Mar 26, 2015

- Slide 1

Cross-Layer Performance Analysis for Decentralized Multihop Wireless Networks Tarik Tabet Mobile Communications Laboratory Ecole Polytechnique Fdrale de Lausanne Lausanne, Switzerland [email protected] Raymond Knopp Mobile Communications Department Eurecom Institute Sophia-Antipolis, France [email protected] Slide 2 Motivation/Goal Rapidly-deployable small-scale multihop wireless networks (e.g. broadband hotspots for emergency/disaster relief) Motivated by Cross-Layer mechanisms (PHY/MAC/Routing) aiming at maximizing the spectral efficiency of the network Tool for characterizing the transport capacity of such networks (bit m/s) from a microscopic point-of-view as a function of topological parameters (e.g. node population density) and system parameters (propagation, bandwidth, Slide 3 Interplay between Tools Multiple-Access/Coding for Decentralized Channels (Collision Channels) Massey+Mathys (IT-1985) Caire + Tuninetti (IT-2000) Random Network Topologies (Spatial Processes) Kleinrock+Nelson (COM-84) Sousa (IT 1992) Baccelli (2003) Geographic Routing Strategies and performance metrics Baccelli et al (2003) Interference statistics Achievable link throughput/delay Slide 4 Network and propagation model Nodes are spatially distributed in the plane according to a homogeneous spatial Poisson process[NelsonK84]. The number of nodes in a region S of area S is: The propagation model is described by the signal attenuation due to the distance r between the transmitter and the receiver and the Rayleigh fading (narrowband/flat): Slide 5 System model and setting Slotted transmission structure. Messages are potentially coded across many slots (interference diversity). Slotted Gaussian Collision channel with fading. An infinite number of packets available for each source (stability of protocols is ignored in this study, no queuing). ACK/NACK feedback signaling channel is error-free and delay- free. Single-user decoding. Slide 6 System model and setting Block-fading channel model. Slot duration Signal strength t Slide 7 System Model and Setting time slot User transmission Slide 8 System model and setting For routing based on average SINR (RS1,RS2), the fading is an i.i.d process across successive slots -> diversity against fading with coding. In a real system, this can be achieved via slow frequency hopping across a large system bandwidth. For (RS3), we assume a long-term static channel (i.e. constant over slots) -> diversity against fading is realized by a form of multiuser diversity in the routing scheme. Each node transmits a packet with probability p and remains silent with probability 1-p such that transmit and receive nodes have spatial Poisson distributions with average node density p and 1-p) respectively. Each node transmits with fixed power P. Slide 9 MAC protocols Nodes access the channel at random and employ simple protocols to retransmit the erroneously received packets. Two retransmission protocols: Slotted Aloha and Incremental Redundancy. Analytical techniques are based on [CaireT01] adapted to this channel interference scenario. Spatial Poisson process characterization leads to a new representation of interference and collisions between concurrent transmissions for the Gaussian collision channel with fading. Slide 10 MAC protocols We compare these strategies to the generalization of the collision channel without feedback or delay constraints [MasseyM85]. As it will be seen later, the measure of success of a transmission will be an achievable ergodic throughput of this channel. 12345 12345 collisionDecoding interval Slide 11 MAC protocols In the case of coded slotted aloha or incremental redundancy, the decoding stops after the reception of an ACK on the feedback channel leading to a finite average delay. When packets from different nodes collide, it may still be possible to successfully decode the packet with the strongest received signal power, which is known as the "capture effect. The coded slotted aloha could be generalized to an - slotted aloha where each codeword is split in parts and transmitted in slots (in order to benefit from some diversity). We consider that the blocks are independent and is fixed. controls the average delay. Slide 12 Signal model The signal model is given by: where the index s denotes the slot, y j,s the received signal at node j, x k,s the transmitted signal from node k, n j,s the background noise at node j. Link performance of different schemes is characterized by the instantaneous average mutual information (information outage probability) Slide 13 Information outage probability The instantaneous average mutual information for a (i, j) pair of nodes: where Slide 14 Information outage probability We need to compute the MGF of V [Sousa92] the p.d.f of the distance between a transmitter and a receiver is given by: Slide 15 Information outage probability We finally obtain : and is the Gamma function. Slide 16 Incremental Redundancy It adjusts the code rate by incrementally transmitting redundancy information until decoding is successful. Node k encodes its message information of b bits each independently of other nodes by using a channel code with code book where N is the slot length and L is the accumulated number of slots. Codewords are divided into L sub-blocks of length N, and we let for denote the punctured code of length obtained from by deleting the last sub-blocks. Slide 17 Incremental Redundancy If successful decoding occurs at the l-th transmission, the effective coding rate for the current codeword is R/l bit/dim where R=b/N. For the sake of computing information theoretic quantities, we let. Following the analysis in [CaireT01], we define the throughput as: bit/dim where is the mean delay measured in slots for the transmission of an information message. Slide 18 Incremental Redundancy In incremental redundancy, the receiver has memory of the past signals since it accumulates mutual information. The probability of successful decoding after l transmitted slots is given by: where and we used the fact that for. The throughput is: Slide 19 Slotted Aloha Again the throughput is defined as: bit/dim. In Aloha, the receiver has no memory of the past signals, and the probability of successful decoding after l transmitted slots is given by: Slide 20 Slotted Aloha The mean delay is then given by: And the throughput: Slide 21 Spatial throughput expressions The spatial throughput is expressed as a function of the product of the number of the simultaneously successful transmissions per unit space by the average jump made by each transmission [NelsonK84]. We carry out its optimization with respect to the channel access probability p (MAC) and target Spectral Efficiency R (PHY) The relationship between the spatial throughput and the Gupta-Kumar transport capacity is described in [Baccelli03]. Slide 22 Expected forward progress The expected forward progress of a packet in the direction of its final destination F, is the distance Z between the transmitter and the receiver (an intermediate node) projected onto a line towards the final destination and the transmission to that receiver is successful. Slide 23 Routing strategies In the following we consider three routing strategies: one that maximizes the expected forward progress by moving the packet to the node most forward towards the final destination (RS1). the second moves the packet to the closest node in range. Similar strategy is considered in [GrossT02] where the transmit range is on the order of, n being the number of nodes in an unit area, and in [YuenY03] in the context of mobile infostations networks (RS2). The third where the next hop is selected to exploit the best channel and to be the most forward -> attempt to exploit instantaneous channel state information at transmission when choosing candidate routes (RS3). Slide 24 Spatial throughput The spatial throughput is defined as where is the expected forward progress for strategy, and (for u=RS1, RS2), for slotted Aloha and for incremental redundancy. Slide 25 Maximal expected forward progress (RS1) We are looking for a receiver that maximizes the forward progress, and we consider a sender centric transmission model We obtain finally Slide 26 Closest node in range (RS2) The p.d.f of the minimum distance between the transmitter and the receiver among all the receive node distances is : The expected forward progress for this strategy is: Slide 27 Channel driven maximal forward progress (RS3) Exploit multi-user diversity for slowly varying channels in dense networks. Instantaneous CSI is available at the transmitter in order to select the next hop which is the most forward and with the best channel. The forward progress is: The outage probability is conditioned on the knowledge of the channel at the transmitter. We make use of a result on stable distributions with exponent 1/2. Slide 28 Channel driven maximal forward progress RS3 The MGF of V is given by: Slide 29 Channel driven maximal forward progress RS3 The outage probability is then: Which leads to an expected forward progress for RS3 where : Slide 30 Numerical results The spatial throughput is expressed as a function of different system parameters: the transmit SNR P/N 0 the target information rate R, the transmit probability p, and the node density. The optimal throughput vs. the target information rate is derived by maximizing over the channel access probability p. Slide 31 Increasing average delay Spatial Throughput (bit m /dim/m 2 ) Rate R Numerical Example: SNR = 5dB, =1 node/m 2 Slide 32 Numerical results The channel driven strategy performs substantially better than the other strategies by exploiting transmissions only to nodes with instantaneously good channels. This suggests that routing should be based on the instantaneous channel strength of the link, which could require fast route updates (in comparison to existing routing protocols for

Related Documents See more >