Download Energy Consumption and Delay in Multi-hop Relay Networks: Direct vs. Hop-by-Hop Routing and more Assignments Computer Science in PDF only on Docsity! COSC6397 Homework Assignment 2 (Multihop Relay) September 15, 2004 Due date: September 15, 2004 In this mini-project, we consider the problem of multi-hop relay in Rayleigh fading networks. In particular, we are interested in establishing the condi- tions when relay through intermediate nodes is more desirable compared to direct transmissions. a. Assuming zero-interference and noise power at N , derive the reception probability P [ S N ≥ Θ] over a link of distance d at a transmit power P0 in Rayleigh fading channel with large-scale attenuation with exponent α. [hint: for Rayleigh fading networks, the received power level follows Rayleigh distribution p(r) = r σ2 exp{− r 2 2σ2 }, where σ2 ∝ P0d −α.] b. Given a one-dimension chain of equidistant nodes with distance d, compare two routing strategies that reliably deliver a packet from node 1 to node n, i.e., 1) transmit directly from node 1 to node n, and 2) transmit hop-by-hop through each intermediate node. To ensure reliability, two mechanisms can be adopted, i.e., i) link layer recov- ery, where retransmissions are performed locally whenever a packet is known to be lost or corrupted; ii) end-to-end recovery, where re- transmissions are performed only when the receiver (in this case, node n) detects a packet is lost and informs the sender to retransmit the message. Note that in either strategies, we do not consider overheads due to detection of lost packets (e.g., acknowledgment etc.). Write computer programs (e.g., in Matlab) that compare the energy con- sumption and delay1 of the two routing strategies. Illustrate your results using figures. 1Assume fixed packet transmission time τ and ignore propagation delay and queuing delay. 1 c. Repeat (b) using deterministic large-scale fading with exponent α. d. The previous problem only considers energy consumption due to trans- mission. This is not realistic as in addition to the RF component, the radio circuit consumes power as well. Adopt following energy model: P0 = Pe + Pradio and Pr = Pe, where Pradio is given by the Rayleigh fading channel with large-scale attenuation with an exponent α. Re- peat (b) with different values of Pe. e. (Bonus) Can you generalize the results to a route strategy that relays through k intermediate nodes (k ∈ [0, n − 2]). Summarize your findings and discuss (qualitatively) what are the limita- tions of the models adopted and how different assumptions may affect the conclusion drawn thus far. Solution: Part (a). P [ S N ≥ Θ] = ∫ ∞ ΘN r σ2 exp{− r2 2σ2 }dr = exp{− ΘN 2σ2 } = exp{− ΘN 2cP0d−α } = exp{− ΘNdα 2cP0 } (1) where c is a constant. Part (b). Next, we compute the amount of energy Esingle(d) to deliver a packet successfully over distance d using direct transmission in Rayleigh fading channel. Esingle(d) = l=∞∑ l=1 lP0 · τ(1 − P ) l−1P = P0 · τ P = P0 · τexp{ ΘNdα 2cP0 } (2) 2
