Device-to-Device Communications for Wireless Video ... - IEEE Xplore

Device-to-Device Communications for Wireless Video Delivery Negin Golrezaei, Mingyue Ji, Andreas F. Molisch, Alexandros G. Dimakis, Giuseppe Caire Dept. of Electrical Engineering University of Southern California emails: {golrezae,mingyuej,molisch,dimakis,caire}@usc.edu Abstract—The increasing demand for wireless video transmission requires new transmission paradigms. This paper reviews our recent work on such a new paradigm, namely the combination of caching of popular video files on wireless devices, with device-to-device (D2D) communication, so that users can obtain files from other wireless devices in their vicinity. The D2D communication is controlled by the base station (BS), and occurs only between devices that are within a small area (cluster) in order to allow high frequency reuse. The cluster size can be optimized for maximum overall system throughput. The caching strategy of the devices can be deterministic or random. Besides numerical optimization of the clustering and caching parameters, we also determine analytical upper and lower bound for how the throughput scales with the number of devices in a cell. For highly concentrated video request distributions, the throughput scales linearly, while in other cases only a slower increase is possible.

I. I NTRODUCTION The recent years have seen an explosive growth in the usage of wireless data transmission, and numerous market predictions (e.g., [1]) anticipate an even stronger growth, by almost two orders of magnitude, over the next 5 years. The major driver of this development is wireless video transmission. Originally, wireless video mostly implied short video clips (YouTube or news channels) on the very small screens of smartphones. The recent popularity of tablets and large-screen phones has opened the possibility for watching feature-length movies at high resolution on mobile devices, thus greatly increasing the amount of data that have to be transmitted, and leading to predictions that video will soon account for the majority of all wireless data traffic. These developments, while opening new business models and consumer satisfaction, threaten to completely clog up the already overburdened cellular networks. Traditionally, increase of cellular capacity has been achieved by one of the following methods: (i) increasing the amount of spectrum allocated to cellular communications, (ii) improving the spectral efficiency of the transmission scheme, or (iii) increasing the density of infrastructure nodes. The first method cannot increase capacity by orders of magnitude, due to the scarcity of spectrum in the frequency range that allows efficient coverage and outdoor-to-indoor communication. The second approach is reaching its limits as the current cellular standard (LTE-Advanced) has a physical layer that is close to the theoretical optimum (capacity-achieving codes, OFDM, multiple-antennas, interference coordination between cells).

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The last approach, which includes the deployment of femtocells, is feasible, but expensive, mainly because of the requirement of high-speed backhaul from each BS. For this reason, new network structures have to be investigated that could provide higher data rates at low cost. For video transmission, we can exploit the fact that demand for video files is highly redundant - in other words, a small number of files accounts for a majority of all requests. Early attempts to exploit this redundancy revolved around the use of cellular video broadcasting (such as the MediaFLO system) but failed because consumers want to view video on demand, and not be bound by predetermined starting times. As an alternative, we suggest that the redundancy of video requests be exploited by caching. Due to the tremendous increase in memory on wireless devices (32 - 64 GByte for tablets, and several hundred GByte for laptops), there is ample storage for caching available. The simplest way of using this storage would have each user cache the most popular files (possibly with individual modifications based on the tastes of a particular user). However, this approach is not efficient, as many files will be duplicated on a large number of devices. Instead, the devices should ”pool” their caching resources, so that different devices cache different files, and then exchange them, when the occasion arises, through device-to-device (D2D) communications. This exchange process is controlled by the base station (BS), which keeps track of which device has which files stored, as well as which devices are close enough to each other to enable shortrange, highly spectral efficient, D2D communications. If a requesting device does not find the file in its neighborhood (or in its own cache), it obtains the file in the traditional manner from the BS. The concept of BS-controlled D2D communications for wireless video was first introduced by us in 2010 [2], and its intuition is also described in [3], [4]. A somewhat different approach was recently introduced under the name ”microcast” by Keller et al. [5], where multiple devices download from the BS and then combine the gleaned information. The difference is that micro casting speeds up the download for a particular user, but does not necessarily increase the sum throughput of the users in the cell, while our approach leads to an overall spectral efficiency increase. In this paper, we review and summarize our previous results on this topic. Section II gives the system model and discusses

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the various simplifications we use for analytical treatment. Section III is devoted to the investigation of file popularity distribution and the question of how the number of requested different files grows as the number of users grow. Section IV optimizes the frequency reuse factor numerically, and Section V finally presents scaling laws that show, in closed form, how the throughput increases with the user density. We conclude this paper with a summary and future challenges. II. M ODEL AND S ETUP For ease of analysis, we consider a network with squareshaped macrocells; the dimensions of each cell are normalized to unity. Inter-cell interference is neglected, a situation that can be approximated through appropriate cell/frequency planning [6]. Each cell/BS serves n users. The BS has full knowledge of the locations and channel states of the devices. Each user can cache a fixed number (same for all users) of files (for simplicity we henceforth set that number to 1), and transmit them to other users ”on demand”. The cell is further subdivided into smaller (disjoint) groups of users called ”clusters”. Only nodes that are part of the same cluster can communicate with each other. To avoid interference within a cluster, only one D2D link can be active per cluster (we discount here the possibility of FDD or TDD to accommodate more users per cluster). Interference between clusters is minimized through a frequency reuse strategy as shown in Fig. 1. In this figure, each square represents a cluster (with length of√one side r, and maximum communication distance R = r 2 ), and the grey squares represent clusters that are active on a particular frequency. We assume a model, such that nodes within a cluster can communicate with each other, and nodes that are in clusters within the ”reuse distance” cannot communicate at all due to interference (red disk), while nodes/clusters outside the reuse distance are not interfered at all. This model is, of course, a major simplification whose assumptions do not hold exactly in practice. Yet, if provides a first approximation to the exact solutions. Furthermore, many of the simplifications do not impact the scaling laws (i.e., the functional form of the increase of throughput with number of users), though they do impact the absolute value of the throughput. As for all wireless networks, maximization of the sum throughput is an obvious goal of system optimization. The network designer can impact two parameters: the caching probabilities (see Sec. III), and the cluster size. For the latter, we can intuitively judge that there is a tradeoff: increasing the cluster size increases the probability that a user will find the file it wants within the cluster (since every device stores at least some files that are different from its neighbors) - in this case we call a cluster ”good”, and if actual transmission (which is subject to the interference constraints) occurs, the cluster is ”active”. On the other hand larger clusters reduce the frequency reuse. We can thus anticipate that there will be an optimum cluster size, and that it will depend on the video request statistics - the more ”concentrated” (i.e., redundant) the requests are, the smaller the optimum cluster size will

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Fig. 1.

An example of the single-cell layout.

be. Maximizing the number of active clusters leads to the maximum throughput of the network, though it does not necessarily lead to the maximum offload of traffic from the BS: for that latter goal, we instead wish to maximize the sum of active clusters plus the number of devices that find the file they desire in their own cache. III. F ILE POPULARITY AND CACHING As mentioned in Sec. I, video files have a very nonuniformly distributed popularity - a small percentage of files accounts for the majority of video traffic. Such files can be (recently released) popular movies, episodes of TV shows, news clips, highlights from sport games, and video (YouTube) clips. Popularity of those files changes, of course, but on a timescale that is slow compared to transmission time and mobility pattern, and can thus be considered constant for our purposes. Popularity distributions are commonly approximated by the Zipf distribution [7]. Any device requests file i with probability i−γr , H(γr , 1, m)

(1)

where m is the total number of files and we define H(γ, a, b) =

b X 1 γ i i=a

and

i = 1, · · · , m.

(2)

The parameter γr describes how redundant the requests are: the higher γr , the higher the redundancy, and the fewer files need to be available in a cache for constant probability of finding the requested file in the cache. Measurements of video requests indicate γr to be in the range [0.5, 1.5]. We note that the scaling behavior of the throughput is fundamentally different for γr < 1 and γr > 1. Another important question is how the number of files m grows with the number of users n. The following three cases occur naturally: • m ∝ const: This situation can occur for users that subscribe to a type of video service that makes a (regularly rotating) set of videos available to subscribers (a number of such services exist currently, though many are not specific to wireless transmission).

m ∝ log(n): when each user has a fixed probability of ”overlap” of its file requests with any other user, the total number of requested files m increases like log(n). This model accounts for the fact that users tend to share some interests (and thus file requests). α α • m ∝ n : m can increase like n , where α > 0. In particular, an increase with α > 1 can be attributed to effects of social networking, where the presence of more users spurs an increasing diversity of file requests. The devices also need to make a decision about which files to cache. The ”filling” of the cache can occur by ”overhearing” the transmission of a file from the BS or between two other devices; it could also occur directly from the BS at off-peak hours, when such a transmission does not materially impact the transmission quality of higher-priority data. In any case, we can anticipate that the filling of a cache takes a time that is shorter than the timescale over which content popularity changes, but longer than the time it takes to actually watch a video file. It is meaningful to consider two strategies for caching: deterministic and random. In the deterministic case, the BS, which has full information and control, instructs devices to cache the most popular files in a disjoint manner, i.e., no file should be cached twice in devices belonging the same cluster. Due to the time it takes to fill a cache (see above), this approach can only be used when the devices in a cluster are stationary over many hours (e.g., tablet computers only used at home). In random caching, each device randomly and independently caches a set of files according to a common probability density function. In our previous work [9] we assumed that the caching distribution is also a Zipf distribution, though with a different parameter γc 6= γr than the request distribution. We also recently found that the exact optimum caching distribution can be obtained as solution to a convex optimization problem [10]. •

(remember that we set the number of cached files per device equal to 1). Conditioned on k, the probability that the cluster is active, E[a|K = k] is the complement of the probability that no D2D communication takes place in the cluster, E[a|K = k] = 1 − Pr[u1 = 1 ∩ u2 = 1 ∩ ... ∩ uk = 1], (4) where Pr[.] represents the probability. Each ui for i = 1, ..., k is a binary random variable that is 1 if the user i cannot find its request file in the CVC (excluding the file in the ith user’s cache, taking into account the possibility of self-requests). Thus, Pr[ui = 1] = 1 − (PCV C (k) − fi ), (5) where fi is the request frequency of the ith popular file and PCV C (k) is the probability of finding the requested file in the CVC. For the case of deterministic caching, PCV C (k) is the probability that the requested file is among the k most popular files. If the devices are assumed to be located on a regular grid, then the number of devices per cluster, k, is a deterministic function of the cluster size. If the users are distributed randomly, then the number of devices in the cluster is binomial random variable with parameters n and r2 , i.e., K = B(n, r2 ), so that the probability that there are k users in the cluster equals to:   n Pr[K = k] = (r2 )k (1 − r2 )n−k , (6) k   n n! . where = (n−k)!k! k From the above, it follows that the expected throughput is E{T } =

n 1 X E[a|K = k] Pr[K = k] r2

1 = 2 r

IV. O PTIMUM COLLABORATION RADIUS Ref. [8] derived equations for the determination of the optimum cluster size, under the simplified model described in Sec. II. Let aj be an indicator function that is 1 if the cluster is active and 0 otherwise. We wish to maximize the total number of active clusters A in the cell, where it immediately follows P that A = aj . Assuming that inter-cluster interference is

k=0 n X

1−

k Y

(7a) !

(1 − (PCV C (k) − fi )) Pr[K = k].

i=1

k=0

(7b) Notice that P r[K = k] is a function of r, so that we now can numerically optimize r to obtain the highest E{T }. 90

j

γ=1.2 γ=1 γ=0.8 γ=0.6

80

where r12 is the number of clusters in the cell. We now first turn to the case of deterministic caching. The devices within a cluster create a ”common virtual cache (CVC)” (the union of all caches in the cluster), which contains the k most popular files, where k is the number of devices

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70 60

E[A]

taken care of by frequency planning, ”good” and ”active” clusters are linked by a constant (henceforth set to 1). Since all clusters are statistically equal, the expected number of active cluster, and thus the expected throughput E{T } (which is linked to E{A} through another constant that we set to unity), is X 1 E{T } = E[aj ] = 2 E[a], (3) r j

50 40 30 20 10 0 0

0.05

0.1

0.15

0.2

0.25 r

0.3

0.35

0.4

0.45

0.5

Fig. 2. The average number of active clusters versus r for n = 500, m = 1000 and different values for γ. From [8]

Figure 2 shows the average number of active clusters as a function of the cluster dimension, for different values of

the Zipf parameter γr . As anticipated, the optimum cluster dimension becomes smaller as the Zipf parameter increases. For the case of random caching, the probability that a cluster is good becomes a function not only of the number of nodes in that cluster, but also of their cache content (remember that for deterministic caching, the number of nodes alone determines the content of the CVC). Due to the random independent caching strategy of each node, the CVC content becomes a random vector, where the probabilities of its entries can be computed from the caching probability distribution. Computation of the expected throughput then requires averaging of all the CVC realizations [11]. V. S CALING LAWS FOR THE THROUGHPUT We now turn to the scaling laws, which describe the functional behavior of the overall throughput as a function of the user density. For this analysis, we concentrate on the case that each device make requests according to a Zipf distribution with γr , and randomly caches according to a Zipf distribution with parameter γc . We note, however, that deterministic and random caching show no fundamental difference in their scaling laws.1 In [9], [12] we established the following lower and upper bounds: Theorem 1: If the Zipf exponent γr > 1, i) Upper bound: For any caching q policy, E[T ] = O(n), q ii) Achievability: Given that c1 n1 ≤ ropt (n) ≤ c2 n1 2 and using a Zipf caching distribution with exponent γc > 1 then E[T ] = Θ(n). q This theorem shows that if we choose ropt (n) = Θ( n1 ) and γc > 1, E[T ] can grow linearly with n. For the request distributions that are less concentrated γr < 1, we obtained the following result: Theorem 2: If γr < 1, i) Upper bound: For any caching policy, E[T ] = O( mnη ) r where η = 1−γ 2−γr , q q η+ η+ ii) Achievability: If c3 mn ≤ ropt (n) ≤ c4 mn and users cache files randomly and independently according to a Zipf distribution with exponent γc , for any exponent n η + , there exists γc such that E[T ] = Θ( mη+ ) where 0 <  < 16 and γc is a solution to the following equation (1 − γr )γc = η + . 1 − γr + γc Thus, for such low concentration of the request distribution, growth is slower; users have to see more users in the neighborhood, i.e., the size of the CVC has to increase. 1 We use the following notation: given two functions f and g, we say that: f (n) = O (g(n)) if there exists a constant c and integer N such that f (n) ≤ cg(n) for n > N ; f (n) = Ω (g(n)) if g(n) = O (f (n)); f (n) = Θ (g(n)) if f (n) = O (g(n)) and g(n) = O (f (n)). 2 c and c s are positive constants that do not depend on n. i

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VI. S UMMARY AND CONCLUSIONS The use of D2D communications has the capability of increasing the throughput of wireless video networks by orders of magnitude. When the transmission of the most popular files can be offloaded to D2D, which has high frequency reuse and thus high area spectral efficiency, the BS is freed up for providing rarely requested video files as well as non-video data. One of the main practical challenges is incentivizing the owners of the devices, as well as content copyright owners. For the device owners, the question arises ”why should I spend my battery/bandwidth on improving the transmission for other users”? This question is somewhat similar to that arising in traditional internet peer-to-peer networks, and similar incentivizing mechanisms can be used [13]. Furthermore, wireless network operators (who benefit from the offloading) might provide additional incentives. In order to win over the copyright owners, strong guarantees will have to be provided that the cached movies cannot be appropriated by the devices on which they are cached, through approaches such as ”sandboxing” the caching area. Again, strategies that have worked in (legal) peer-to-peer networks can be adopted. Overall, BS-controlled D2D transmission is a very promising method for dramatically increasing the video throughput in wireless networks. R EFERENCES [1] http://www.cisco.com/en/US/solutions/collateral/ns341/ns525/ns537 /ns705/ns827/white paper c11-520862.html. [2] G. Caire, A. G. Dimakis, J. Kuo, A. F. Molisch, M. J. Neely and A. Ortega, ”Video-Aware Wireless Networks”, Intel-Cisco VAWN Program Workshop, 2010. [3] N. Golrezaei, A.G. Dimakis and A.F. Molisch, ”Wireless Video Content Delivery through Distributed Caching and Peer-to-Peer Gossiping” Asilomar Conference on Signals, Systems, and Computers, 2011, [4] N. Golrezaei, A.G. Dimakis, A.F. Molisch, and G. Caire, ”Femtocaching and Device-to-Device Collaboration: A New Architecture for Wireless Video Distribution”, IEEE Communications Magazine, in press, 2012. [5] L. Keller, A. Le, B. Cici, H. Seferoglu, C. Fragouli, and A. Markoloulou, ”Microcast: Cooperative video streaming on smartphones”, Proc. 10th Int. Conf. Mobile systems appl. services, 2012. [6] A. F. Molisch, ”Wireless Communications”, 2nd ed., IEEE Press Wiley, 2011. [7] M. Cha, H.Kwak, P. Rodriguez, Y.Y. Ahn, and S. Moon, ”I tube, you tube, everybody tubes: analyzing the world’s largest user generated content video system”, Proceedings of the 7th ACM SIGCOMM conference on Internet measurement, 1–14, 2007. [8] N. Golrezai, A. F. Molisch, and A. Dimakis, Base-Station Assisted Device-to-Device Communications for High-Throughput Wireless Video Networks, IEEE ICC Workshop on Video-Aware Wireless Networks 2012. [9] N. Golrezaei, A.G. Dimakis, and A.F. Molisch, ”Wireless Device to Device Communications with Distributed Caching, Proc. IEEE ISIT, 2012. [10] M. Ji and G. Caire, ”Caching optimization for device-to-device communications”, to be submitted. [11] N. Golrezai, A. F. Molisch, and A. G. Dimakis, ”Base-Station Assisted Device-to-Device Communications for Wireless Video”, to be submitted. [12] N. Golrezai, A. G. Dimakis, and A. F. Molisch, Scaling Behaviors of Wireless Device-to-Device Communications with Distributed Caching, arXiv:1208.1290. [13] B. Cohen, ”Incentives build robustness in BitTorrent” Workshop on Economics of Peer-to-Peer systems, Vol. 6, 68–72, 2003.