the bandwidthpart (BWP), while the second and third ones apply disjoint userand resource selection with either single-end or dual-end BWPstrategies. Distinct from existing contiguous FDRA approaches,the proposed schemes comply with standards specifications forfifth-generation (5G) and beyond 5G communications, and havelower computational complexity hence are more practical. Simu-lation results show that all of the proposed algorithms can achievenear-optimal performance in terms of throughput and packet lossrate for low to moderate traffic load, and the first one can stillperform relatively well even with a large number of users.
Index Terms —Beyond 5G (B5G), quality of service (QoS),frequency-domain resource allocation (FDRA), scheduling.
I. I
NTRODUCTION I N a wireless communications system with a next-generation NodeB (gNB) and multiple user equipments(UEs), a pivotal issue to tackle is the scheduling of avail-able time and frequency resources to the UEs in order tosatisfy certain quality of service (QoS) requirements such asthroughput, fairness, latency, and/or reliability. According tothe specifications by the 3rd Generation Partnership Project(3GPP) [1], [2], there are two types of downlink frequency-domain resource allocation (FDRA): type 0 and type 1. Indownlink FDRA of type 0, the resource block (RB) assignmentinformation comprises a bitmap indicating the resource blockgroups (RBGs) that are allocated to the scheduled UE, wherean RBG consists of a set of consecutive virtual RBs definedby higher layer parameters [1]. In downlink FDRA of type 1,the RB assignment information signifies to a scheduled UEa set of contiguously allocated non-interleaved or interleavedvirtual RBs within the active bandwidth part (BWP) [1]. Twokey discrepancies between type-0 and type-1 FDRA are (1)type 0 is on the RBG level while type 1 is on the RB level,and (2) the resources (RBGs or RBs) assigned to each UE canbe non-contiguous for type 0, while they must be contiguousfor type 1.
The authors are with the Next Generation and Standards Group, In-tel Corporation, Santa Clara, CA 95054 USA (e-mail: [email protected];[email protected]).This work has been submitted to the IEEE for possible publication.Copyright may be transferred without notice, after which this version mayno longer be accessible.
A variety of scheduling methods for contiguous FDRAhave been proposed previously [3]–[8], predominantly forsingle-carrier frequency division multiple access in the Long-Term-Evolution-Advanced system. An optimal algorithm waspresented in [3], which yielded the best performance but wasquite intricate. To reduce the complexity, a greedy heuristicallocation was then proposed in [3] which performed ad-jacent RB allocation expansion around a localized optimalRB for each UE. At each iteration, the UE and feasibleRB combination arousing the largest increase in weightedcapacity was selected. In [4], a two-step FDRA scheme wasproposed prioritizing the most demanding UEs in terms oftheir QoS requirements. The authors of [5] proposed a sub-optimal algorithmic solution to address the problem of ergodicsum-rate maximization with the constraint of consecutive RBallocation, where the performance gap to optimal solution waslimited to 10%. The invention in [6] also contained two stepswhere the allocation leading to maximum throughput was firstfound without considering the contiguity constraint, which wasthen iteratively refined to reach an allocation satisfying con-tiguity. The algorithm presented in [7] was based on channelgain matrix and iterative RB cluster selection with highestchannel gain. More prior art can be found in [8]. The existingstrategies, however, mainly concentrate on throughput and donot take into account other QoS criteria such as delay andpacket drop rate [3]–[7], and/or involve high computationalcomplexity when the number of UEs is large [4], [6]. Inthis article, we put forth three scheduling algorithms withtype-1 (i.e., contiguous) FDRA which are aligned with 3GPPstandards for fifth-generation (5G) and beyond-5G (B5G)communications [1], [2] and have relatively low computationalcomplexity thus viable to deploy in practice. In the firstproposed algorithm, FDRA and UE scheduling are jointlyconducted to achieve near-optimal performance, whereas inthe second and third proposed algorithms, UE selection isexecuted first, followed by RB allocation, whose major ad-vantage is low complexity. Moreover, all of the proposedalgorithms are flexible in terms of scheduling metric such assum-rate, proportional fairness (PF) [9] and modified largestweighted delay first (M-LWDF) [10]. System-level simulationsare carried out to validate and compare the performance of theproposed algorithms, using several traffic types with diversepacket sizes, arrival rates, and QoS requirements. a r X i v : . [ c s . N I] O c t Fig. 1: Input and output relation per slot in the UE and resourcescheduling process for a multi-UE scenario with type-1 FDRA.II. S
YSTEM M ODEL AND P ROBLEM F ORMULATION
In this work, we investigate a downlink cellular systemcomprising of one gNB and K UEs indexed by the set K = { , ..., K − } , where the UEs’ traffic types can beheterogenous with dissimilar QoS requirements. The transmis-sion BWP W is orthogonally divided into B RBs indexedby the set B = { , ..., B − } . The payload for UE k isdenoted by L k . There are two constraints in type-1 FDRAin 3GPP 5G and B5G specifications [1], [2]: (1) exclusivity,meaning an RB can only be allocated to at most one UE;(2) contiguity, i.e., the RBs assigned to each UE must becontiguous. Fig. 1 illustrates the input and output relation perslot in the UE and resource scheduling process with type-1FDRA [1], [2]. The input incorporates the UE set K , RB set B , payload and channel state information (CSI) per UE, wherethe CSI usually embodies rank indicator (RI), precoding matrixindicator (PMI), and channel quality indicator (CQI) [1]. Theoutput includes the selected UE set K (cid:63) , selected RB set B (cid:63) implied by resource indication value (RIV) per selected UE,and RI, PMI, and modulation and coding scheme (MCS) perselected UE, where an RIV corresponds to a starting virtualRB and a length pertaining to contiguously allocated RBs [1].In some of the proposed algorithms to be elaborated inSection III, the calculation of transport block size (TBS) [1]over a certain number of RBs is needed. If wideband (WB)CSI [1] is available, where WB denotes the entire active BWP,the TBS is directly computed using the WB CSI. If subband(SB) CSI is available (while RI is still WB) [1], where an SB isequivalent to an RBG herein, the TBS over all the selected RBs(or RBGs) is calculated via the procedure below: (1) Converteach SB CQI to SB MCS, (2) compute the effective MCS overall the selected RBs (or RBGs), and (3) calculate the TBS overall the selected RBs (or RBGs) using the effective MCS andWB RI. In this article, the effective MCS equals the medianof the MCSs over all the selected RBs (or RBGs), but it canalso be the average, maximum, or other quantities related toSB MCS. Further, to obtain WB CQI to be utilized in some ofthe proposed algorithms, the effective MCS is computed overthe entire active BWP, which is then converted back to CQI.For UE k on RB b , given the estimated channel H k,b andprecoding matrix codebook [1], the RI, PMI, and MCS can beobtained via Algorithms 1 and 2 in [11], after which TBS k,b is calculated via the method mentioned above. The achievablerate of UE k on RB b in each slot is r k,b = TBS k,b . Let B k denote the set of RBs allocated to UE k , the achievablerate of UE k is r k = (cid:80) b ∈B k r k,b . The scheduling metric(e.g., sum-rate, PF, M-LWDF) can be flexible depending onthe system requirement. Considering QoS requirement, we select M-LWDF as the scheduling metric as an example,which is expressed as [10] µ k,b = − (log δ k /τ k ) d k r k,b /R k ,where δ k , τ k , d k , and R k denote the acceptable packet dropprobability, delay threshold (the maximum allowable delayfrom packet generation to packet scheduling), head-of-line(HOL) delay, and historical average rate of UE k , respectively.The optimization problem is formulated as(P1): max {B ,..., B K − }⊆A (cid:88) k ∈K (cid:88) b ∈B k µ k,b subject to B k ∩ B k (cid:48) = ∅ , ∀ k (cid:54) = k (cid:48) , k, k (cid:48) ∈ K ,d k ≤ τ k , ∀ k ∈ K (1)where A is the set of all possible RB allocations satisfyingthe contiguity constraint. (P1) is non-convex whose optimalsolution requires exhaustive search with prohibitively highcomputational complexity. Therefore, in the next section, wepropose three practical sub-optimal algorithms to tackle (P1).III. S CHEDULING A LGORITHMS
A. Proposed Three Scheduling Algorithms
Since it is almost impossible to obtain the optimal solutionto (P1) with reasonable computational complexity, we proposethree sub-optimal algorithms to solve (P1). Inspired by theobservation that (cid:80) k ∈K (cid:80) b ∈B k µ k,b in (1) is likely to bemaximized if the UEs who yield the largest (cid:80) b ∈B k µ k,b while consuming the minimum resources are scheduled first,we propose an algorithm named Joint Allocation with DualEnds (JADE), whose procedures are detailed in Algorithm1. Essentially, JADE jointly prioritizes the UE and RB(s) ineach allocation step that produces the largest scheduling metricwith the minimum number of RBs, where the RB selection isperformed and compared between both ends of the active BWPto take advantage of frequency diversity. It is worth noting thata variant of JADE, where the RBs are allocated from only oneend, rather than both ends, of the BWP, can be applied as well.As the variant is likely to yield inferior performance to JADEdue to less frequency diversity, its performance is not shownherein.Note that in JADE, the number of TBS and schedulingmetric calculation is proportional to K due to the iterationfor each remaining UE and RB. To further reduce the com-putational complexity, two lower-complexity algorithms aredesigned, i.e., Disjoint Allocation with Single End (DASE)and Disjoint Allocation with Two Ends (DATE). The maindesign principle of DASE and DATE is to guarantee theQoS for UEs with the most stringent delay and acceptablepacket drop probability requirements. In both DASE andDATE, UE selection is done first based on their delay andacceptable packet drop probability requirements as well as thenumber of RBs needed, followed by RB selection. The onlydifference between DASE and DATE lies in that RB selectionis conducted from only one end of the BWP in DASE, whileboth ends of the BWP are considered and compared for RBselection in DATE. Detailed steps for DASE and DATE areprovided in Algorithm 2 and Algorithm 3, respectively. B. Scheduling Algorithm with Type-0 FDRA
Ideally, the performance of the proposed algorithms shouldbe compared with that of the optimal type-1 FDRA which,
Algorithm 1
Joint Allocation with Dual Ends (JADE)
Require:
Initialize K (cid:63) = ∅ , B (cid:63) = ∅ . while K (cid:54) = ∅ and B (cid:54) = ∅ do for ∀ k ∈ K do Calculate the number of RBs needed, n k, start , totransmit L k starting from the first remaining RB in B and going forward, until r k, start ≥ L k or B = ∅ .Denote the selected RB set as B k, start . Calculate the number of RBs needed, n k, end , totransmit L k starting from the last remaining RB in B and going backward, until r k, end ≥ L k or B = ∅ .Denote the selected RB set as B k, end . If n k, start ≤ n k, end , store B k, start and r k, start as B k and r k , respectively; otherwise store B k, end and r k, end as B k and r k , respectively. Calculate (cid:80) b ∈B k µ k,b . end for k (cid:63) = argmax k (cid:80) b ∈B k µ k,b . Calculate MCS k (cid:63) , the final MCS for UE k (cid:63) over B k (cid:63) . K (cid:63) ← K (cid:63) ∪ { k (cid:63) } , B (cid:63) ← B (cid:63) ∪ B k (cid:63) . K ← K \ { k (cid:63) } , B ← B \ B k (cid:63) . end while return K (cid:63) , B (cid:63) , and MCS k , ∀ k ∈ K (cid:63) .however, requires exhaustive search over UEs, the startingposition of RBs per UE, and the number of RBs per UE,whose complexity is prohibitively high and hence almost im-possible to realize. On the other hand, although also requiringexhaustive search, the optimal type-0 FDRA is possible torealize capitalizing on a different and smaller search space.Additionally, if the same frequency granularity is assumedfor both type-0 and type-1 FDRA, the optimal type-0 al-location is expected to be superior to the optimal type 1,since discontinuous FDRA enjoys higher flexibility in termsof best UE and resource combination selection. To this end,we compare the performance of the proposed schedulingalgorithms with one using the optimal type-0 FDRA whichserves as a benchmark. In type-0 FDRA, the scheduling metricis first calculated per UE per RBG, then the UE and RBGcombination corresponding to the largest scheduling metric isselected for scheduling and excluded from further selectionafterwards in the current slot. Subsequently, the schedulingmetric is recalculated per UE per RBG, followed by best UEand RBG combination selection and exclusion, so on and soforth, until there is no remaining UE or RBG. C. Complexity Analysis
Besides the RBG-level type-0 FDRA, we also comparethe proposed algorithms with a representative sub-optimalcontiguous FDRA algorithm in the industry published in [3],which is named Localized Expansion of Adjacent Positions(LEAP) herein, to evaluate the performance enhancement bythe proposed algorithms over LEAP. The weighted capacitymetric in LEAP is replaced by the scheduling metric for faircomparison. Assuming each UE needs M RBs on average, andthe number of RBs in an RBG is M RB , the computational com-plexity of all the considered algorithms is provided in Table I. Algorithm 2
Disjoint Allocation with Single End (DASE)
Require:
Initialize K (cid:63) = ∅ , B (cid:63) = ∅ . while K (cid:54) = ∅ and B (cid:54) = ∅ do for ∀ k ∈ K do (cid:46) UE selection begins ∆ d k = τ k − d k . Calculate the number of RBs needed, n k , to trans-mit L k based on WB CQI of UE k . end for K (cid:63) temp = argmin k ∆ d k . if |K (cid:63) temp | = 1 then k (cid:63) = argmin k ∆ d k . else K (cid:63) temp = argmin k δ k . if |K (cid:63) temp | = 1 then k (cid:63) = argmin k δ k . else K (cid:63) temp = argmin k n k . if |K (cid:63) temp | = 1 then k (cid:63) = argmin k n k . else Randomly select a UE k (cid:63) . end if end if end if (cid:46) UE selection ends and RB selection begins
Calculate the number of RBs needed, n k (cid:63) , start , totransmit L k (cid:63) starting from the first remaining RB in B and going forward, until r k (cid:63) , start ≥ L k (cid:63) or B = ∅ .Denote the selected RB set as B k (cid:63) , and allocate B k (cid:63) to UE k (cid:63) . (cid:46) RB selection ends
Calculate MCS k (cid:63) , the final MCS for UE k (cid:63) over B k (cid:63) . K (cid:63) ← K (cid:63) ∪ { k (cid:63) } , B (cid:63) ← B (cid:63) ∪ B k (cid:63) . K ← K \ { k (cid:63) } , B ← B \ B k (cid:63) . end while return K (cid:63) , B (cid:63) , and MCS k , ∀ k ∈ K (cid:63) .As expected, type-0 FDRA possesses the highest complexitydue to exhaustive search over all UE and RBG combinations.In a typical example where K = 30 , B = 270 , M = 10 ,and M RB = 4 , the complexity of JADE is slightly lower thanthat of LEAP, both of which are approximately an order ofmagnitude lower than type-0 FDRA. DASE has the lowestcomplexity which is slightly lower than that of DATE, sincethese two algorithms exploit disjoint UE and RB selection.IV. S IMULATION R ESULTS
System-level simulations are conducted to assess and com-pare the performance of the proposed three type-1 FDRAalgorithms. Table II lists the simulation settings, where thetraffic models comprise both eMBB (enhanced Mobile Broad-band) and URLLC (Ultra-Reliable Low-Latency Communica-tions) [12] (including arVr2, powerDist2, and ITS [13], wherearVr2 denotes the second type of augmented reality/virtualreality, powerDist2 represents the second type of power dis-tribution grid fault and outage management, and ITS stands
Algorithm 3
Disjoint Allocation with Two Ends (DATE)
Require:
Initialize K (cid:63) = ∅ , B (cid:63) = ∅ . while K (cid:54) = ∅ and B (cid:54) = ∅ do UE selection: Identical to Steps 2-21 in DASE. (cid:46)
RB selection begins Calculate the number of RBs needed, n k (cid:63) , start , totransmit L k (cid:63) starting from the first remaining RB in B and going forward, until r k (cid:63) , start ≥ L k (cid:63) or B = ∅ .Denote the selected RB set as B k (cid:63) , start . Calculate the number of RBs needed, n k (cid:63) , end , to trans-mit L k (cid:63) starting from the last remaining RB in B andgoing backward, until r k (cid:63) , end ≥ L k (cid:63) or B = ∅ . Denotethe selected RB set as B k (cid:63) , end . If n k (cid:63) , start ≤ n k (cid:63) , end , denote B k (cid:63) , start as B k (cid:63) , otherwisedenote B k (cid:63) , end as B k (cid:63) . Allocate B k (cid:63) to UE k (cid:63) . (cid:46) RB selection ends Calculate MCS k (cid:63) , the final MCS for UE k (cid:63) over B k (cid:63) . K (cid:63) ← K (cid:63) ∪ { k (cid:63) } , B (cid:63) ← B (cid:63) ∪ B k (cid:63) . K ← K \ { k (cid:63) } , B ← B \ B k (cid:63) . end while return K (cid:63) , B (cid:63) , and MCS k , ∀ k ∈ K (cid:63) .TABLE I: Complexity Comparison Algorithm Type-1 Type-0JADE DASE DATE LEAPNumber ofTBS calculation MK MK MK MK MK BK MM RB ] K Numberof RB amountcalculation 0
K K MK MK MK BK MM RB ] K Sumcomplexity for K = 30 , B = 270 , M = 10 , M RB = 4 1 e ⇓O (1 e
4) 3 e ⇓O (1 e
2) 6 e ⇓O (1 e
2) 8 e ⇓O (1 e
4) 2 e ⇓O (1 e for intelligent transportation system [13]). The total numberof UEs in our simulations vary from 10 to 50, and the ratiosof eMBB, arVr2, powerDist2, and ITS UEs are about 1:1:1:1.Table III details the parameters for the traffic models studiedin our simulations. We note that URLLC traffic can also bescheduled by puncturing the ongoing eMBB transmission, butthat scheme has its own drawbacks as well and is out of thescope of this paper whose overarching focus is the schedulingof different traffic types using the same time resource.The overall and two close-up views of packet throughputfor various traffic types are illustrated in Fig. 2 and Fig. 3,respectively. The maximum throughput degradation of the pro-posed algorithms against the type-0 algorithm and maximumthroughput gain over LEAP are summarized in Table IV. Fig. 4shows the packet loss rate, where a packet is considered lost ifit is not entirely scheduled before reaching its delay threshold.For LEAP, the swift increase in packet loss at 30 UEs in Fig. 4 TABLE II: Simulation Settings Configuration ValueTransmit power 23 dBmNumber of gNB antennas 4Cell radius 250 mUE distribution UniformNumber of antennas per UE 4Number of UEs per gNB 10-50Channel EPA20 (6.0 km/h) (ExtendedPedestrian A model with 20 HzDoppler frequency)Numerology 30kHz sub-carrier spacing,100MHz bandwidthCSI feedback delay 1 slotTraffic model eMBB, arVr2, ITS, powerDist2Traffic ratio 1:1:1:1Number of slots 1200 per seedNumber of seedsper simulation run 10Number of RBs per RBG 4
TABLE III: Parameters for Traffic Models used in Simula-tions [13] eMBB arVr2 ITS powerDist2Delay threshold (ms) 100 7 7 6Acceptable packetdrop probability 10% 0.1% 0.001% 0.001%Packet size (bits) 12000 32768 10960 2000Packet arrival rate(packets/second) 1000 60 100 1200 for ITS and arVr2 unveils its instability and sensitivity to theUE amount and/or locations. The following key observationscan be drawn from these results:1) In general, JADE outperforms DASE, DATE as well asLEAP. The superiority of JADE over DASE and DATE isespecially evident when the number of UEs is large (e.g., 50),as shown by the throughput and packet loss rate for 50 UEsin Fig. 2 to Fig. 4. Comparing JADE and LEAP, as shown inFig. 3 and Fig. 4, JADE yields higher throughput and lowerpacket loss rate in most cases, with a maximum throughputgain of 9.9% (see Table IV). The reason is that LEAP allocatesRBs locally around the first best RB for each UE, but if thechannel quality happens to change abruptly around the firstRB, the overall channel quality may degrade hence incurringperformance loss.2) JADE has comparable and sometimes even better perfor-mance in contrast with the type-0 algorithm, as shown by thethroughput for arVr2 UEs in Fig. 3, since type-0 FDRA isbased on the RBG level (4 RBs per RBG in the simulation)while type 1 is of RB-level which has a finer frequencygranularity hence higher flexibility. The maximum throughputdegradation of JADE against type-0 FDRA is only 0.9%.3) Dual-end FDRA surpasses its single-end counterpart, asvalidated by DATE and DASE, due to its higher frequencydiversity.4) As demonstrated by the left plot of Fig. 3, Table IV, andFig. 4, DASE and DATE perform well and even exceed LEAPwhen the number of UEs is not very large, i.e., up to 40UEs in this case. Since these two algorithms enjoy the leastcomplexity, they can be used when traffic load is not too high.
TABLE IV: Throughput Comparison
Algorithm JADE DASE DATEMaximum throughputdegradation against Type 0 0.9% 2.8% 2.5%Maximum throughput gain over LEAP 9.9% 8.9% 11.0%
Fig. 2: Packet throughput of the proposed three schedulingalgorithms with type-1 FDRA, as well as LEAP in [3] and anRBG-level type-0 FDRA.V. C
ONCLUSION
We have proposed three practical multi-UE schedulingalgorithms with type-1 FDRA, i.e., JADE, DASE, and DATE,and compared their performance with each other and withan optimal non-contiguous RBG-level FDRA method and atypical contiguous FDRA algorithm LEAP in the industry.Numerical results demonstrate that JADE can achieve near-optimal performance and outperform LEAP in terms of QoSrequirements while having low computational complexity.Additionally, DASE and DATE perform similarly to JADEfor small to moderate numbers of UEs, but with substantiallylower computational complexity, thus can be adopted in prac-tice under low traffic load conditions. The proposed algorithmsare applicable to both downlink and uplink. This work canbe extended by considering coarser frequency granularities incontiguous FDRA to mitigate RIV overhead [14].R
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