IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING, VOL. 6, NO. 3, JUNE 2012

257

Fundamentals of Inter-Cell Overhead Signaling in Heterogeneous Cellular Networks Ping Xia, Student Member, IEEE, Han-Shin Jo, Member, IEEE, and Jeffrey G. Andrews, Senior Member, IEEE

Abstract—Heterogeneous base stations (e.g., picocells, microcells, femtocells, and distributed antennas) will become increasingly essential for cellular network capacity and coverage. Up until now, little basic research has been done on the fundamentals of managing so much infrastructure—much of it unplanned—together with the carefully planned macro-cellular network. Inter-cell coordination is in principle an effective way of ensuring different infrastructure components behave in a way that increases, rather than decreases, the key quality of service (QoS) metrics. The success of such coordination depends heavily on how the overhead is shared, and the rate and delay of the overhead sharing. We develop a novel framework to quantify overhead signaling for inter-cell coordination, which is usually ignored in traditional 1-tier networks, and assumes even more importance in multi-tier heterogeneous cellular networks (HCNs). We derive the overhead quality contour for general -tier HCNs—the achievable set of overhead packet rate, size, delay, and outage probability—in closed-form expressions or computable integrals under general assumptions on overhead arrivals and different overhead signaling methods (backhaul and/or wireless). The overhead quality contour is further simplified for two widely used models of overhead arrivals: Poisson and deterministic arrival process. This framework can be used in the design and evaluation of any inter-cell coordination scheme. It also provides design insights on backhaul and wireless overhead channels to handle specific overhead signaling requirements. Index Terms—Heterogeneous cellular network, inter-cell coordination, inter-cell overhead sharing.

I. INTRODUCTION ETEROGENEOUS cellular networks (HCNs)—comprising traditional macro base stations (BSs) and heterogeneous infrastructure such as picocells, femtocells, and distributed antennas—have recently emerged as a flexible and cost-effective way of handling the exploding and uneven wireless data traffic demands, which are expected to increase indefinitely [1]–[3]. Not surprisingly, there has been very enthusiastic interest in industry towards making HCNs a reality.

H

A. Inter-Cell Coordination Techniques in HCNs The management of HCNs is significantly more difficult than the traditional 1-tier macrocell case, which is already considered challenging. The different kinds of BSs have distinct spatial densities, transmit powers, cell sizes, and backhaul capabilities. Further, the overlaid infrastructure will often be added over time in ad hoc locations [1]–[4]. Centralized control of all these BSs involves a potentially enormous amount of overhead messaging and is considered impractical. Decentralized inter-cell coordination is in principle an effective way of organizing HCNs for coordinated multipoint (COMP), cooperative scheduling and handoffs. In general, inter-cell coordination enables neighboring cells to successfully coexist and allows cooperative gains [5], which includes improvements to signal-to-interference-plus-noise ratio (SINR), spectral efficiency, and/or outage rates. Many coordination techniques are shown to have large cooperative gains in theory. However, the assessment of these gains usually ignores the inherent cost of overhead sharing: the overhead (e.g., CSI and user scheduling) is shared at limited rate with quantization error and delay [6], [7]. Practical concerns on overhead lead to nontrivial gaps between real and theoretical cooperative gains. An example is downlink joint processing COMP in the 1-tier case, which ideally introduces a multifold throughput improvement [5], [8], [9]. However, industrial simulations and field trials show that real throughput gain is disappointing—less than 20%—and the major limiting factor is sharing CSI and other overhead among cells [6], [7], [10], [11]. Mathematically, the achievable gain is a function of overhead parameters: 1) , the overhead packet interarrival time (the expected value of is the inverse of the expected packet rate); 2) , the overhead packet bit size; and 3) , the overhead delay. It is therefore important to evaluate cooperative gains in terms of the achievable values of these overhead signaling parameters. B. Previous Models for the Overhead Parameters

Manuscript received June 13, 2011; revised November 01, 2011; accepted December 18, 2011. Date of publication December 26, 2011; date of current version May 11, 2012. This work was supported in part by Motorola Solutions and in part by the National Science Foundation. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Erik Larsson. P. Xia and J. G. Andrews are with the Wireless Networking and Communications Group, Department of Electrical and Computer Engineering, The University of Texas at Austin, Austin, TX 78712 USA (e-mail: [email protected]; [email protected]). H.-S Jo is now with the Department of Electronics and Control Engineering, Hanbat National University, Daejeon 305–719, Korea (e-mail: [email protected]. kr). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JSTSP.2011.2181939

The model of limited overhead bit rate, which is the product and packet size , is previously of overhead packet rate considered for wireless overhead signaling [12]. It is not considered for backhaul signaling in the traditional 1-tier macrocell case (except that overhead includes user data [13], [14]), assuming macro BSs are equipped with high capacity backhaul. However, it is not always the case for BSs in HCNs. In particular, femtocells often use third-party IP-based backhaul (e.g., DSL and cable modem) that is aggregated by a gateway and so has much lower rate [1], [15]. Besides average rate, the natural dynamics in overhead interarrival time are often ignored. In coordination techniques

1932-4553/$26.00 © 2011 IEEE

258

IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING, VOL. 6, NO. 3, JUNE 2012

where inter-cell overhead is driven or influenced by unplanned incidents (e.g., during inter-cell handoffs overhead is generated when a user crosses cell boundaries), the interarrival time varies over time. However, previous works simply assume as a constant value (e.g., several symbol time [16]). Perhaps the most important piece missing from previous works is an appropriate model on overhead delay in general multi-tier HCNs. In 1-tier macrocell case, the backhaul interface between neighboring BSs is modeled as nearly delay-free [5], [8], [9], [17]. This assumption may hold if macrocells are directly interconnected by high speed Ethernet [11], but is far from reality in most network configurations [6], [7], [18]. More than likely, it is not applicable to overlaid BSs with generally lower capacities and more complicated protocols [1], [15]. For wireless signaling (e.g., to-be-defined overhead channels in LTE-A), the overhead delay is also very different from the 1-tier case due to distinct statistics of spatial interference in HCNs [19]–[22]. With even moderate mobility, delay in side information results in an irreducible performance bound that cannot be overcome even with much higher rate and more frequent overhead messages [23]. In summary, the appropriate models on overhead parameters in multi-tier HCNs are currently missing but of critical importance for the design and evaluation of coordination techniques. It is thus desirable to develop a general framework to quantify as a function the feasible set of overhead parameters of various HCNs setups, rather than heuristically for each possible network realization. C. Contributions In Section II, we develop general models for the overhead parameters in HCNs: 1) a Gamma distribution model on overhead interarrival time , which contains two important and opposite special cases: deterministic and Poisson overhead arrivals; 2) queuing models on backhaul servers (e.g., switches, routers and gateways) to characterize backhaul overhead delay ; and 3) a stochastic geometry model on HCN spatial interference to characterize wireless overhead delay . From such models, we propose a novel framework overhead quality contour to quantify feasible overhead parameters as a function of overhead channel realizations and overhead arrivals. We derive its general expressions in computable integrals for backhaul (Section III) and wireless overhead signaling (Section IV), which are simplified to closed-form results in two widely assumed overhead arrivals: deterministic and Poisson. We show mathematically and through numerical simulations that previous models, compared with our framework, are overoptimistic about achievable overhead rate, delay and outage probability, which explains the nontrivial gaps between their predictions and the real cooperative gains. The overhead quality contour can be used for the following general purposes. Evaluation and Optimization of HCN Coordinations: The overhead quality contour can be directly used for the analysis of specific HCN coordination techniques by determining: 1) the feasibility of these techniques, i.e., if their overhead requirements (e.g., overhead outage below some threshold) lie in the

Fig. 1. Base station locations and backhaul deployments of a 3-tier heterogeneous cellular network, comprising for example macro (tier 1), pico (tier 2), and femto (tier 3) BSs.

overhead quality contour; and 2) if feasible, their possible overin difhead signaling options, i.e., achievable set of ferent overhead signaling methods (backhaul and/or wireless). The gains of proposed coordination techniques can then be maximized by choosing the appropriate overhead signaling option. Design of HCN Overhead Channels: During the deployment of HCNs, the proposed framework is also useful in providing design insights on overhead channel setups to facilitate inter-cell coordinations. Based on the overhead quality contour, we derive tight lower bound in Section III on backhaul servers’ rate as a function of overhead signaling requirements and backhaul connection scenarios (i.e., the number of backhaul servers). Similarly, the lower bound on wireless overhead channel bandwidth is characterized in Section IV. The optimal setups to achieve these lower bounds are also identified. II. SYSTEM MODEL A heterogeneous cellular network—comprising types of base stations (BSs) with distinct spatial densities and transmit powers—can be modeled as a -tier network, where one tier consists of one type of BSs. For convenience, we associate the tier numbers with different types of BSs based on their transmitting powers. For example, in a HCN with high-power macrocells and successively lower power picocells and femtocells, we simply denote them as tier 1, 2, and 3, respectively (see Fig. 1). The locations of BSs (e.g., pico and femto BSs) in each tier can be modeled by an appropriate spatial random process, since their locations are usually unplanned. Surprisingly, it is also a reasonable model for HCNs including macro BSs [19]–[22]. Therefore, we assume all tiers are independently distributed on the and BSs in are distributed according to Poisson plane

XIA et al.: FUNDAMENTALS OF INTER-CELL OVERHEAD SIGNALING IN HCNs

259

For various values of , the average interarrival time is still . This model of includes two widely used models on overhead arrivals as special cases: deterministic and Poisson arrivals. Deterministic Overhead Arrivals: The interarrival time can be a constant determined by and based on standards or other agreements. An example is joint frequency allocation in LTE: base stations utilize certain preamble bits in each frame as their coordination message, to specify the frequency allocations for their users’ data in this frame. Therefore, the overhead message is generated in every 10 ms (i.e., each LTE frame) gives constant interarrival time [24]. In (1), (2)

Fig. 2. Diagram illustrating the backhaul connection between a femto and pico BSs. When overhead is shared between these two BSs through their backhaul, the overall delay consists of processing latencies from the backhaul servers (shown as rectangular boxes) and physical transmission latencies from the links among servers (e.g., fiber optic, dedicated wires, and microwave).

Point Process (PPP) with intensity . Note that this assumption only affects the SINR characterization of the wireless overin Lemma 1), while our results head channel (i.e., its CDF on overhead signaling hold under various SINR distributions. intends to coordinate In a -tier network, a base station , from whom it receives with its neighboring base station the strongest long-term average power (which means strongest needs to coninterference if not coordinated). Therefore, , such as its user schedstantly know the key parameters of thus has to peruling and/or the scheduled user’s CSI. The form overhead signaling to —that is, compressing these paeirameters into an overhead message and transmitting it to ther through backhaul (termed backhaul signaling) or wireless overhead channels (termed wireless signaling). Assumption 1: In this paper, we do not consider retransmission schemes of overhead messages due to their time sensitivity. Thus, one overhead message will be outdated once a new overhead message is generated. Denote as the bit size of each overhead message. In the following, we describe the models on other overhead parameters: message interarrival time and delay . A. Overhead Message Interarrival Time Assumption 2: The overhead arrival is assumed to be a stationary homogeneous arrival process with packet rate , i.e., the packet interarrival times have the same distribution with . At its most general, we assume the interarrival time is gamma distributed with parameter (1)

means convergence in distribution. where Poisson Overhead Arrivals: The interarrival time can also be random, determined by the users or other cells rather than and themselves. An example is user cell associations. As the users roam around, they choose their serving cells based on certain metrics including received power and congestion. Such choices will change the cell parameters (e.g., user sched, which means a new overuling and resource allocations) at . The head message should be generated and shared with overhead arrivals are thus random and often modeled as Poisson process with exponential interarrival time (3) It is known that exponential distribution is also a special case of . (1) with These two special cases of practical interest provide insights into two opposite extremes since for a given rate, deterministic arrivals are the least random while Poisson arrivals are the most random (maximum entropy). An arbitrary overhead arrival model is therefore bounded by these two extreme cases (which also have practical significance). B. Overhead Delay in Backhaul Signaling1 When the overhead message is transmitted through the backand , its delay generally comhaul network between prises two parts: 1) processing latencies from switches, routers and gateways (generally termed backhaul servers) in the backhaul path; and 2) the transmission delay of the wire (e.g., fiber optic and copper wires) or wireless links (e.g., microwave). See Fig. 2 for an example. The latter kind of latency is quite small and often ignored, except that BSs are directly interconnected using high-speed backbone without any intermediate backhaul servers [11]. For example, as the backhaul path between clustered picocells or co-located BSs contains few servers, the backhaul delay can be as low as 1 ms [18], [25], [26]. 1Backhaul is the intermediate link between operator’s core network and base stations. Such a link can be either wired (e.g., fiber lines and copper wires) or wireless (microwave), and the backhaul is thus further categorized as wireline or wireless backhaul. It is important to clarify the fundamental differences of wireless backhaul and wireless overhead channel in the following subsection. In the former case, the overhead is transmitted to backhaul servers (e.g., routers and gateways) through microwave, and will be routed in the backhaul network. In the latter case, overhead is directly shared between BS and BS without routing.

260

IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING, VOL. 6, NO. 3, JUNE 2012

Assumption 3: We assume the backhaul servers have exponential service time, the th of which allocates service rate (bps) to overhead packets. According to Assumption 1, each backhaul server will drop overhead packet(s) in its system upon the arrival of new overhead. in Assumption 3 are dependent Note that the parameters on the scheduling policies of backhaul servers. In the following, we list a few common examples. Example 1 (Pre-Emptive Scheduling): In this case, servers recognize the extreme delay sensitivity of overhead packets and identify them as the highest priority traffic. Thus, overhead will be served before all other traffic in a pre-emptive way [27] and . its allocated rate is indeed the total service rate Example 2 (High-Priority Scheduling): Servers identify overhead as a real-time flow with stringent delay and serve them before packets with an elastic delay requirement (e.g., non-real-time traffic such as web surfing) [28]. Suppose other , the service rate real time traffic is Poisson with total rate . experienced by overhead packets will be Example 3 (Equal-Priority Scheduling): All traffic is scheduled with equal priority at the servers. This is close to the worst case since the delay sensitivity of overhead traffic is ignored [28]. Suppose the data traffic are Poisson with rate , we then have . Under Assumption 1 and 3, the overhead delay from the th backhaul server is (4)

In this subsection, the overhead delay in backhaul signaling is is also derived. In the following, we modeled and its CDF characterize wireless overhead delay by using our SIR results [22] in -tier HCNs. C. Overhead Delay in Wireless Overhead Channel The wireless channel can be modeled as (7) where is the short-term fading, is the wall penetration loss (e.g., femtocells are usually deployed indoors), is the Euclidean distance between transmitter and receiver, and is the path loss exponent. In this paper, we consider independent and identically distributed (i.i.d.) Rayleigh fading with unit mean . Denote as the transmitting power of power, i.e., and as path loss exponent and BSs in the th tier while . wall penetration of their channels to Conventional cellular networks are generally interference-limited while thermal noise is negligible. Interference is even more significant in HCNs due to the overlaid BSs, generally of high density. Therefore, in this paper we neglect has the thermal noise. Under the cell selection policy that strongest long-term (i.e., with fading averaged out) power at , Lemma 1 below derives the signal-to-interference ratio . See (SIR) CDF of the overhead messages received at Lemma 1 and 3 and Theorem 1 in [22] for proof. associates with th Lemma 1 [22]: The probability that tier is

where is the effective service rate and is thus overhead packet rate per second. For overhead messages not dropped during transmission, the end-to-end backhaul delay is (5) where is the number of backhaul servers passed by overhead to . The values of and in (5) messages from depend on the specific backhaul configurations between and . For the backhaul connection between macro BSs, is typically around 10 to 20 and is thousands of packets per second [18]. In the most general case, the cumulative distribution function (CDF) of delay is very complicated and still under investigation [29], [30]. In our paper, we consider a scefor any . The CDF is nario of practical interest: then [31]

(8) where and . Under this of the discondition, the probability density function between and , and the cumulative distritance bution function of received SIR at for an arbitrary are distance

(9)

(6) where . Note that and in (6) are packet size (in bits) and backhaul servers’ packet proin cessing rates. We now derive an important property of below, which will be frequently used in the sequel. Property 1: . In the special case of , we have . Proof: See Appendix A.

(10) where (11) can be reasonably assumed According to Assumption 1, to drop existing overhead packets upon the arrival of new

XIA et al.: FUNDAMENTALS OF INTER-CELL OVERHEAD SIGNALING IN HCNs

overhead, as backhaul servers in Assumption 3. The overhead packets, if not dropped during transmission, therefore experience delay given by (12)

261

A. General Case and Main Results Theorem 2: For backhaul overhead signaling between and with interarrival time the overhead quality contour is

,

is the overhead channel where is the overhead packet size, bandwidth and the distribution of SIR is given in (10). D. Fundamental Evaluation Metric With overhead interarrival time and delay modeled, we here define overhead outage . Definition 1: An overhead message is successful if it arrives before being outdated (i.e., , since at the destination an overhead is not outdated until a new one is generated) and ). Otherwise, it is defined before a hard deadline (i.e., as in outage. The outage defined above is the probability that an overhead block is not fully received before a certain deadline specified by the coordination techniques. It is indeed the overhead block error, not including the effect of coding and complicated overhead transmission schemes [23]. Based on Definition 1, the fundamental evaluation metric of this paper—the overhead quality contour is thus defined as (13) is the overhead interarrival time, is the overhead where packet size, is the required overhead deadline (i.e., maximal tolerable delay), and is the corresponding outage probability. Note that the delay is fully characterized by and , and thus . is not explicitly included in This metric above determines the feasible set of overhead paas a function of overhead signaling conrameters figurations in HCNs (e.g., overhead arrival process and channel parameters). As will be illustrated in Sections III and IV, this framework can be used for the evaluation and design of coordination techniques and HCN overhead channel setups.

III. OVERHEAD QUALITY CONTOUR IN BACKHAUL SIGNALING This section presents the main results for backhaul overhead signaling. The overhead quality contour is quantified when and share overhead through their dedicated backhaul. We consider the general scenario that the backhaul overhead delay is dominated by the processing latencies from backhaul servers, which is true for most backhaul network setups [6], [7], [18]. Of course, the analysis in this section does not apply to the case, for example, when macro BSs are directly interconnected with using high-speed backbone without any intermediate servers [11]. However the backhaul delay in these counter examples (which are not very common in HCNs) is often negligible [18], [25], [26]. In this section, denote the number of backhaul servers passed by overhead messages as , and their overhead pro. cessing rates as

(14) where

are defined in (6), is the gamma function and is the lower incomplete gamma function given by (15)

Proof: See Appendix B. Theorem 2 quantifies all plausible overhead parameters that can be supported by given backhaul configurations. Since many coordination techniques often have additional requirements on ), their several overhead parameters (e.g., requiring feasible overhead sets are strict subsets of . In theory, these subsets can be determined from Theorem 2 by, for example, in (14). However, it is computationally restricting under a given hard in practice to derive feasible set of outage requirement. In the following, we derive simpler bounds on (14), which can be easily used to characterize the feasible set of several overhead parameters given others. According to its definition and observations from Theorem 2, the outage probability is an increasing function on the overhead rate while a decreasing function on the deadline requirement . For example, the outage probability is zero when and as shown in Theorem 2. Therefore, it has the following two lower bounds. Lower Overhead Rate: By letting the overhead packet rate go to zero, overhead packets have very long lifetimes (i.e., ) and overhead outage only comes from the probability of not meeting the hard deadline (i.e., ):

(16) Relaxed Delay Deadline: By letting delay deadline go to infinity, the overhead delay deadline is relaxed and outage only comes from the probability of being outdated during transmis): sion (i.e., (17)

262

IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING, VOL. 6, NO. 3, JUNE 2012

Remark 3: For backhaul signaling, a lower bound for overhead outage probability is

where

is the average service rate and is the inverse incomplete gamma function given by

(22) where and are given in (16) and (17), respectively. Remark 3 can be used to estimate feasible overhead sets for various coordination techniques. For example, for coordination , we can estimate its feasible set techniques requiring by simply solving . Such of an estimation is fairly accurate, because numerical simulations is reain Section V show that the lower bound sonably tight under general overhead arrivals. It is interesting to compare feasible overhead parameters quantified by our framework with previous works. Previous models do not capture the randomness in overhead inter-arrival time , which is assumed to be the constant [16]. Overhead backhaul delay in (5) is often neglected or simply assumed to be its averaged value [5], [8], [9], [17] (18)

Proof: See Appendix C. The lower bounds in Corollary 4 are expected to be tight, since they are based on the tight bounds in Remark 3. B. Special Cases: Deterministic and Poisson Overhead Arrivals Corollary 5: For backhaul signaling under deterministic overhead arrivals, the overhead quality contour is (23) Proof: Deterministic overhead arrival corresponds to the with . Before case of we proceed to derive overhead rate and delay contours, we state two important results as follows:

Under the above simplified models, the overhead quality contour will reduce to (24)

(25) (19) is the indicator function. Obviously the feasible where overhead parameters defined in (19) are vastly different from , (14). For example, under given backhaul servers’ rates overhead outage in (19) can be zero under finite values of and . However, the lower bound in Remark 3 shows that iff and . Therefore, the natural randomness in and crucially determines the feasible overhead signaling contours and will be discussed more in Section V. can be used for In general, the overhead quality contour the design and evaluation of coordination techniques in HCNs. For example, in below we provide backhaul design guidelines to effectively support overhead signaling required by coordination techniques. Corollary 4: For a given overhead requirement from coordination techniques, the backhaul configuration, i.e., , must satisfy the following inequalithe values of and ties:

is the indicator function. Note that for a random where is the variable . By using Chebyshev’s inequality on probability that and letting , the results in (25) follow. Based on the equations immediately above, the outage probain Theorem 2 bility below is derived by letting

(26) where is the indicator function, and holds from Prop. erty 1 by letting Under deterministic overhead arrivals, the lower bound in (17) is simplified as

(20) (21) (27)

XIA et al.: FUNDAMENTALS OF INTER-CELL OVERHEAD SIGNALING IN HCNs

where holds directly from (24). Combining the two lower bounds under deterministic overhead arrivals, i.e., (16) and (27), we have

(28) It is important to note that the lower bound above is exactly given in Corollary 5. Remark 6: Deterministic overhead arrivals minimize the outage probability, by achieving the lower bound in Remark 3. The above remark implies that ignoring the randomness in the overhead arrival process will lead to an underestimation of overhead outage. Numerical results show that this lower bound is not tight. Corollary 7: For backhaul signaling with Poisson overhead arrivals, the overhead quality contour is

263

Remark 8: For a given sum of service rates, equal rate allocation among backhaul servers minimizes the overhead outage, independent on overhead arrival process. Remark 6 and 8 together imply that the overhead outage is minimized when overhead arrivals are deterministic and backhaul servers have the same overhead processing rate . In summary, in this section we have quantified the overhead quality contour—the feasible set of overhead parameters —for backhaul signaling in general HCNs. We show that previous models—which ignore the inherent and delay randomness in overhead inter-arrival time —underestimate the overhead outage and therefore are not accurate in quantifying the cost of overhead sharing. The derived overhead quality contour also provides design insights on backhaul network configurations, e.g., predicting the required overhead processing rates from backhaul servers and identifying the optimal rate allocation among them. IV. OVERHEAD QUALITY CONTOUR IN WIRELESS SIGNALING

(29) . where Proof: Poisson overhead arrivals correspond to the special with : case of

Dedicated wireless links (e.g., out-of-band GSM or to-be-defined overhead channels in LTE-A) are also used by coordination techniques to share overhead (e.g., CSI feedback). Since the radio environment in HCNs is very different from 1-tier macrocell case, the wireless overhead channels present new characteristics such as SINR distributions. In this section, we quantify the overhead quality contour for wireless signaling in HCNs, as(denoted as ) and distance suming arbitrary tier index of and (denoted as ). between A. General Case and Main Results Theorem 9: For wireless overhead signaling between and with interarrival time the overhead quality contour is

(30) The equality comes from the fact that and , while equality holds from Property 1 (letting ). See the proof of Property 1 for the last two steps. For a given sum of service rates , the delay CDF is maximized for any and iff all service . Thererates are equal, i.e., fore, equal rate allocation among backhaul servers minimizes the overhead outage under deterministic arrivals in Corollary 5. It is also the optimal choice for Poisson overhead arrivals beand cause it simultaneously maximizes in Corollary 7. Such a conclusion in fact holds under general overhead arrivals. The maximized CDF implies that the delay is stochastically minimized. The outage is therefore minimized, probability independent on the overhead arrival process.

,

(31) is the required SIR for where . overhead deadline and the subscript is the tier index of Proof: See Appendix D. Theorem 9 quantifies the possible pairs of for arbitrary wireless overhead channel setups. However, for the same reason stated below Theorem 2, we derive simpler bounds in (31). on Remark 10: The overhead outage in Theorem 9 can be bounded as (32) Using the same argument in Section III, the lower bound on or overhead outage can be achieved by letting . The upper bound on can be found based on the fact that

264

IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING, VOL. 6, NO. 3, JUNE 2012

. By restricting several overhead parameters in (32) as required by coordination techniques, the bounds determine their feasible overhead sets in an easier way than Theorem 9. Remark 10 shows the clear dependence between overhead function) and outage and the distribution of SINR ( ( function). Therefore, with appropriate models on SINR and overhead interarrival time , the overhead quality contour in Theorem 9 provides more accurate insights than previous works on feasible overhead parameters in HCNs. of all tiers have the same path loss Corollary 11: When exponent , for a given overhead requirement from coordination techniques, the bandwidth of wireless overhead channel must satisfy following inequalities:

TABLE I NOTATION AND SIMULATION SUMMARY

(33) where , and is the cosecant function. Proof: See Appendix E. It is generally hard to provide design guidelines for wireless overhead channel (e.g., the bandwidth ) directly from the overhead quality contour or even its bounds. This is mainly beas in Lemma 1. In cause of the complicated expression of can be Corollary 11 we discuss it in a special case where simplified. B. Special Cases: Deterministic and Poisson Overhead Arrivals Corollary 12: For wireless signaling with deterministic overhead arrivals, the overhead quality contour is

The results on overhead quality contour in Theorem 9 are greatly simplified in these special cases. Under deterministic arrivals, the lower bound on in Remark 10 reduces to

(34) Proof: Based on the proof of Theorem 9, overhead outage under deterministic overhead arrival is

(35) where is the indicator function. Corollary 13: For wireless signaling with Poisson overhead arrivals, the overhead quality contour is

(37) It is seen that, similar to backhaul signaling, deterministic arrivals are also optimal in wireless signaling. In other words, ignoring natural randomness in overhead arrivals leads to underestimation of wireless overhead delay and outage, which is nontrivial as shown through numerical results below. In summary, in this section we have quantified the feasible for wireless signaling set of overhead parameters , which in HCNs. The results are expressed as a function of is the SIR distribution. Thus, they are applicable to various wireless overhead channels (e.g., in-band versus out-band) and HCN models (e.g., grid model versus PPP model for BS locations), by using the appropriate SIR distribution functions. V. NUMERICAL RESULTS AND DISCUSSION

(36) Proof: The proof follows simply by replacing the general expression with .

In this section, we consider a 3-tier heterogeneous network as shown in Fig. 1, comprising for example macro (tier 1), pico (tier 2) and femto (tier 3) BSs. Notation and system parameters is a pico BS. According to the are given in Table I. Suppose , the overhead quality contour is investigated tier index of in the following three scenarios.

XIA et al.: FUNDAMENTALS OF INTER-CELL OVERHEAD SIGNALING IN HCNs

Fig. 3. Overhead outage p versus overhead arrival rate  in all three scenarios. The delay requirement d is 0:3 [T ] = 0:3= , i.e., overhead signaling is al)=(B) = 1000 lowed to occupy 30% time slots. The overhead service rate ( packets/s.

Scenario I: belongs to 1st tier: The backhaul path between pico and macro BSs includes backhaul servers from the . core network and the picocell aggregator, i.e., belongs to 2nd tier: Since nearby pico BSs Scenario II: are often clustered by sharing the same backhaul aggregator [3], and its neighbor the number of backhaul servers between is . belongs to 3rd tier: The backhaul servers Scenario III: between pico and femto BSs consist of the picocell aggregator, the femtocell gateway, and those from the core network and fem. tocell’s IP network, i.e., In all three scenarios, we assume all backhaul servers have the same rate for overhead packets, which is optimal per Remark 8. Due to the lack of real network data, we did not test our models on actual inter-cell overhead signaling in this paper. A. Overhead Quality Contour in Backhaul Signaling Versus Backhaul Configurations: The overhead quality contour in various backhaul configurations (i.e., number of and their rate ) is shown in Figs. 3 and backhaul servers 4. Obviously, the overhead outage decreases as the number of servers decreases and/or their rate increases. However, two important observations are worth noting: 1) reducing the number of backhaul servers is critically important since the is way below the other two outage in scenarios II ; 2) it is difficult to ensure very small scenarios ) purely by increasing backhaul servers’ outage (e.g., rate , since the outage curve in Fig. 4 is almost flat in the . Under this circumstance, our conjecture region of is that appropriate retransmission schemes and certain level of coding should also be deployed for further outage reduction. Insights on Backhaul Deployments: According to the specific overhead requirements, the minimum rate of backhaul servers is derived in Corollary 4 based on the lower bound in Remark 3. This bound is achieved under deterministic arrivals (as stated in Remark 6) but suspected to be loose under Poisson arrivals—the opposite extreme of deterministic. However, Fig. 3 shows that it is fairly tight even for Poisson arrivals, especially in small

265

Fig. 4. Overhead outage p versus average packet service rate =B in the three scenarios. The overhead rate  = 50 packets/s, i.e., an overhead on average has lifetime (T ) = 1= = 20 ms. The overhead delay requirement d is 0:3 [T ] = 6 ms.

) of practical interest. Therefore, outage region (i.e., the results in Corollary 4 provide accurate guidelines on the deployment of backhaul overhead channels in HCNs. Comparison With Previous Models: Fig. 3 also shows the appreciable difference in overhead outage between Poisson and deterministic arrivals. For example, with the same overhead rate of 10 packets/s in scenario III, deterministic arrivals incur 0.1 outage (usually an acceptable packet error percentage) while Poisson arrivals incur 0.3 outage (generally unacceptable). In other words, the randomness in overhead arrivals is an important factor for overhead signaling characterization but missed from previous works. Fig. 5 shows the more comprehensivecomparison of our results with previous simplified models in scenario II. It is seen that previous simplified models, ignoring the randomness in overhead arrivals and backhaul delay, are highly inaccurate even though their underlying assumption of low-latency backhaul interface is satisfied in scenario II (mean delay is 1 ms). Under an outage re, they predict that backhaul quirement of, for example, channel can support up to 250 packets/s, which in fact is between 75 (Poisson arrivals) and 125 packets/s (deterministic arrivals). B. Overhead Quality Contour in Wireless Signaling Versus Overhead Channel Configurations: Fig. 6 shows the overhead outage in three scenarios, i.e., different types of . The overhead outage is significantly lower in scenario I, as the macro BSs have the large transmitting power and smaller path loss exponent. Fig. 6 also shows that the gap in overhead outage increases as the overhead arrival rate goes up. versus wireless overhead Fig. 7 illustrates the outage . The observation here is similar to channel bandwidth Fig. 4: increasing bandwidth can easily reduce outage to about 0.1 but is not a cost-effective way for further outage reduction. Therefore, retransmission schemes, coding and diversity techniques will be useful in this situation. Comparison with Previous Models: Two key differences from previous models contribute to our more accurate character-

266

IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING, VOL. 6, NO. 3, JUNE 2012

Fig. 5. Overhead outage p versus overhead arrival rate  in scenario II. The delay requirement d is 0:3 [T ] = 0:3= , i.e., overhead signaling is allowed to )=(B) = 1000 packets/s occupy 30% time slots. The overhead service rate ( and the number of backhaul servers N = 1, which together translate to a mean delay of ( ) = 1 ms. Previous simplified models assume constant overhead delay = ( ) = 1 ms and constant overhead arrivals = ( ) = 1= .

D

D

D

T

T

Fig. 7. Overhead outage p versus wireless overhead channel bandwidth W . The overhead rate  = 100 packets/s, and the delay requirement d is 0:3 [ ] = 0:3= , i.e., overhead signaling is allowed to occupy 30% time slots.

T

; and 2) the average overhead delay (12)

derived from (5) and

backhaul channel

(38)

wireless channel. Fig. 8 depicts the optimal choice in Scenario I under deterministic and Poisson arrivals. In general, the backhaul channel is preferred for slow overhead traffic, while the wireless channel is more preferred for fast overhead sharing. Comparing Fig. 8(a) and (b), it is seen that as the randomness of overhead arrivals increases, wireless signaling becomes more preferable. VI. CONCLUSION

Fig. 6. Overhead outage p versus overhead arrival rate  for wireless signaling. The delay requirement d is 0:3 [ ] = 0:3= , i.e., overhead signaling is allowed to occupy 30% time slots. The overhead channel bandwidth is 50 kHz.

T

ization of the overhead signaling in HCNs: 1) the consideration of overhead arrival dynamics, because Fig. 6 shows that Poisson overhead arrivals incur higher outage than deterministic arrivals (no randomness in as assumed in previous models) by 0.05 to 0.1; 2) the appropriate spatial model on BS locations in HCNs, which is fundamental to spatial interference statistics and . The comparison of overhead channel SINR distribution spatial models (our PPP-based model versus previous assumed grid model) is extensively discussed in [19]–[22]. C. Optimal Overhead Signaling Method Numerical results show that in all three scenarios, the optimal choices between backhaul versus wireless signaling are determined by two important measures: 1) the overhead arrival rate

This paper has presented a new framework to quantify the feasible set of inter-cell overhead delay, rate and outage as a function of plausible HCN deployments. This framework allows a more realistic but analytically tractable assessment on inter-cell coordination in HCNs by quantifying the inherent impact of the overhead signaling. It also provides design guidelines on HCN overhead channels (backhaul and wireless) to accommodate specific coordination techniques. Future extensions to this approach can include sophisticated overhead retransmission schemes or overhead signaling between multiple (more than two) cells. Investigations and testing of the overhead models would also be useful. APPENDIX A. Proof of Property 1 For

, Property 1 obviously holds, since

(39)

XIA et al.: FUNDAMENTALS OF INTER-CELL OVERHEAD SIGNALING IN HCNs

267

B. Proof of Theorem 2 According to its definition, the successful overhead will not be dropped by the backhaul servers. Therefore, its delay is the sum latencies from all the backhaul servers as in (5). With the delay CDF given in (6), the overhead outage is derived as

(41) holds from the definition of in (6) and integration by comes from the fact that parts. The equality (Property 1 by letting ). C. Proof of Corollary 4 Fig. 8. Optimal overhead channel choice in Scenario I under deterministic and Poisson overhead arrivals. The wireless overhead channel bandwidth is 50 kHz : and its overhead average delay [ ] = 2 ms. The delay requirement d is 0:3 [ ] = 0:3= . The mark “ ” means wireless signaling is preferred with lower outage, while “ ” means backhaul signaling is preferred. (a) Deterministic overhead arrivals. (b) Poisson overhead arrivals.

D

T

For

2

As seen in Remark 8, equal rate allocation minimizes the overhead outage for a given sum rate. Under this backhaul setup, the CDF of delay as in (5) is gamma distributed with CDF given as (42)

, we have where we have

. Based on the proof of Theorem 2,

(40) Note that in cient holds from (39).

is indeed the coeffi. Thus, the equality

where mark 3, inequality

. Based on the argument in Refollows by letting or . For

268

IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING, VOL. 6, NO. 3, JUNE 2012

a given overhead requirement must satisfy

, the value of

and

Using the bound immediately above in the lower bound of (33) follows.

,

ACKNOWLEDGMENT The authors would like to thank Dr. A. Ghosh and Dr. B. Mondal of Motorola Solutions (Now Nokia Siemens) for their valuable technical inputs and feedback regarding this paper.

REFERENCES

Inequality follows from back for .

and

holds by substituting

D. Proof of Theorem 9 The outage probability

in wireless signaling is

(43) As belongs to the th tier, the wireless overhead delay is characterized as

where then follows.

. The outage probability

E. Proof of Corollary 11 As shown in Corollary 2 in [22], the CDF plified under equal path loss exponents

where the function

is sim-

is

(44)

[1] V. Chandrasekhar, J. G. Andrews, and A. Gatherer, “Femtocell networks: A survey,” IEEE Commun. Mag., vol. 46, no. 9, pp. 59–67, Sep. 2008. [2] A. Khandekar, N. Bhushan, J. Tingfang, and V. Vanghi, “LTE advanced: Heterogeneous networks,” in Proc. Eur. Wireless Conf., Jun. 2010, pp. 978–982. [3] “Picocell mesh: Bringing low-cost coverage, capacity and symmetry to mobile WiMAX,” White Paper, Tropos Network Mar. 2007. [4] J. Zhang and J. G. Andrews, “Distributed antenna systems with randomness,” IEEE Trans. Wireless Commun., vol. 7, no. 9, pp. 3636–3646, Sep. 2008. [5] D. Gesbert, S. Hanly, H. Huang, S. S. Shitz, O. Simeone, and W. Yu, “Multi-cell MIMO cooperative networks: A new look at interference,” IEEE J. Sel. Areas Commun., vol. 28, no. 9, pp. 1380–1408, Dec. 2010. [6] S. Ramprashad and G. Caire, “Cellular vs. network MIMO: A comparison including the channel state information overhead,” in Proc. IEEE Int. Symp. Personal Indoor and Mobile Radio Commun., Sep. 2009, pp. 878–884. [7] S. Ramprashad, G. Caire, and H. Papadopoulos, “Cellular and network MIMO architectures: MU-MIMO spectral efficiency and costs of channel state information,” in Proc. IEEE Asilomar Conf. Signals, Syst., Comput., Nov. 2009, pp. 1811–1818. [8] S. Shamai and B. M. Zaidel, “Enhancing the cellular downlink capacity via co-processing at the transmitting end,” in Proc. IEEE Veh. Technol. Conf., 2001, vol. 3, pp. 1745–1749. [9] O. Somekh, B. M. Zaidel, and S. Shamai, “Sum rate characterization of joint multiple cell-site processing,” IEEE Trans. Inf. Theory, vol. 53, no. 12, pp. 4473–4497, Dec. 2007. [10] S. Annapureddy, A. Barbieri, S. Geirhofer, S. Mallik, and A. Gorokhov, “Coordinated joint transmission in WWAN,” in Proc. IEEE Commun. Theory Workshop, May 2010. [11] R. Irmer, H. Droste, P. Marsch, M. Grieger, G. Fettweis, S. Brueck, H.-P. Mayer, L. Thiele, and V. Jungnickel, “Coordinated multipoint: Concepts, performance, and field trial results,” IEEE Commun. Mag., vol. 49, no. 2, pp. 102–111, Feb. 2011. [12] D. J. Love, R. W. Heath, Jr., V. K. N. Lau, D. Gesbert, B. D. Rao, and M. Andrews, “An overview of limited feedback in wireless communication systems,” IEEE J. Sel. Areas Commun., vol. 26, no. 8, pp. 1341–1365, Oct. 2008. [13] O. Somekh, O. Simeone, A. Sanderovich, B. M. Zaidel, and S. Shamai, “On the impact of limited-capacity backhaul and inter-users links in cooperative multicell networks,” in Proc. 42nd Annu. Conf. Inf. Sci. Syst., 2008, pp. 776–780. [14] A. Sanderovich, O. Somekh, H. V. Poor, and S. Shamai, “Uplink macro diversity of limited backhaul cellular network,” IEEE Trans. Inf. Theory, vol. 55, no. 8, pp. 3457–3478, Aug. 2009. [15] 3GPP TS 25.467 v9.3.0: Utran Architecture for 3G Home NodeB (HNB) (Release 9), Jun. 2010, 3GPP. [16] J. Zhang, M. Kountouris, J. G. Andrews, and R. W. Heath, Jr., “Multimode transmission for the MIMO broadcast channel with imperfect channel state information,” IEEE Trans. Commun., vol. 59, no. 3, pp. 803–814, Mar. 2011. [17] G. Foschini, K. Karakayali, and R. A. Valenzuela, “Coordinating multiple antenna cellular networks to achieve enormous spectral efficiency,” in IEE Proc. Commun., Aug. 2006, vol. 152, no. 4, pp. 548–555. [18] D. Wei, “Leading edge-LTE requirements for bearer networks,” Huawei Communicate, pp. 49–51, Jun. 2009. [19] P. J. Fleming, A. L. Stolyar, and B. Simon, “Closed-form expressions for other-cell interference in cellular CDMA,” Univ. of Colorado, Denver, Tech. Rep., Dec. 1997.

XIA et al.: FUNDAMENTALS OF INTER-CELL OVERHEAD SIGNALING IN HCNs

[20] J. G. Andrews, F. Baccelli, and R. K. Ganti, “A tractable approach to coverage and rate in cellular networks,” IEEE Trans. Commun., vol. 59, no. 11, pp. 3122–3134, Nov. 2011. [21] H. S. Dhillon, R. K. Ganti, F. Baccelli, and J. G. Andrews, “Modeling and analysis of K-tier downlink heterogeneous cellular networks,” IEEE J. Sel. Areas Commun., Apr. 2012 [Online]. Available: http://arxiv.org/abs/1103.2177, to be published [22] H.-S. Jo, Y. Sang, P. Xia, and J. G. Andrews, “Heterogeneous cellular networks with flexible cell association: A comprehensive downlink SINR analysis,” IEEE Trans. Wireless Commun. Jul. 2011 [Online]. Available: http://arxiv.org/abs/1107.3602, submitted for publication [23] M. A. Maddah-Ali and D. Tse, “Completely stale transmitter channel state information is still very useful,” in Proc. Allerton Conf. Commun., Control, Comput., Sep. 2010, pp. 1188–1195. [24] A. Ghosh, J. Zhang, J. G. Andrews, and R. Muhamed, Fundamentals of LTE. Englewood Cliffs, NJ: Prentice-Hall, 2010. [25] Further Advancements for E-UTRA Physical Layer Aspects (Release 9), 3GPP TR 36.814 v9.0.0, Mar. 2010, 3GPP. [26] G. K. Venkatesan and K. Kulkarni, “Wireless backhaul for LTE—Requirements, challenges and options,” in Proc. IEEE Int. Symp. Adv. Netw. Telecomm. Syst., Dec. 2008, pp. 1–3. [27] M. Wernersson, S. Wänstedt, and P. Synnergren, “Effects of QoS scheduling strategies on performance of mixed services over LTE,” in Proc. IEEE Int. Symp. Personal Indoor Mobile Radio Commun., 2007, pp. 1–5. [28] B. Sadiq, R. Madan, and A. Sampath, “Downlink scheduling for multiclass traffic in LTE,” EURASIP J. Wireless Commun. Netw., Jul. 2009, Article ID: 510617. [29] S. V. Amari and R. B. Misra, “Closed-form expression for distribution of the sum of independent exponential random variables,” IEEE Trans. Reliab., vol. 46, no. 4, pp. 519–522, Dec. 1997. [30] S. Favaro and S. G. Walker, “On the distribution of sums of independent exponential random variables via Wilks’ integral representation,” Acta Applicandae Math., vol. 109, no. 3, pp. 1035–1042, Mar. 2010. [31] G. Bolch, S. Greiner, H. de Meer, and K. S. Trivedi, Queueing Networks and Markov Chains: Modeling and Performance Evaluation With Computer Science Applications. New York: Wiley-Interscience, 1998.

Ping Xia (S’10) received the B.S. degree in information electronics and engineering (with high honors) from Tsinghua University, Beijing, China, in 2008 and the M.S. degree in electrical and computer engineering from University of Texas (UT) at Austin in 2010. He is currently pursuing the Ph.D. degree in the Wireless Networking and Communications Group (WNCG), Department of Electrical and Computer Engineering, UT Austin. His research focuses on the heterogeneous cellular networks comprising macro, pico, and femto cells. Research topics include access control, interference management, and inter-cell coordination in such networks. He held intern positions at Dell in summer 2010 and at Huawei North America R&D Center in summer 2011.

269

Han-Shin Jo (M’10) received the B.S., M.S., and Ph.D. degrees in electrical and electronics engineering from Yonsei University, Seoul, Korea, in 2001, 2004, and 2009, respectively. He is currently an Assistant Professor with the Department of Electronics and Control Engineering, Hanbat National University, Daejeon, Korea. He was a Postdoctoral Research Fellow in the Wireless Network and Communications Group, Department of Electrical and Computer Engineering, University of Texas at Austin from 2009 to 2011. He developed LTE systems in Samsung Eletronics in 2011-12. He received 2011 ETRI Journal Award. His research interests include Small cells, Heterogeneous etwork, Wireless ad-hoc network, Stochastic geometry, and Wireless broadband transmission. He is currently a Postdoctoral Fellow in the Department of Electrical and Computer Engineering, University of Texas at Austin. His expertise is on both theoretical and practical aspects of multiuser wireless systems and networks. His research interests include theoretical analysis and interference management for femtocell/heterogeneous networks, theoretical analysis and transmission and resource allocation algorithm for MIMO/network MIMO systems, and stochastic geometry models for radio interference in wireless networks.

Jeffrey Andrews (S’98–M’02–SM’06) received the B.S. degree in engineering (with High Distinction) from Harvey Mudd College, Claremont, CA, in 1995 and the M.S. and Ph.D. degrees in electrical engineering from Stanford University, Stanford, CA, in 1999 and 2002, respectively. He is an Associate Professor in the Department of Electrical and Computer Engineering at the University of Texas (UT) at Austin, where he was the Director of the Wireless Networking and Communications Group (WNCG) from 2008 to 2012. He developed code division multiple access systems at Qualcomm from 1995 to 1997, and has consulted for entities including the WiMAX Forum, Microsoft, Apple, Clearwire, Palm, Sprint, ADC, and NASA. He is coauthor of two books, Fundamentals of WiMAX (Prentice-Hall, 2007) and Fundamentals of LTE (Prentice-Hall, 2010), and holds the Earl and Margaret Brasfield Endowed Fellowship in Engineering at UT Austin. His research interests are in communication theory, information theory, and stochastic geometry applied to wireless cellular and ad hoc networks. Dr. Andrews received the ECE departments first annual High Gain award for excellence in research from UT Austin. He served as an associate editor for the IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS from 2004 to 2008, was the Chair of the 2010 IEEE Communication Theory Workshop, and is the Technical Program co-Chair of ICC 2012 (Communication Theory Symposium) and Globecom 2014. He has also been a guest editor for two recent IEEE JOURNAL OF SELECTED AREAS IN COMMUNICATIONS special issues on stochastic geometry and femtocell networks. He received the National Science Foundation CAREER award in 2007 and has been coauthor of five best paper award recipients, two at Globecom (2006 and 2009), Asilomar (2008), the 2010 IEEE Communications Society Best Tutorial Paper Award, and the 2011 Communications Society Heinrich Hertz Prize.

Fundamentals of Inter-Cell Overhead Signaling in ... - IEEE Xplore

Index Terms—Heterogeneous cellular network, inter-cell coor- dination ...... Overhead outage p versus average packet service rate =B in the three scenarios.

1MB Sizes 27 Downloads 228 Views

Recommend Documents

IEEE Photonics Technology - IEEE Xplore
Abstract—Due to the high beam divergence of standard laser diodes (LDs), these are not suitable for wavelength-selective feed- back without extra optical ...

wright layout - IEEE Xplore
tive specifications for voice over asynchronous transfer mode (VoATM) [2], voice over IP. (VoIP), and voice over frame relay (VoFR) [3]. Much has been written ...

Device Ensembles - IEEE Xplore
Dec 2, 2004 - time, the computer and consumer electronics indus- tries are defining ... tered on data synchronization between desktops and personal digital ...

wright layout - IEEE Xplore
ACCEPTED FROM OPEN CALL. INTRODUCTION. Two trends motivate this article: first, the growth of telecommunications industry interest in the implementation ...

Evolutionary Computation, IEEE Transactions on - IEEE Xplore
search strategy to a great number of habitats and prey distributions. We propose to synthesize a similar search strategy for the massively multimodal problems of ...

I iJl! - IEEE Xplore
Email: [email protected]. Abstract: A ... consumptions are 8.3mA and 1.lmA for WCDMA mode .... 8.3mA from a 1.5V supply under WCDMA mode and.

Error Characterization in the Vicinity of Singularities in ... - IEEE Xplore
plified specification and monitoring of the motion of mo- bile multi-robot systems ... framework and its application to a 3-robot system and present the problem of ...

Gigabit DSL - IEEE Xplore
(DSL) technology based on MIMO transmission methods finds that symmetric data rates of more than 1 Gbps are achievable over four twisted pairs (category 3) ...

NEXT: In-Network Nonconvex Optimization - IEEE Xplore
Abstract—We study nonconvex distributed optimization in multiagent networks with time-varying (nonsymmetric) connec- tivity. We introduce the first algorithmic ...

IEEE CIS Social Media - IEEE Xplore
Feb 2, 2012 - interact (e.g., talk with microphones/ headsets, listen to presentations, ask questions, etc.) with other avatars virtu- ally located in the same ...

Grammatical evolution - Evolutionary Computation, IEEE ... - IEEE Xplore
definition are used in a genotype-to-phenotype mapping process to a program. ... evolutionary process on the actual programs, but rather on vari- able-length ...

SITAR - IEEE Xplore
SITAR: A Scalable Intrusion-Tolerant Architecture for Distributed Services. ∗. Feiyi Wang, Frank Jou. Advanced Network Research Group. MCNC. Research Triangle Park, NC. Email: {fwang2,jou}@mcnc.org. Fengmin Gong. Intrusion Detection Technology Divi

striegel layout - IEEE Xplore
tant events can occur: group dynamics, network dynamics ... network topology due to link/node failures/addi- ... article we examine various issues and solutions.

Digital Fabrication - IEEE Xplore
we use on a daily basis are created by professional design- ers, mass-produced at factories, and then transported, through a complex distribution network, to ...

DISTRIBUTED RESOURCE ALLOCATION IN ... - IEEE Xplore
a social forage swarming model, where the search for the most appropriate .... swarm under a general condition satisfied by almost any realistic profile. To this ...

Iv~~~~~~~~W - IEEE Xplore
P. Arena, L. Fortuna, G. Vagliasindi. DIEES - Dipartimento di Ingegneria Elettrica, Elettronica e dei Sistemi. Facolta di Ingegneria - Universita degli Studi di Catania. Viale A. Doria, 6. 95125 Catania, Italy [email protected]. ABSTRACT. The no

Device Ensembles - IEEE Xplore
Dec 2, 2004 - Device. Ensembles. Notebook computers, cell phones, PDAs, digital cameras, music players, handheld games, set-top boxes, camcorders, and.

Fountain codes - IEEE Xplore
7 Richardson, T., Shokrollahi, M.A., and Urbanke, R.: 'Design of capacity-approaching irregular low-density parity check codes', IEEE. Trans. Inf. Theory, 2001 ...

Multipath Matching Pursuit - IEEE Xplore
Abstract—In this paper, we propose an algorithm referred to as multipath matching pursuit (MMP) that investigates multiple promising candidates to recover ...

Insufficiency of Linear-Feedback Schemes in Gaussian ... - IEEE Xplore
Jul 10, 2014 - by the point-to-point capacity to the receiver with the largest noise variance. That the performance of linear-feedback schemes with a common ...

A New Approach in Synchronization of Uncertain Chaos ... - IEEE Xplore
Department of Electrical Engineering and. Computer Science. Korea Advanced Institute of Science and Technology. Daejeon, 305–701, Republic of Korea.

Fepstrum Representation of Speech - IEEE Xplore
ABSTRACT. Pole-zero spectral models in the frequency domain have been well studied and understood in the past several decades. Exploiting the duality ...