Distributed DTX Alignment with Memory
DDistributed DTX Alignment with Memory
Hauke Holtkamp, Guido DietlDOCOMO Euro-LabsD-80687 Munich, GermanyEmail: { holtkamp, auer } @docomolab-euro.comHarald HaasInstitute for Digital CommunicationsJoint Research Institute for Signal and Image ProcessingThe University of Edinburgh, EH9 3JL, Edinburgh, UKE-mail: [email protected] 20, 2018 Abstract
This paper addresses the assignment of transmission and sleep timeslots between interfering transmitters with the objective of minimalpower consumption. In particular, we address the constructive align-ment of Discontinuous Transmission (DTX) time slots under link rateconstraints. Due to the complexity of the combinatorial optimizationproblem at hand, we resort to heuristic assignment strategies. We de-rive four time slot alignment solutions (sequential alignment, randomalignment, p-persistent ranking and DTX alignment with memory)and identify trade-offs. One solution, DTX alignment with memory,addresses trade-offs of the other three by maintaining memory of pastalignment and channel quality to buffer short term changes in channelquality. All strategies are found to exhibit similar convergence behav-ior, but different power consumption and retransmission probabilities.DTX alignment with memory is shown to achieve up to 40% savingsin power consumption and more than 20% lower retransmission prob-ability than the State-Of-The-Art (SotA).
To reduce their power consumption, future Base Stations (BSs) will usevery short sleep modes—called Discontinuous Transmission (DTX)—which1 a r X i v : . [ c s . I T ] N ov nterrupt their transmission [ ? ]. DTX can be employed for energy savingwhen a communication system has spare capacity, e.g. at night in cellularnetworks. It can be easily integrated into Orthogonal Frequency DivisionMultiple Access (OFDMA) systems without incurring delays by not schedul-ing resources for transmission during one or more time slots and then settingthe transmitter to DTX mode instead for the duration of these unscheduledtime slots. For the transmitter, this is a local power saving measure. Whenseen from a network perspective, these regular interruptions in transmissioncan be aligned to reduce interference and power consumption. Such align-ment has not been studied in detail, but is related to the field of channelallocation.Generally, in channel allocation, the challenge is to assign frequencychannels to different cells or links of a network such that mutual interfer-ence is minimized. To be applicable for future small-cell cellular networks,such channel allocation needs to be distributed, uncoordinated and dynamic.Distributed operation prevents the delay and backhaul requirements im-posed by a central controller. If the allocation is also uncoordinated, itdoes not require message exchange through a backhaul of limited capac-ity. Also, as networks, channels and traffic change rapidly, the allocationmust be highly dynamic and update often. Problems of this type are knownto be NP-hard [ ? ]. Therefore, different suboptimal approaches have beenproposed. The simplest approach to distributing channels over a networkis a fixed assignment in which it is predefined which links will use whichchannels, e.g. see [ ? ]. However, this is inflexible to changing or asymmetrictraffic loads. For flexibility, dynamic channel allocation methods are re-quired. A simple dynamic channel allocation method, Sequential ChannelSearch [ ? ], assigns channels with sufficient quality in a predefined order.This technique allows adjusting the number of channels flexibly, but is sub-optimal due to its strong channel overlap between neighbors. Taking thechannel quality into consideration by measurement is proposed in the Mini-mum Signal-to-Interference-and-Noise-Ratio (SINR) method [ ? ]. This tech-nique offers increased spectral efficiency, but can lead to instabilities whenallocations happen synchronously. Ellenbeck et al. [ ? ] introduce methodsof game theory and respond to the instabilities by adding p-persistence toavoid simultaneous bad player decisions. However, the proposed methodonly applies to single user systems and does not address target rates. Dy-namic Channel Segregation [ ? ] introduces the notion of memory of channelavailability, allowing a transmitter to track which channels tend to be fa-vorable for transmission. However, the algorithm only applies to sequentialchannel decisions based on an idle or busy state in circuit switched networks2nd cannot be applied to the concurrent alignment of channels as is requiredin OFDMA networks.In this paper, we combine the findings from past channel allocation re-search and adapt them for aligning DTX time slots in an OFDMA frame. Wederive four distributed uncoordinated dynamic time slot alignment strate-gies for the cellular downlink, in which BSs independently prioritize timeslots for transmission while maintaining system stability. The remainder ofthe paper is structured as follows. Section 2 formulates the system modeland the problem at hand. The considered four alternative solutions are de-scribed in Section 3. Findings obtained from simulation are presented inSection 4. The paper is concluded in Section 5. We make the following assumptions about the network. BSs in a reuse-oneOFDMA cellular network schedule a target rate, B k , per OFDMA frame tobe transmitted to each mobile k = { , . . . , K } . All time slots are availablefor scheduling in all cells. Mobiles report perceived SINR from the previousOFDMA frame, s n,t,k , on subcarrier n = { , . . . , N } , time slot t = { , . . . , T } to their associated BS. BSs have a DTX mode available for each time slotduring which transmission and reception are disabled and power consump-tion is significantly reduced to P S compared to power consumption duringtransmission, which is a function of the power allocated to each ResourceBlock (RB), ρ Tx . DTX is available fast enough to enable it within individualtime slots of an OFDMA transmission such that transmission time slots arenot required to be consecutive. A BS can schedule no transmission in oneor more time slots and go to DTX mode instead. Scheduling a DTX timeslot in one BS reduces the interference on that time slot to all other BSs.The OFDMA frames of all BSs are assumed to be aligned such that theinterference over one time slot and subcarrier is flat and that all BSs canperform alignment operations in synchrony. The OFDMA frame consists of N T
RBs. The channel is subject to block fading. Interference is treated asnoise.To describe the resource allocation problem formally, we define the func-tion Π : { , . . . , T } × { , . . . , N } → { , , . . . , K } ( n, t ) (cid:55)→ k, (1)which maps to each RB a user k or 0, where 0 indicates that the RB is notscheduled. 3ach cell tries to minimize its power consumption by scheduling timeslots for transmission and sleep. With r n,t,k the capacity of resource ( n, t )if it is scheduled to k , the optimization problem for the total BS powerconsumption, P total , is as follows.minimize Π P total = P S T S T + ρ Tx N Tx + P (cid:18) T − T S T (cid:19) (2a)subject to N Tx = (2b) |{ n ∈ { , . . . , N }| (Π( n, t ) (cid:54) = 0 ∀ t ∈ { , . . . , T } ) }| T S = (2c) |{ t ∈ { , . . . , T }| (Π( n, t ) = 0 ∀ n ∈ { , . . . , N } ) }| B k ≤ (cid:88) { ( n,t ) | Π( n,t )= k } r n,t,k ∀ k. (2d)With | · | the cardinality operator, T S is the number of time slots in whichfor all n , no user is allocated and the BS can enable DTX and N Tx is thenumber of RBs that are scheduled for transmission. The constraint (2d)provides the rate guarantee for each user.The difficulty lies in finding the mapping Π. Under a brute force ap-proach, there exist ( K + 1) NT possible combinations. Due to the largenumber RBs present in typical OFDMA systems like Long Term Evolu-tion (LTE), the computation of the solution is infeasible. Consequently, weresort to heuristic methods in the next section.Some of the methods compared in this paper make use of a time slotranking. In other works, e.g. [ ? ], ranking is proposed to be based on SINR.However, in a multi-user OFDMA system each subcarrier and mobile ter-minal have a different SINR, thus generating a problem of comparabilitybetween time slots. Consequently, we propose to compare time slots bytheir hypothetical sum capacity, B t , over all mobiles and subcarriers with B t = K (cid:88) k =1 N (cid:88) n =1 log (1 + s n,t,k ) . (3) In this section, we derive four strategies to tackle the problem at hand whichdiffer in performance and complexity.4 .1 Sequential alignment
This strategy is to always allocate as many time slots for transmission asrequired in sequential order and set the remainder to DTX. This leads tostrongest overlap and consequently highest interference on the first time slotand lowest overlap and possibly no transmissions at all on the last time slot.This strategy does not make use of the available channel quality informa-tion and provides valuable insights into questions of stability, reliability andconvergence. It serves as a deterministic upper bound.
Random alignment refers to randomly selecting transmission time slots forevery OFDMA frame and setting the remainder to DTX. This strategy pro-vides a reference for achievable gains, allows to assess the worst cast effectsof randomness and represents the state of the art in today’s unsynchronizedunaligned networks.
The synchronous alignment of uncoordinated BSs can lead to instabilities,when neighboring BSs–perceiving similar interference information–schedulethe same time slots for transmission. This leads to oscillating schedulingwhich never reaches the desired system state [ ? ]. To address this problem, weintroduce p-persistence to break the unwanted synchrony by only changingestablished DTX schedules with a probability p = 0 .
3. In initial tests, thevalue of p did not have a significant effect on the power consumption. Theexact tuning of p is out of the scope this paper. P-persistent ranking firstranks time slots by their sum capacity as in (3), schedules time slots in thatorder, but only applies this new selection with probability p . Otherwise, theschedule from the last iteration remains active. After ranking, time slots areselected for transmission in order of B t . The remainder of time slots is setto DTX. To counter oscillation and achieve a convergent network state we introducememory of past schedules into the alignment process. The rationale behindthe distributed DTX alignment with memory algorithm is as follows. Takinginto account current time slot capacities, B t , past scores and slot allocations,each BS first updates the internal score of each time slot and then returns the5riority of time slots by score. In case of equal scores, time slots are furthersub-sorted by B t . The score is updated in integers. All time slots whichwere used for transmission in the previous OFDMA frame receive a scoreincrement of one. Furthermore, the time slot with highest B t , R , receivesan increment of one. Time slots which were not used for transmission in theprevious OFDMA frame receive a decrement of one, except for R . Scoreshave an upper limit ψ ul beyond which there is no increment and a lowerlimit ψ ll below which there is no decrement. The difference between ψ ul and ψ ll can be interpreted as the depth of the memory buffer. Algorithm 1
Distributed DTX alignment with memory
Input: ψ, Υ u R ← sort-desc-by-capacity(Υ) for all υ in Υ u do if ψ ( υ ) < ψ ul then ψ ( υ ) ← ψ ( υ ) + 1 end if end for for all υ in Υ uu \{ R } do if ψ ( υ ) > ψ ll then ψ ( υ ) ← ψ ( υ ) − end if end for ψ ( R ) ← ψ ( R ) + 1 V ← sort-desc-by-score( R, ψ, Υ) return ψ, V, Υ u The described steps are summarized in Algorithm 1 with scoring map ψ , ranking tuple R , and priority tuple V . The set of used time slots Υ u andunused time slots Υ uu make up the set of time slots Υ, the cardinality ofwhich is T . The function ’sort-desc-by-capacity(Υ)’ returns a list of timeslots ordered descending by B t . The function ’sort-desc-by-score( R, ψ,
Υ)’returns a list of time slots ordered primarily by descending score and secon-darily by descending B t . After the execution of Algorithm 1, the first T Tx time slots in V are scheduled for transmission.In the following, we illustrate the iterations over three OFDMA framesof Algorithm 1 for a system with three time slots. In the example, thealgorithm delays the change of Υ u from c to b to buffer scheduling changes.The iteration begins with arbitrarily chosen Υ = { a, b, c } , ψ = { a : 0 , b :2 , c : 5 } : 6. Υ u = { c } , R = ( b, c, a ) → ψ = { a : 0 , b : 3 , c : 5 } , V = ( c, b, a )2. Υ u = { b, c } , R = ( b, c, a ) → ψ = { a : 0 , b : 5 , c : 5 } , V = ( b, c, a )3. Υ u = { b } , R = ( b, a, c ) → ψ = { a : 0 , b : 5 , c : 4 } , V = ( b, c, a )When applied, Algorithm 1 strongly benefits time slots which were usedfor transmission in the past ( b, c in step 1 of the example). These time slotstend to repeatedly receive score increments until they all have maximumscore ψ ul ( b, c in step 2 of the example). When the score is equal for sometime slots ( b, c in step 2 of the example), the ranking is based on B t . A timeslot which was used for transmission and has highest B t , R , receives thehighest increment (slot b in step 2 of the example). When a time slot hashighest B t , but was not selected for transmission in the previous OFDMAframe, it receives a score increment, but is not guaranteed to be used fortransmission (slot b in step 1 of the example). When a time slot repeatedlyhas highest B t , it reaches ψ ul ( b in the example). The algorithm thus buffersshort term changes in the channel quality setting in favor of long term timeslot selection. We analyze the four alignment strategies using computer simulations withregard to power consumption, convergence, reliability of delivered rates andalgorithmic complexity after the introduction of the simulation environmentand the RB scheduling scheme.
The four strategies were tested in a network simulation with 19-cell hexag-onal arrangement with uniformly distributed mobiles and fixed target ratesper mobile. Data was collected only from the center cell which is thus sur-rounded by two tiers of interfering cells. Power consumption of a cell ismodeled as a function of transmission power as described in [ ? ]. Table 4.1lists additional parameters used which approximate an LTE system. Thesimulation is started with the assumption of full transmission power on allresources with a power consumption of 350 W per cell as a worst-case initialconfiguration. 7arameter ValueCarrier frequency 2 GHzIntersite distance 500 mPathloss model 3GPP UMa, NLOS,shadowing [ ? ]Shadowing standard deviation 8 dBBandwidth 10 MHzTransmission power per RB 0.8 WThermal noise temperature 290 KInterference tiers 2 (19 cells)Mobile target rate 2 Mbps and 3 MbpsOFDMA subframes (time slots) 10Subcarriers 50Mobiles 10 ψ ul ψ ll ? ](idle; load factor; DTX) 200 W; 3.75; 90 WTable 1: Simulation ParametersIn order to assess the performance of the four strategies, it is necessaryto make assumptions about how the individual RBs are scheduled within atime slot. In order to avoid masking effects of the algorithms under test,we have applied a sequential RB allocation. Sequential resource alloca-tion is performed after the DTX alignment step is completed and allocatesas many bits to an OFDMA resource block as possible according to theShannon capacity, followed in order by the next resource in the same timeslot (sequentially), until the target rate has been scheduled to each mobile.Time slots are scheduled in the order provided by each of the four strategies.This sequential resource scheduler deliberately omits the benefits of multi-user diversity. This leads to underestimating achievable rates in simulationcompared to a system which exploits multi-user diversity, but allows a faircomparison of the quality of different DTX alignment algorithms. To assess achievable power savings and the dynamic adaptivity over a largerange of cell loads, we inspect the cell total power consumption in Fig. 1.At low load very few RBs are required to deliver the target rate and moretime slots can be scheduled for DTX than at high traffic loads, leading to8igure 1: BS power consumption over different cell sum rates.monotonously rising power consumption over increasing target rates for allalignment methods.Sequential alignment causes the highest power consumption over anytarget rate with an almost linear relationship between user target rates andpower consumption. Sequential alignment consumes high power, as it sched-ules many RBs to achieve the target rate due to the high interference levelpresent.This power consumption is significantly lower for the State-Of-The-Art(SotA), random alignment. The randomness of time slot alignment createsa much lower average interference than with sequential alignment allowingmore data to be transmitted in each RB. As fewer RBs are required, lesspower is consumed.P-persistent ranking and DTX with memory both achieve similarly lowpower consumption of up to 40% less than random alignment. The relation-ship between power consumption and target rate is noticeably non-linear,as it is flat at low target rates and grows more steeply at high target rates.This behavior is caused by the low interference level these strategies manageto create. Only at high rates, when the number of sleep time slots has tobe significantly decreased, does the interference increase, leading to higherpower consumption.Also noteworthy is the fact that at 1 Mbps and 3 Mbps, random align-ment performs nearly as good as p-persistent ranking. At these extremepoints the network is almost unloaded and almost fully loaded, respectively.Consequently, either most time slots are scheduled for DTX or none, leav-ing very little room for optimization compared to randomness. The largestpotential for time slot alignment for power saving is in networks which aremedium loaded. Under medium load, the number of transmission and DTXtime slots is similar, causing the effects of alignment to be most pronounced.9igure 2: BS power consumption over OFDMA frames at 1 Mbps per mobile.Figure 3: BS power consumption over OFDMA frames at 2 Mbps per mobile.
Another relevant aspect is the convergence of the network to a stable state.As each BS makes iterative adjustments to its selection of time slots fortransmission, the speed of convergence as well as the convergence to a stablepoint of operation are relevant criteria. The effect of the iterative executionof the four strategies on the cell power consumption is illustrated in Fig. 2.Power consumption is found to converge to a stable value within withinsix OFDMA frames (alignment iterations). All strategies converge to theaverage power consumption values shown in Fig. 1. The simulation startsfrom a worst-case schedule of transmission on all RBs and then iterativelyschedules time slots for transmission and DTX. In the case of 1 Mbps peruser, one transmission time slot is sufficient to schedule the target rate. Withtransmissions only taking place during one time slot, there is very littledifference between a random alignment and p-persistent ranking or DTXwith memory. At 2 Mbps per user, see Fig. 3, random alignment occasionallycauses higher interference than p-persistent ranking or DTX with memory,leading to higher power consumption. Also, p-persistent ranking convergesmore slowly than DTX alignment with memory.10 .0 1.5 2.0 2.5 3.0User target rate in Mbps020406080100 R e t r a n s m i ss i o n p r o b a b ili t y i n p e r c e n t Sequential alignmentRandom alignment (SotA)P-persistent rankingDTX alignment with memory
Figure 4: Retransmission probability over targeted rate.
An important aspect in dynamical systems with target rates is that sched-uled target rates cannot always be fulfilled. As RB scheduling is based onchannel quality information which was collected in the previous OFDMAframe, the actual channel quality during transmission may differ, leading tolower than expected rates. Thus, although certain target rates are scheduledand although the system is not fully loaded, a BS may fail to deliver thetargeted rate and require retransmission of some RBs. We assess this metricby considering the retransmission probability for each strategy. The resultsare shown in Fig. 4 against a range of user target rates.Easiest to interpret is sequential alignment which does not require re-transmission for target rates up to 2.3 Mbps due to its determinism. Theincrease in the retransmission probability at high rates is not caused by afailure of the alignment, but by system overload. When high rates are com-bined with bad channel conditions, the system may be unable to deliverthe target data rate, independent of the alignment strategy. This increaseof the retransmission probability at high rates is present for all alignmentstrategies and constitutes outage.The retransmission probability is highest for random alignment. This iscaused by the strong fluctuation of interference under randomized schedul-ing. Channel quality measurements used for RB scheduling are of very littlereliability, as the interference changes quickly due to random time slot align-ment, resulting in increased retransmission probability.P-persistent ranking performs slightly better than random alignment at1 Mbps target rate. At 2 Mbps per user, where the alignment potential ishighest, oscillation causes the highest retransmission probability.DTX alignment with memory achieves a much lower retransmission prob-ability in the range of 15% to 20%, due to the reduction in interferencefluctuation introduced by the memory score.11 .5 Complexity
With regard to complexity, sequential and random alignment are of minimalcomplexity. These strategies involve no algorithmic decision-making on theset of transmission time slots. P-persistent ranking requires one ranking andtime slot selection with probability p per iteration. The highest complexityis present in DTX with memory, which requires two executions of the timeslot sort, one for the generation of the score and one for the output of theranking. Although DTX with memory comprises the highest complexityin comparison, these operations pose a small burden on modern hardwareas the number of time slots is typically small. For example, typical LTEsystems are designed with 10 subframes. To conclude our evaluation, we have found that DTX with memory providesthe best results. Under the present assumptions, it provides both a lowerpower consumption and lower retransmission probability than the SotA andp-persistent ranking. Future DTX capable networks can and should exploitthis alignment potential.5 Conclusion