Multi-objective Antenna Selection in a Full Duplex Base Station
aa r X i v : . [ c s . I T ] S e p Wireless Personal Communications manuscript No. (will be inserted by the editor)
Multi-objective Antenna Selection in a Full DuplexBase Station
Mohammad Lari · Sina Asaeian the date of receipt and acceptance should be inserted later
Received: date / Accepted: date
Abstract
The use of full-duplex (FD) communication systems is a new wayto increase spectral efficiency. For this reason, it has received serious attentionin the new generation of wireless communication systems. The main challengeof FD systems is self-interference that needs to be reduced appropriately. Inthis paper, we have considered an FD multi-antenna base station in a cel-lular network and we have used the antenna selection technique to resolvethe self-interference issue. We have also provided a new criterion to select anappropriate antenna. In this new criterion, the antenna selection is modeledas a multi-objective optimization problem. Here, the antennas which simulta-neously minimizes interference channel gain and maximizes uplink (UL) anddownlink (DL) channel gains are selected for transmission and reception. Thebase station has to perform well in both the UL and DL and reduce theself-interference simultaneously. Therefore, the multi-objective criterion has abetter performance than the single-objective criterion. Although, in conven-tional antenna selection with the single-objective criterion, only the functionof the UL and DL channels or the interference channel is considered. Finally,the simulations show that the new criterion has a higher throughput rate thanthe other conventional single-objective antenna selection techniques.
Keywords
Antenna Selection · Full Duplex Communication · Multi-objectiveOptimization
In recent years, and especially with the growing use of smart equipment andphones, we see a superb increase in users traffic in telecommunication net-
M. LariElectrical and Computer Engineering Faculty, Semnan University, Semnan, IranE-mail: m [email protected] Mohammad Lari, Sina Asaeian works. Field research suggests that data traffic in the next decade will beabout 1000 times the current level [1]. To this end, the new generation of com-munication systems has considered various and different plans to respond tothis volume of requested traffic. Proposed solutions include miniaturizing andcondensing network cells, using new and unutilized frequency bands as well asnew waveforms to increase spectral efficiency and better utilization of availableresources [1, 2]. One of the new waveform is the full-duplex (FD) transmissionand reception. This trick is a new method in comparison to half-duplex (HD)transmission. Due to the increase in spectral efficiency in FD communicationscompared to HD, this method has considered in this paper.In all telecommunication systems, there are two or more nodes that thesenodes are usually exchanging data together one by one. A node sometimesacts as a transmitter and sends data to another node. The same node at an-other time plays the role of a receiver and receives data from the other node.Therefore, most telecommunication nodes have both transmitter and receiver.In current communication systems which work as HD, the transmission andreception of a node occur at different time slots or at different frequency bands.In the first case, the node sends data in a certain time slot and receives datain another time slot too. Also, in the second case, although the node sendsand receives at the same time, but transmits and receives at a different fre-quency bandwidth and there is no interference in simultaneous transmissionand reception. However, in FD systems, sending and receiving a node is donesimultaneously in the same frequency bandwidth. In this way, when the re-ceiver of a node is on and receives data, its transmitter also works at the sametime and sends data. Therefore, the output power of the transmitter, whichis usually strong, can easily leak into the receiver and create self-interference.The self-interference may even reach up to 100dB higher than the noise powerat the receiver. For this reason, self-interference is exactly the cause that com-munication systems have not yet been implemented as FD [3, 4]. Currently,due to the researches done and the practical experiments made in the labora-tory, it has been possible to reduce this interference to a certain extent withinthe receiver noise power. For this reason, utilizing the FD method has beenproposed for new generations of communication systems [5].The main problem with the FD systems is the intense self-interference fromthe transmitter to the receiver of the same node. There are various methodsto reduce this interference. Reducing interference is often done in the propa-gation domain, in the analog domain in the radio frequency (RF) section ofthe receiver or in the digital domain [4, 5]. Due to the high severity of thisinterference, practical systems should use the appropriate methods in all threeareas of propagation, analog, and digital domains, simultaneously. So, in theend, the remaining interference reaches to (or less than) receiver noise floor [5].Then, the FD system can send and receive simultaneously without any prob-lems in a similar frequency band. Therefore, to communicate with anothernode, compared to an HD system, FD systems requires a shorter time slotand lower frequency bandwidth. This means (almost) doubling the spectral ulti-objective Antenna Selection in a Full Duplex Base Station 3 efficiency that is highly desirable for the new generation of communicationsystems.Interference cancellation in the propagation domain is very important. Be-cause the intensity of the interference is high and if this self-interference gets tothe RF section of the receiver, causes saturation of RF circuits and completelyinterrupts receiver’s functionality [6]. The methods for reducing interferencein the propagation domain often include antenna selection [7, 8], the use ofelectromagnetic absorbers between transmit and receive antennas [9] and theuse of orthogonal polarizations [10,11] for sending and receiving with the leasteffect of coupling. The propagation domain techniques are not able to removethe self-interference completely. Therefore, before converting the signal to dig-ital values, another portion of the interference should be removed in the analogdomain. Otherwise, due to the limited dynamic range of the analog to digitalconverter, some parts of the data may be lost. Due to the limited processinggain that exists in the analog section of the receiver, the elimination of interfer-ence in this section often involves estimating the interference and subtractingit from the received analog signal [12]. Then, the analog signal converts to dig-ital values and the remaining self-interference in the digital domain diminishesgreatly. Due to the high processing gain in the digital section, digital interfer-ence cancellation techniques are very diverse. Among them, we can point outthe interference alignments [13] and the methods based on subspace [14, 15].In most of these methods, the degree of freedom in multi-antenna systems areused to separate the interference space from the desired signal.In addition to self-interference cancellation, the antenna selection can alsosimplify and reduce the volume and power consumption of the RF sectionin both transmitter and receiver [16]. Hence, the use of this method is verycommon in multi-antenna communication systems. This article also used thistrick to reduce interference. Several articles have addressed this issue. One ofthe best in this field is [17] in which the FD system is considered as multi-antenna and by using an antenna selection or beam selection, the interferenceis reduced and, even in some situations, has been completely canceled. Thismethod is also used in [18] with relay selection in amplify and forward (AF)relays to reduce interference. The authors of [18] also calculated the outageprobability. Antenna selection in a multi-antenna FD communication systemis also explored in [19] and [20] where two nodes are exchanging data simul-taneously and within the same frequency band. In [19], the self-interference isreduced by selecting one antenna in the transmitter and one antenna in thereceiver of the first node and in the same way one antenna in the transmitterand one antenna in the receiver of the second node. Then the authors calculatethe average sum rate and the average sum symbol error rate. In [20] which ismore general than [19], the number of selected antennas per node for sendingand receiving is not necessarily equal to one and can be higher. In this case,authors with appropriate approximations have calculated the average sum rateof the bi-directional communication system. In addition, different criteria forselecting an appropriate antenna at a base station in a cellular communication
Mohammad Lari, Sina Asaeian network that works as an FD is studied in [21] and the outage probability wascalculated in both downlink (DL) and uplink (UL) paths.The FD base station, which is our subject of the article, has the ability tosend data for a user terminal in the DL path and receive data from anotheruser terminal in the UL path simultaneously in the same frequency band-width. Obviously, if the FD base station reduces its self-interference as muchas possible and provides service to both DL and UL users at one time slotin the same frequency band, spectral efficiency will increase. In the cellularnetwork, the use of FD base station has several advantages. One is that theprocessing unit at the base station is usually strong and powerful. Therefore,the complex interference cancellation technique can be implemented in thebase station more easily. Another advantage is that when the base station isimplemented as an FD, there is the possibility of increasing spectral efficiencywithout changing the terminal equipments. Even, the terminals do not evenneed to know about the functionality of the base station as FD. Accordingto this description, here, the base station of a cellular network is consideredto be FD, and the antenna selection has been used to reduce self-interferencein it. In the following, the two antenna selection criteria which are studiedin [21] will be discussed and the disadvantage of those two criteria will bedescribed. Then, a new criterion for selecting the antenna at the base stationwill be presented. Since the goal of the base station is to provide the bestservice to users in both DL and UL paths with the least self-interference, soin general, we are facing a multi-objective optimization problem. Therefore,the proposed criterion for antenna selection has also been designed and solvedas a multi-objective optimization. Finally, with simulations, it will be shownthat the new criterion has a good performance, especially in comparison withthe common antenna selection techniques.In the following, first, the system model will be described in section 2and the common criteria for antenna selection at the base station will bestated. Then, in section 3, the multi-objective criteria for antenna selectionare explained, and in section 4 the simulation results are presented. Finally,in section 5, the conclusion is given.
The system model according to Fig. 1 is comprised of an FD base stationwith M T transmit and M R receive antennas. In general, K D user terminalson the DL path receive data from the base station and K U terminals on theUL path is sending data to the base station. Terminals work as HD. Thatis, each terminal sends its data to the base station at a certain time slotand in another time slot, it receives its data from the base station. The timeslot for sending and receiving for each user are not the same. Therefore, theFD base station can serve K D user terminals on the DL path and K U userterminals on the UL path, at the same time. The user‘s multiple access willbe considered as one of the most common and orthogonal methods such as ulti-objective Antenna Selection in a Full Duplex Base Station 5 Fig. 1
FD multi-antennas base station orthogonal frequency division multiple access (OFDMA). Since the functionof the base station is FD, so the base station provides each of its time-frequencyresource blocks to one DL and one UL user simultaneously. For simplicity andwithout losing generality, we assume that the base station has allocated its firsttime-frequency resource block to the first user terminal on the DL path andthe first user terminal on the UL path, and other time-frequency blocks areavailable for other users. Because multiple access of the network is consideredto be orthogonal, users of different blocks do not interfere with each other. Forthis reason, in Fig. 1, only one user in the DL path and one user in the ULpath is considered. From hereafter, we only consider the first time-frequencyresource block and the first DL and UL user terminals. Because the basestation works as FD, the self-interference enters from the transmitter to thereceiver. Also, due to the fact that the UL user transmits in the same time-frequency resource block which the DL user receives its own data, there is anintra-user interference between these two terminals. In Fig. 1, self-interferenceand intra-user interference are specified as dashed lines. Because the DL andUL users are often away from each other and as the base station are not athigh altitudes, the intra-user interference is not as severe as self-interference.Therefore, for simplicity, this interference is not considered in the following.The base station has M T transmit antennas and the power gains of thesechannels in the DL path will be shown by { h , h , ..., h M T } . Similarly, the Mohammad Lari, Sina Asaeian channel power gains between the UL user and M R receive antennas is { g , g , ..., g M R } .In the interference channel, there are M R × M T paths and their power gainscan be presented as A = α α . . . α M T α α . . . α M T ... ... . . . ... α M R α M R . . . α M R M T The spatial channels of the interference and the DL and UL paths are un-correlated and Rayleigh with zero mean and unit variance [19]. Therefore,the power gains of these channels have an exponential distribution [22]. Theintra-user interference has been neglected too. In each use of the channel, thebase station selects one antenna at the transmitter and one antenna at thereceiver. After antenna selection, the channel power gain at the DL and ULwill be shown with h and g respectively and the power gain of the interferencechannel is α . If the received power by the user terminal in the DL path isequal to P D and the received power by the base station in the UL path isequal to P U , the signal power to noise plus interference power ratio (SINR) inthe DL and UL path are respectively [21] γ D = P D hσ (1) γ U = P U gσ + ηP D α (2)where σ is the noise power and 0 ≤ η ≤ η = 0 shows the full eliminationof the interference and η = 1 means complete leakage of the interference withinthe FD receiver. After selecting the suitable antenna in the DL and UL paths,and according to (1) and (2), the sum throughput rate of the DL and UL userscan be written as [21] C T = C D (1 − p o,D ) + C U (1 − p o,U ) . (3)Here, p o,D and p o,U represent outage probability in the DL and UL pathsrespectively p o,D = P ( γ D < γ D,T ) (4) p o,U = P ( γ U < γ U,T ) (5)and P ( . ) indicates the probability of an event. Also, C D and C U show theoutage capacity in the DL and UL and γ D,T and γ U,T are threshold level onthe SINR in the DL and UL paths. It is clear that the outage capacity can bewritten as C D = log (1 + γ D,T ) (6) ulti-objective Antenna Selection in a Full Duplex Base Station 7 C U = log (1 + γ U,T ) (7)In [21], two single-objective criteria for antenna selection are considered. Oneof them selects one transmit and one receive antenna which maximizes theDL and UL gains and the other selection criterion minimize the interferencechannel gain by selecting one antenna at the transmitter and one antenna atthe receiver. These two criteria are explained more in the following.2.1 Maximum Gain Criterion in DL and UL PathIn this criterion, one transmit antenna at the base station with the maximumDL channel gain is selected. In this way h = max { h , h , ..., h M T } (8)Similarly, one receive antenna with the maximum UL channel gain is selected.Thus, g = max { g , g , ..., g M R } (9)When the transmit and receive antennas are determined according to (8) and(9), the interference channel gain α will also be determined. Similar to [21],this criterion is abbreviated as MM-AS (max-max antenna selection) in thefollowing.2.2 Minimum Gain Criterion on Interference PathIn this criterion, one transmit and one receive antenna are selected to minimizethe self-interference channel gain. So that, the minimum interference will beentered to the receiver. Therefore, α = min { α , α , ..., α M R , α , α , ..., α M R , ... } (10)In other words, α is equal to the smallest element of the matrix A . If theelement on row i and column j of the matrix A have the minimum value, itmeans that the i -th receive antenna ( i = 1 , , ..., M R ) and the j -th transmitantenna ( j = 1 , , ..., M T ) at the base station will be used in the UL and DLpaths. When transmit and receive antennas are determined, the DL and ULchannel gains, h and g are also specified. In the following, this criterion isabbreviated as LI-AS (loop-back interference antenna selection) [21]. Mohammad Lari, Sina Asaeian
In [21], it has been shown by analysis and simulation that when the DLthroughput rate is more important, MM-AS is a more appropriate criterioncompared to the LI-AS. In contrast, when the UL throughput rate is moreimportant, LI-AS is more appropriate than the MM-AS. This behavior is alsojustifiable. In the MM-AS method, self-interference is not considered at thebase station. Therefore, the MM-AS criterion is suitable for a DL user who isnot involved with self-interference. Similarly, in the LI-AS method, the antennaselection is just based on the self-interference of the base station. Therefore,this criterion is suitable for the UL users. Note that, the UL user‘s signal isreceived by interference due to the FD function of the base station.From the viewpoint of the network and the base station, maximizing thesum throughput rate of both DL and UL users is more important. Therefore,the best antenna for selecting in the DL and UL paths are those antennasthat maximize the DL and UL gains and minimize the interference gain aswell. In other words, in this situation we face a multi-objective problem. Sothe transmit and receive antennas which are selected must provide the threegoals. These three goals are the maximization of the DL gain, the maximiza-tion of the UL gain and the minimization of the interference gain. Therefore,the problem of antenna selection can be described as a multi-objective opti-mization problem according to (11). In (11), i and j represent the antennaindex at the receiver and transmitter of the base station and h demonstratesthe power gain of the channel in the DL path, g presents the power gain ofthe channel on the UL path and α shows the power gain of the interferencepath. As it is clear, (11) has taken all three optimization (8), (9) and (10) intoconsideration. Hence, this problem is called multi-objective [23, 24]. max i,j h max i,j g min i,j α (11)The multi-objective optimization problem often does not have a unique answer.This means that there is no definite choice of transmit and receive antennasthat meets all three objectives in (11) at the same time. Therefore, in multi-objective problems, we have a set of solutions instead of a unique answer. Thisset is called the optimal Pareto points (see [23,24] for a more precise descriptionand mathematical definition of the optimal Pareto points). In multi-objectiveoptimization problems, one of the optimal Pareto responses is usually used asthe final solution of the problem.Multi-objective optimization problem solving methods are very diverse.Among these methods, the weighted sum method is simple and of course veryefficient [23]. In this method, the objective functions of the problem are com-bined with different weights and create a new objective function. In this way,the multi-objective problem changes to a common single-objective problem, ulti-objective Antenna Selection in a Full Duplex Base Station 9 which is simple to solve [23]. According to these explanations, we can trans-form the multi-objective optimization problem (11) into a single-objective op-timization problem in (12) which 0 ≤ w ≤ ≤ w ≤ ≤ w ≤ i,j − w h − w g + w α. (12)In (11), since the first two targets were considered to be maximal h and g ,they were entered in (12) with a negative sign. Often the importance of theDL and UL users are the same. Therefore, we can assume that the coefficientsof w and w are equal. Also, because the total weight is considered to be one,we can rewrite (12) in a simpler way and in the form ofmin i,j − (cid:18) − w (cid:19) h − (cid:18) − w (cid:19) g + wα. (13)According to (13), one antenna will be selected at the transmitter and receiverof the base station to minimize (13). As it was said, weights determine theimportance of each of the objective functions and this importance may changein good and bad channel conditions. In the problem (13), when w becomeslarger, the importance of the interference channel and interference cancellationbecome more important. As the same way, the performance of the systembecomes more similar to the LI-AS. Eventually when w = 1, the optimizationproblem (13) is exactly equivalent to the LI-AS criterion. In contrast, when w decreases, the importance of the interference channel becomes less and less,and the importance of the direct channel increases in the DL and UL paths. Inthis case, the performance of the system with multi-objective antenna selectionis similar to the MM-AS and in a certain degree of w = 0 , exactly equalsthe MM-AS criterion. The precise adjustment of the parameter w in solvingthe multi-objective optimization problem does not follow a definite method,and is often carried out by an expert and according to the conditions of theproblem [23,24]. In this paper, in order to simplify the multi-objective problemsolving, experimentally and in terms of trial and error, a mathematical relationis proposed for setting w .This experimental relation is confirmed in the nextsection by simulations. In this section, the performance of an FD base station with a new antenna se-lection criterion is reviewed and Monte Carlo simulation results are presented.For this purpose, we have P D σ = P U σ = γ and γ shows the average signal power to noise power ratio (SNR) in the DLand UL paths. Also γ D,T = γ U,T =10dB is assumed. For Monte Carlo simulation,
Fig. 2
Comparison of the new multi-objective criterion for antenna selection with the twoprevious criteria (MM-AS and LI-AS) for relatively low and relatively high interference w . In this figure, M T = 4 , M R = 4 and γ =15dB. In the blue curves with a square marker, η = − η = 0dB . In Fig. 2, the sum throughput rate with MM-AS and LI-AS can becompared with each other. For relatively low interference ( η = − η = 0dB), the throughput rate with theLI-AS is higher than the MM-AS. Therefore, in varying degrees of interference,the MM-AS and LI-AS criteria have different performance. The reason for thisdifference, as already explained, is that, in the MM-AS criterion for selectingan antenna, no attention is paid to interference channel and the antennas thathave the maximum gain on the DL and UL paths are selected. This criterion issuitable for a low interference situation. But when the interference is intense,the selection of the antenna with the LI-AS criterion performs better becauseit pays attention to the interference channel and selects antennas that have theleast gain in the interference channel. The multi-objective antenna selectioncriterion, discussed in this article, tries to combine both criteria and improvesperformance in all situations. In Fig. 2, it is clear that the multi-objectiveantenna selection with w = 0 and w = 1 performs similar to those of MM-ASand LI-AS. However, the most important point in Fig. 2 is the performanceimprovement of the criterion presented in this paper, in comparison with theMM-AS and LI-AS. When the interference is relatively low ( η = − ≤ w ≤ .
65 . When w ≈ .
3, this sum throughput ratewill be maximized. When the interference is relatively intense ( η = 0dB), themulti-objective antenna selection for 0 . ≤ w ≤ w ≈ .
6, the throughput rate will ulti-objective Antenna Selection in a Full Duplex Base Station 11
Fig. 3
Comparison of the new multi-objective criterion for antenna selection with the twoprevious criteria (MM-AS and LI-AS) for different values of the average SNR be maximized. Therefore, by setting the w parameter appropriately, selectingthe antenna with a new multi-objective criterion will certainly have a betterperformance in comparison with the common antenna selection methods. Theparameter w specifies the importance of the different objective functions inweighted sum method and the appropriate value of this parameter dependson the different conditions of the channel. In Fig. 3 we have plotted the sumthroughput rate again for the three different criteria based on w . As in theprevious figure, M T = 4 , M R = 4 and here η = − γ = 15dB (blue curves with square markers)and γ = 12dB (red curves with stellar markers). As in Fig. 2, the curves arecomparable in different aspects. The most important point is the differencein the performance of the multi-objective criterion when γ is changed. When γ = 15dB, the sum throughput rate reaches its maximum value for w ≈ . γ = 12dB, the sum throughput rates for w ≈ . η . So, the correctsetting of w is of great importance, according to the conditions of the channelsuch as γ and η .The proper setting of the parameter w is often carried out empirically byan expert [23, 24]. To simplify the proper adjustment of this parameter, withtrial and error, a suitable empirical value for w is proposed as w = 0 . η . + 0 .
02 ˘ γ − . . (14)In this case, ˘ γ shows the average SNR in dB. To verify the validity of thisexperimental equation, various simulations have been carried out for differentchannel and system parameters such as η , γ , γ D,T , γ U,T , M T and M R . In allof these cases, the multi-objective selection criterion has had a better perfor-mance than the two criteria of MM-AS and LI-AS. Two of these simulationsare shown in Fig. 4 and 5, and the rest are not drawn to prevent repetition.Note that equation (13) is empirically considered for valuing w and has been Fig. 4
Comparison of the new multi-objective antenna selection criterion with two previouscriteria (MM-AS and LI-AS) in different channel conditions when the number of transmitand receive antennas is 4 confirmed by various simulations. Since the weighted sum method is a verysimple technique for solving the multi-objective optimization problem, havinga proper estimate for w can solve the multi-objective problem quite easilyand straightforwardly. However, other methods that do not need to estimatethe w parameter can also be used to solve the multi-objective optimizationproblem. In Fig. 4, the sum throughput rate is plotted according to γ . In theblue curves with a square marker, η = − η = 0dB is assumed. As before, the number of transmit andreceive antennas is M T = 4, M R = 4 and one transmit and one receive an-tenna is selected in the base station in each time the channel is used. In orderto calculate the sum throughput rate with the multi-objective antenna selec-tion criterion, the parameter w is established in accordance with (13). As it isclear, the function of the new antenna selection in all values of γ and for bothvalues of η is better than the performance of the commonly used MM-AS andLI-AS. For example, for η = − γ = 10dB , the sum throughputrates in the proposed method is 2.46bits/sec/Hz better than the throughputrate in the LI-AS method. Also, for η = − γ = 20dB , the sumthroughput rate of the multi-objective method is 0.62bits/sec/Hz higher thanthe sum throughput rate in the MM-AS method. The same comparison can bemade in severe interference situations. For η = 0dB and in γ = 10dB, the sumthroughput rate in the proposed method is 1.22bits/sec/Hz better than thesum throughput rate in the LI-AS method. Also, for η = 0dB and γ = 20dB,in the multi-objective method, the sum throughput rates is 1.41bits/sec/Hzhigher than the sum throughput rate of the MM-AS.For having another comparison, similar to Fig. 4, the sum throughput rateis plotted versus γ for M T = 8 and M R = 8 in Fig. 5. Here again, the pa-rameter w is adjusted according to (13). The performance of the new antennaselection in all situations is better than the conventional one. Comparing Fig.4 and 5, it is clear that the sum throughput rate in Fig. 5 reaches its maximum ulti-objective Antenna Selection in a Full Duplex Base Station 13 Fig. 5
Comparison of the new multi-objective antenna selection criterion with two previouscriteria (MM-AS and LI-AS) in different channel conditions when the number of transmitand receive antennas is 8 value much faster than Fig. 4. For example, for γ = 10dB and η = − gamma for M T = 4, M R = 4 and η = − η = 0dB. Here, we use two differentmethods to solve the multi-objective optimization and compare the obtainedresults. First, the solution with the weighted sum method is depicted withblue curves and square markers in the figure. Then, the second solution withthe exponential weighted criterion method [23, 24] is plotted with red stellarmarkers. The exponential weighted criterion method has a similar parameter w and this parameter is adjusted to its proper value by trial and error. How-ever, in weighted sum method, w can be set by (13). The performance of twosolutions are nearly the same. Although the weighted sum method is moresimple to use and simulate. In this paper, a new criterion for selecting an antenna in an FD base station ispresented. In this new criterion, antenna selection has been modeled as a multi-objective optimization problem. In this case, multi-objective optimization isconsidered simultaneously with the maximization of the gain in the DL andUL paths along with the minimization of the gain in the interference channeland is solved by the weighted sum method. An experimental equation is alsoproposed for parameter setting to simplify using weighted sum method. Sim-ulation results show performance improvement in the new antenna selectionmethod than the previous ones.
Fig. 6
Comparison of weighted sum method and exponential weighted criterion method formulti-objective optimization solution
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