Managing interference in a network of macrocells underlaid with femtocells presents an important, yet challenging problem. A majority of spatial (frequency time) reuse based approaches partition the users based on coloring the interference graph, which is shown to be suboptimal. Some spatial time reuse based approaches schedule the maximal independent sets (MISs) in a cyclic, (weighted) round-robin fashion, which is inefficient for delay-sensitive applications. Our proposed policies schedule the MISs in a non-cyclic fashion, which aim to optimize any given network performance criterion for delay-sensitive applications while fulfilling minimum throughput requirements of the users. Importantly, we do not take the interference graph as given as in existing works; we propose an optimal construction of the interference graph. We prove that under certain conditions, the proposed policy achieves the optimal network performance. For large networks, we propose a low-complexity algorithm for computing the proposed policy. We show that the policy computed achieves a constant competitive ratio (with respect to the optimal network performance), which is independent of the network size, under wide range of deployment scenarios. The policy can be implemented in a decentralized manner by the users. Compared to the existing policies, our proposed policies can achieve improvement of up to 130 in large-scale deployments.
Some policies based on spatial time reuse, partition the UEs based on the coloring of the interference graph h @cite_30 @cite_29 @cite_0 @cite_40 @cite_41 , which is not efficient. In general, a set of UEs with the same color (i.e. the UEs who can transmit simultaneously) may not be maximal (See Fig. 1 a), in the sense that there may be UEs who do not interfere but have different colors (we will also show this in the motivating example in Subsection ). In this case, it is more efficient to also let those non-interfering UEs to transmit simultaneously, although they have different colors. Hence, the partitioning based on coloring the interference graph is not efficient, because the average number of active UEs (i.e. the average cardinality of the subsets of UEs with the same color) is low.
@cite_30 @cite_41 @cite_29 @cite_0 @cite_40
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In the interference scheduling problem, one is given a set of n communication requests described by source-destination pairs of nodes from a metric space. The nodes correspond to devices in a wireless network. Each pair must be assigned a power level and a color such that the pairs in each color class can communicate simultaneously at the specified power levels. The feasibility of simultaneous communication within a color class is defined in terms of the Signal to Interference plus Noise Ratio (SINR) that compares the strength of a signal at a receiver to the sum of the strengths of other signals. The objective is to minimize the number of colors as this corresponds to the time needed to schedule all requests. We introduce an instance-based measure of interference, denoted by I, that enables us to improve on previous results for the interference scheduling problem. We prove the upper and lower bounds in terms of I on the number of steps needed for scheduling a set of requests. For general power assignments, we prove a lower bound of @W(I ([email protected])) steps, where @D denotes the aspect ratio of the metric. When restricting to the two-dimensional Euclidean space (as in the previous work) the bound improves to @W(I [email protected]). Alternatively, when restricting to linear power assignments, the lower bound improves even to @W(I). The lower bounds are complemented by an efficient algorithm computing a schedule for linear power assignments using only O(Ilogn) steps. A more sophisticated algorithm computes a schedule using even only O(I+log^2n) steps. For dense instances in the two-dimensional Euclidean space, this gives a constant factor approximation for scheduling under linear power assignments, which shows that the price for using linear (and, hence, energy-efficient) power assignments is bounded by a factor of O([email protected]). In addition, we extend these results for single-hop scheduling to multi-hop scheduling and combined scheduling and routing problems, where our analysis generalizes the previous results towards general metrics and improves on the previous approximation factors. In the interference scheduling problem, one is given a set of n communication requests described by pairs of points from a metric space. The points correspond to devices in a wireless network. In the directed version of the problem, each pair of points consists of a dedicated sending and a dedicated receiving device. In the bidirectional version the devices within a pair shall be able to exchange signals in both directions. In both versions, each pair must be assigned a power level and a color such that the pairs in each color class (representing pairs communicating in the same time slot) can communicate simultaneously at the specified power levels. The feasibility of simultaneous communication within a color class is defined in terms of the Signal to Interference Plus Noise Ratio (SINR) that compares the strength of a signal at a receiver to the sum of the strengths of other signals. This is commonly referred to as the "physical model" and is the established way of modelling interference in the engineering community. The objective is to minimize the number of colors as this corresponds to the time needed to schedule all requests. We study oblivious power assignments in which the power value of a pair only depends on the distance between the points of this pair. We prove that oblivious power assignments cannot yield approximation ratios better than Ω(n) for the directed version of the problem, which is the worst possible performance guarantee as there is a straightforward algorithm that achieves an O(n)-approximation. For the bidirectional version, however, we can show the existence of a universally good oblivious power assignment: For any set of n bidirectional communication requests, the so-called "square root assignment" admits a coloring with at most polylog(n) times the minimal number of colors. The proof for the existence of this coloring is non-constructive. We complement it by an approximation algorithm for the coloring problem under the square root assignment. This way, we obtain the first polynomial time algorithm with approximation ratio polylog(n) for interference scheduling in the physical model. We report on a novel technique called spatial coupling and its application in the analysis of random constraint satisfaction problems (CSP). Spatial coupling was invented as an engineering construction in the area of error correcting codes where it has resulted in efficient capacity-achieving codes for a wide range of channels. However, this technique is not limited to problems in communications, and can be applied in the much broader context of graphical models. We describe here a general methodology for applying spatial coupling to random constraint satisfaction problems and obtain lower bounds for their (rough) satisfiability threshold. The main idea is to construct a distribution of geometrically structured random K-SAT instances - namely the spatially coupled ensemble - which has the same (rough) satisfiability threshold, and is at the same time algorithmically easier to solve. Then by running well-known algorithms on the spatially coupled ensemble we obtain a lower bound on the (rough) satisfiability threshold of the original ensemble. The method is versatile because one can choose the CSP, there is a certain amount of freedom in the construction of the spatially coupled ensemble, and also in the choice of the algorithm. In this work we focus on random K-SAT but we have also checked that the method is successful for Coloring, NAE-SAT and XOR-SAT. We choose Unit Clause propagation for the algorithm which is analyzed over the spatially coupled instances. For K = 3, for instance, our lower bound is equal to 3.67 which is better than the current bounds in the literature. Similarly, for graph 3-colorability we get a bound of 2.22 which is also better than the current bounds in the literature. Using stochastic geometry, we develop a tractable uplink modeling paradigm for outage probability and spectral efficiency in both single and multi-tier cellular wireless networks. The analysis accounts for per user equipment (UE) power control as well as the maximum power limitations for UEs. More specifically, for interference mitigation and robust uplink communication, each UE is required to control its transmit power such that the average received signal power at its serving base station (BS) is equal to a certain threshold ρ o . Due to the limited transmit power, the UEs employ a truncated channel inversion power control policy with a cutoff threshold of ρ o . We show that there exists a transfer point in the uplink system performance that depends on the following tuple: BS intensity λ, maximum transmit power of UEs P u , and ρ o . That is, when P u is a tight operational constraint with respect to (w.r.t.) λ and ρ o , the uplink outage probability and spectral efficiency highly depend on the values of λ and ρ o . In this case, there exists an optimal cutoff threshold ρ o *, which depends on the system parameters, that minimizes the outage probability. On the other hand, when P u is not a binding operational constraint w.r.t. λ and ρ o , the uplink outage probability and spectral efficiency become independent of λ and ρ o . We obtain approximate yet accurate simple expressions for outage probability and spectral efficiency, which reduce to closed forms in some special cases. We address interference avoidance by resource partitioning in densely deployed femtocell networks. The main objective is to protect user equipments (UEs) that are located near the cell boundary of two or more femtocells from detrimental downlink interference. The available frequency bands are divided into subbands that are distributed among femtocells in a way that directly adjacent cells do not occupy the same subbands. For this purpose, a novel centrally controlled resource partitioning method is developed based on graph coloring that assigns subbands in terms of resource efficiency. The proposed algorithm strikes a balance between interference protection and spatial frequency reuse of subbands, and is well suited for randomly deployed wireless networks. System-level simulations reveal that cell edge capacities are significantly boosted without causing a degradation in average system throughput. Motivated by a frequency assignment problem in cellular networks, we introduce and study a new coloring problem that we call minimum conflict-free coloring (min-CF-coloring). In its general form, the input of the min-CF-coloring problem is a set system @math , where each @math is a subset of X. The output is a coloring @math of the sets in @math that satisfies the following constraint: for every @math there exists a color @math and a unique set @math such that @math and @math . The goal is to minimize the number of colors used by the coloring @math . Min-CF-coloring of general set systems is not easier than the classic graph coloring problem. However, in view of our motivation, we consider set systems induced by simple geometric regions in the plane. In particular, we study disks (both congruent and noncongruent), axis-parallel rectangles (with a constant ratio between the smallest and largest rectangle), regular hexagons (with a constant ratio between the smallest and largest hexagon), and general congruent centrally symmetric convex regions in the plane. In all cases we have coloring algorithms that use O(log n) colors (where n is the number of regions). Tightness is demonstrated by showing that even in the case of unit disks, @math colors may be necessary. For rectangles and hexagons we also obtain a constant-ratio approximation algorithm when the ratio between the largest and smallest rectangle (hexagon) is a constant. We also consider a dual problem of CF-coloring points with respect to sets. Given a set system @math , the goal in the dual problem is to color the elements in X with a minimum number of colors so that every set @math contains a point whose color appears only once in S. We show that O(log |X|) colors suffice for set systems in which X is a set of points in the plane and the sets are intersections of X with scaled translations of a convex region. This result is used in proving that O(log n) colors suffice in the primal version. In a wireless powered communication network, where user equipments (UEs) harvest radio frequency energy from an access point (AP) and send data to the AP, there exists the near-far problem with respect to energy harvesting efficiency due to UEs’ random locations. In this paper, we introduce the concept of delay-aware energy balancing by minimizing the average transmission delay while taking into account the issue of unbalanced harvested energy distribution. In particular, we propose an adaptive harvest-then-cooperate protocol, where every UE first harvests the energy emitted by the AP and then sends data to the AP directly or via other UEs acting as relays in a time-division multiplexing manner. In this protocol, the AP selects the combination of transmission power and routing topology by matching load and energy distributions in the network while minimizing the average transmission delay. Furthermore, we develop a method generating scheduling schemes for this protocol to avoid data overflow in the UE relay. To determine the combination with minimum delay, we approximate the average delay as a Markov decision process and propose a low-complexity sample path-based algorithm to obtain a near-optimal solution. Simulation results demonstrate that the proposed protocol is able to balance the energy distribution while minimizing the transmission delay. Abstract Suppose G is a graph and T is a set of nonnegative integers. A T -coloring of G is an assignment of a positive integer ƒ( x ) to each vertex x of G so that if x and y are joined by an edge of G , then |ƒ(x) - ƒ(y)ƒ| is not in T . T -colorings were introduced by Hale in connection with the channel assignment problem in communications. Here, the vertices of G are transmitters, an edge represents interference, ƒ( x ) is a television or radio channel assigned to x , and T is a set of disallowed separations for channels assigned to interfering transmitters. One seeks to find a T -coloring which minimizes either the number of different channels ƒ( x ) used or the distance between the smallest and largest channel. This paper surveys the results and mentions open problems concerned with T -colorings and their variations and generalizations. In this paper, we consider CSMA policies for scheduling of multihop wireless networks with one-hop traffic. The main contribution of this paper is to propose Unlocking CSMA (U-CSMA) policy that enables to obtain high throughput with low (average) packet delay for large wireless networks. In particular, the delay under U-CSMA policy becomes order-optimal. For one-hop traffic, delay is defined to be order-optimal if it is O(1), i.e., it stays bounded, as the network-size increases to infinity. Using mean field theory techniques, we analytically show that for torus (grid-like) interference topologies with one-hop traffic, to achieve a network load of @math , the delay under U-CSMA policy becomes @math as the network-size increases, and hence, delay becomes order optimal. We conduct simulations for general random geometric interference topologies under U-CSMA policy combined with congestion control to maximize a network-wide utility. These simulations confirm that order optimality holds, and that we can use U-CSMA policy jointly with congestion control to operate close to the optimal utility with a low packet delay in arbitrarily large random geometric topologies. To the best of our knowledge, it is for the first time that a simple distributed scheduling policy is proposed that in addition to throughput utility-optimality exhibits delay order-optimality. We investigate spatial interference statistics for multigigabit outdoor mesh networks operating in the unlicensed 60-GHz "millimeter (mm) wave" band. The links in such networks are highly directional: Because of the small carrier wavelength (an order of magnitude smaller than those for existing cellular and wireless local area networks), narrow beams are essential for overcoming higher path loss and can be implemented using compact electronically steerable antenna arrays. Directionality drastically reduces interference, but it also leads to "deafness," making implicit coordination using carrier sense infeasible. In this paper, we make a quantitative case for rethinking medium access control (MAC) design in such settings. Unlike existing MAC protocols for omnidirectional networks, where the focus is on interference management, we contend that MAC design for 60-GHz mesh networks can essentially ignore interference and must focus instead on the challenge of scheduling half-duplex transmissions with deaf neighbors. Our main contribution is an analytical framework for estimating the collision probability in such networks as a function of the antenna patterns and the density of simultaneously transmitting nodes. The numerical results from our interference analysis show that highly directional links can indeed be modeled as pseudowired, in that the collision probability is small even with a significant density of transmitters. Furthermore, simulation of a rudimentary directional slotted Aloha protocol shows that packet losses due to failed coordination are an order of magnitude higher than those due to collisions, confirming our analytical results and highlighting the need for more sophisticated coordination mechanisms. The massive multiple-input multiple-output (MIMO) technology has great potential to manage the rapid growth of wireless data traffic. Massive MIMO achieves tremendous spectral efficiency by spatial multiplexing many tens of user equipments (UEs). These gains are only achieved in practice if many more UEs can connect efficiently to the network than today. As the number of UEs increases, while each UE intermittently accesses the network, the random access functionality becomes essential to share the limited number of pilots among the UEs. In this paper, we revisit the random access problem in the Massive MIMO context and develop a reengineered protocol, termed strongest-user collision resolution (SUCRe). An accessing UE asks for a dedicated pilot by sending an uncoordinated random access pilot, with a risk that other UEs send the same pilot. The favorable propagation of massive MIMO channels is utilized to enable distributed collision detection at each UE, thereby determining the strength of the contenders’ signals and deciding to repeat the pilot if the UE judges that its signal at the receiver is the strongest. The SUCRe protocol resolves the vast majority of all pilot collisions in crowded urban scenarios and continues to admit UEs efficiently in overloaded networks. Suppose in a graph G vertices can be either red or blue. Let k be odd. At each time step, each vertex v in G polls k random neighbours and takes the majority colour. If it does not have k neighbours, it simply polls all of them, or all less one if the degree of v is even. We study this protocol on graphs of a given degree sequence, in the following setting: initially each vertex of G is red independently with probability α < 1 2 , and is otherwise blue. We show that if α is sufficiently biased, then with high probability consensus is reached on the initial global majority within O ( log k log k n ) steps if 5 ? k ? d , and O ( log d log d n ) steps if k d . Here, d ? 5 is the effective minimum degree, the smallest integer which occurs ? ( n ) times in the degree sequence. We further show that on such graphs, any local protocol in which a vertex does not change colour if all its neighbours have that same colour, takes time at least ? ( log d log d n ) , with high probability. Additionally, we demonstrate how the technique for the above sparse graphs can be applied in a straightforward manner to get bounds for the Erd?s-Renyi random graphs in the connected regime. In commercial-off-the-shelf (COTS) multi-core systems, the execution times of tasks become hard to predict because of contention on shared resources in the memory hierarchy. In particular, a task running in one processor core can delay the execution of another task running in another processor core. This is due to the fact that tasks can access data in the same cache set shared among processor cores or in the same memory bank in the DRAM memory (or both). Such cache and bank interference effects have motivated the need to create isolation mechanisms for resources accessed by more than one task. One popular isolation mechanism is cache coloring that divides the cache into multiple partitions. With cache coloring, each task can be assigned exclusive cache partitions, thereby preventing cache interference from other tasks. Similarly, bank coloring allows assigning exclusive bank partitions to tasks. While cache coloring and some bank coloring mechanisms have been studied separately, interactions between the two schemes have not been studied. Specifically, while memory accesses to two different bank colors do not interfere with each other at the bank level, they may interact at the cache level. Similarly, two different cache colors avoid cache interference but may not prevent bank interference. Therefore it is necessary to coordinate cache and bank coloring approaches. In this paper, we present a coordinated cache and bank coloring scheme that is designed to prevent cache and bank interference simultaneously. We also developed color allocation algorithms for configuring a virtual memory system to support our scheme which has been implemented in the Linux kernel. In our experiments, we observed that the execution time can increase by 60 due to inter-task interference when we use only cache coloring. Our coordinated approach can reduce this figure down to 12 (an 80 reduction). We consider the generalized dirty-paper channel Y=X+S+N,E X sup 2 spl les P sub X , where N is not necessarily Gaussian, and the interference S is known causally or noncausally to the transmitter. We derive worst case capacity formulas and strategies for "strong" or arbitrarily varying interference. In the causal side information (SI) case, we develop a capacity formula based on minimum noise entropy strategies. We then show that strategies associated with entropy-constrained quantizers provide lower and upper bounds on the capacity. At high signal-to-noise ratio (SNR) conditions, i.e., if N is weak relative to the power constraint P sub X , these bounds coincide, the optimum strategies take the form of scalar lattice quantizers, and the capacity loss due to not having S at the receiver is shown to be exactly the "shaping gain" 1 2log(2 spl pi e 12) spl ap 0.254 bit. We extend the schemes to obtain achievable rates at any SNR and to noncausal SI, by incorporating minimum mean-squared error (MMSE) scaling, and by using k-dimensional lattices. For Gaussian N, the capacity loss of this scheme is upper-bounded by 1 2log2 spl pi eG( spl Lambda ), where G( spl Lambda ) is the normalized second moment of the lattice. With a proper choice of lattice, the loss goes to zero as the dimension k goes to infinity, in agreement with the results of Costa. These results provide an information-theoretic framework for the study of common communication problems such as precoding for intersymbol interference (ISI) channels and broadcast channels. In this paper, we study a colouring problem motivated by a practical frequency assignment problem and, up to our best knowledge, new. In wireless networks, a node interferes with other nodes, the level of interference depending on numerous parameters: distance between the nodes, geographical topography, obstacles, etc. We model this with a weighted graph (G,w) where the weight function w on the edges of G represents the noise (interference) between the two end-vertices. The total interference in a node is then the sum of all the noises of the nodes emitting on the same frequency. A weighted t-improper k-colouring of (G,w) is a k-colouring of the nodes of G (assignment of k frequencies) such that the interference at each node does not exceed the threshold t. We consider here the Weighted Improper Colouring problem which consists in determining the weighted t-improper chromatic number defined as the minimum integer k such that (G,w) admits a weighted t-improper k-colouring. We also consider the dual problem, denoted the Threshold Improper Colouring problem, where, given a number k of colours, we want to determine the minimum real t such that (G,w) admits a weighted t-improper k-colouring. We first present general upper bounds for both problems; in particular we show a generalisation of Lovasz@?s Theorem for the weighted t-improper chromatic number. Motivated by the original application, we then study a special interference model on various grids (square, triangular, hexagonal) where a node produces a noise of intensity 1 for its neighbours and a noise of intensity 1 2 for the nodes at distance two. We derive the weighted t-improper chromatic number for all values of t. In this paper, we consider CSMA policies for scheduling packet transmissions in multihop wireless networks with one-hop traffic. The main contribution of the paper is to propose a novel CSMA policy, called Unlocking CSMA (U-CSMA), that enables to obtain both high throughput and low packet delays in large wireless networks. More precisely, we show that for torus interference graph topologies with one-hop traffic, U-CSMA is throughput optimal and achieves order-optimal delay. For one-hop traffic, the delay performance is defined to be order-optimal if the delay stays bounded as the network-size increases. Simulations that we conducted suggest that (a) U-CSMA is throughput-optimal and achieves order-optimal delay for general geometric interference graphs and (b) that U-CSMA can be combined with congestion control algorithms to maximize the network-wide utility and obtain order-optimal delay. To the best of our knowledge, this is the first time that a simple distributed scheduling policy has been proposed that is both throughput utility optimal and achieves order-optimal delay. In this paper we study the resource allocation problem for the multiuser orthogonal frequency division multiplexing (OFDM)-based cognitive radio (CR) systems with proportional rate constraints. The mutual interference introduced by primary user (PU) and cognitive radio user (also referred to secondary user, SU) makes the optimization problem of CR systems more complex. Moreover, the interference introduced to PUs must be kept under a given threshold. In this paper, the highest achievable rate of each OFDM subchannel is calculated by jointly considering the channel gain and interference level. First, a subchannel is assigned to the SU with the highest achievable rate. The remaining subchannels are always allocated to the SU that suffers the severest unjustness. Second, an efficient bit allocation algorithm is developed to maximize the sum capacity, which is again based on the highest achievable rate of each subchannel. Finally, an adjustment procedure is designed to maintain proportional fairness. Simulation results show that the proposed algorithm maximizes the sum capacity while keeping the proportional rate constraints satisfied. The algorithm exhibits a good tradeoff between sum capacity maximization and proportional fairness. Furthermore, the proposed algorithm has lower complexity compared with other algorithms, rendering it promising for practical applications. Copyright © 2011 John Wiley & Sons, Ltd. (By jointly considering the channel gain and the interference level of the OFDM-based cognitive radio systems, the highest achievable rate of each subchannel can be calculated, which indicates the ability of carrying bits of the subchannel. Using the normalized cost index list, an efficient algorithm is proposed to maximize the sum capacity of the cognitive OFDM systems while keeping the proportional rate constraints satisfied.) A generalization of the Gaussian dirty-paper problem to a multiple access setup is considered. There are two additive interference signals, one known to each transmitter but none to the receiver. The rates achievable using Costa's strategies (i.e. by a random binning scheme induced by Costa's auxiliary random variables) vanish in the limit when the interference signals are strong. In contrast, it is shown that lattice strategies ("lattice precoding") can achieve positive rates independent of the interferences, and in fact in some cases - which depend on the noise variance and power constraints - they are optimal. In particular, lattice strategies are optimal in the limit of high SNR. It is also shown that the gap between the achievable rate region and the capacity region is at most 0.167 bit. Thus, the dirty MAC is another instance of a network setup, like the Korner-Marton modulo-two sum problem, where linear coding is potentially better than random binning. Lattice transmission schemes and conditions for optimality for the asymmetric case, where there is only one interference which is known to one of the users (who serves as a "helper" to the other user), and for the "common interference" case are also derived. In the former case the gap between the helper achievable rate and its capacity is at most 0.085 bit. Consider an n-vertex graph G = (V, E) of maximum degree Δ, and suppose that each vertex v ∈ V hosts a processor. The processors are allowed to communicate only with their neighbors in G. The communication is synchronous, that is, it proceeds in discrete rounds. In the distributed vertex coloring problem, the objective is to color G with Δ + 1, or slightly more than Δ + 1, colors using as few rounds of communication as possible. (The number of rounds of communication will be henceforth referred to as running time.) Efficient randomized algorithms for this problem are known for more than twenty years [ 1986; Luby 1986]. Specifically, these algorithms produce a (Δ + 1)-coloring within O(log n) time, with high probability. On the other hand, the best known deterministic algorithm that requires polylogarithmic time employs O(Δ2) colors. This algorithm was devised in a seminal FOCS’87 paper by Linial [1987]. Its running time is O(log* n). In the same article, Linial asked whether one can color with significantly less than Δ2 colors in deterministic polylogarithmic time. By now, this question of Linial became one of the most central long-standing open questions in this area. In this article, we answer this question in the affirmative, and devise a deterministic algorithm that employs Δ1+o(1) colors, and runs in polylogarithmic time. Specifically, the running time of our algorithm is O(f(Δ)log Δ log n), for an arbitrarily slow-growing function f(Δ) = ω(1). We can also produce an O(Δ1+η)-coloring in O(log Δ log n)-time, for an arbitrarily small constant η > 0, and an O(Δ)-coloring in O(Δe log n) time, for an arbitrarily small constant e > 0. Our results are, in fact, far more general than this. In particular, for a graph of arboricity a, our algorithm produces an O(a1+η)-coloring, for an arbitrarily small constant η > 0, in time O(log a log n). In multi-hop radio networks, such as wireless ad-hoc networks and wireless sensor networks, nodes employ a MAC (Medium Access Control) protocol such as TDMA to coordinate accesses to the shared medium and to avoid interference of close-by transmissions. These protocols can be implemented using standard node coloring. The ( Δ + 1 ) -coloring problem is to color all nodes in as few timeslots as possible using at most Δ + 1 colors such that any two nodes within distance R are assigned different colors, where R is a given parameter and Δ is the maximum degree of the modeled unit disk graph using R as a scaling factor. Being one of the most fundamental problems in distributed computing, this problem is well studied and there is a long chain of algorithms prescribed for it. However, all previous works are based on abstract models, such as message passing models and graph based interference models, which limit the utility of these algorithms in practice. In this paper, for the first time, we consider the distributed ( Δ + 1 ) -coloring problem under the more practical SINR interference model. In particular, without requiring any knowledge about the neighborhood, we propose a novel randomized ( Δ + 1 ) -coloring algorithm with time complexity O ( Δ log ? n + log 2 ? n ) . For the case where nodes cannot adjust their transmission power, we give an O ( Δ log 2 ? n ) randomized algorithm, which only incurs a logarithmic multiplicative factor overhead.