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1、Stochastic Process Project: Buff er Assisted Communication Over Fading Channels Instructed by Ping-Yi Fan Due on Nov 25, 2012 William Wei-Ran Huang2012311324 Institute for Interdisciplinary Information Sciences Abstract In this paper, we described the buff er assisted block fading channel model. Usi
2、ng this model and the martingale theorem, we calculated the time ET which denotes the expectation time when the buff er is empty or full. We also analyzed the relationship between ET and initial location b0and between ET and the data coming rate R. Keywords fading channel; martingale; Rayleigh distr
3、ibution; buff er. 1Introduction Emerging multi-media and internet applications require transmitting at high data rates with good quality. The role of wireless communication in information exchange is growing rapidly because of increased demand for mobility. Since limited physical resources are share
4、d by many users in wireless networks, new technologies that are extremely effi cient with respect to both power consumption and bandwidth should be deployed. A serious challenge to having good communication quality in wireless systems is the time-varying fading environments that wireless systems exp
5、erience. When the signal is transmitted, it is refl ected and scattered over surrounding objects, which causes the signal to be received over many diff erent paths Fig. 1. This is called multi-path phenomenon. These paths can add constructively or destructively. When they add destructively, they cau
6、ses fading and the received signal-to-noise ratio (SNR) can drop severely. In wireless environments, multi-path reception causes the energy of the Email: wwrhuang 2BLOCK FADING CHANNEL MODEL received signal to be varying randomly. Where the magnitudes of the signals arriving by the various paths hav
7、e a distribution known as the Rayleigh distribution, this is known as Rayleigh fading 4. Fig. 1: In wireless telecommunications, multi-path is the propagation phenomenon that results in radio signals reaching the receiving antenna by two or more paths. 2Block Fading Channel Model In this section, we
8、 describe the channel model used throughout the paper, i.e., the block fading channel model 1. Wireless communication channels are usually modeled by discrete time systems. The output is given by y(n) = h(n)x(n) + z(n) where x(n) is the transmitted signal during the time interval n; z(n) is the addi
9、tive Gaussian white noise (AGWN) with zero mean and variance N0, i.e., z(n) N(0,N0); and h(n) is a discrete stochastic process, which describes the fading. The block diagram of the fading channel is shown in Fig. 2. Fig. 2: The block diagram of the fading channel In block fading channel model, we as
10、sume that the channel gain over a fading channel is constant when each packet is being transmitted but independently varies from one packet Page 2 of 14 2BLOCK FADING CHANNEL MODEL to its next one. In other words, h(n) is a constant during the time interval n (each packet lasts TB) and h(i) and h(j)
11、 are independent where i 6= j. For Rayleigh fading, the channel gain h(n) has the Rayleigh distribution, which is fh(h) = h 2 exp( h2 22 ) and the channel power gain (n) = h(n)2has the exponential distribution, which is f() = 1 22 exp( 22 ). Suppose that Ptdenotes the transmission power; W denotes t
12、he system bandwidth; N0 denotes the power spectral density of additive Gaussian white noise; d denotes the distance between transmitter and receiver and denotes the path loss factor.According to the Shannon theorem 3, the channel capacity C(n) is C(n) = W log(1 + (n)Pt WN0d ).(1) Because (n) is a ra
13、ndom variable for a certain n, C(n) is also a random variable. This means that transmission rate is up and down. In order to transmit data over the fading channel continuously, we need a buff er to store data before they are transmitted. Fig. 3: System model 1 Fig. 3 shows the block fading channel m
14、odel. Here we use a FIFO buff er to store the data. Data arrives from some higher layer application and is placed into the buff er. Data is removed from the buff er, encoded and transmitted over a fading channel. After information is received, the data is eventually decoded and sent to a peer applic
15、ation at the receiver. Page 3 of 14 3SIMPLIFIED CHANNEL MODEL Suppose that at the initial time n = 0, the length of data in the buff er is b0and the length of buff er is L.Data arrives from some higher layer application with rate R and R EC(n). Thus in each time interval, there are a0= RTB data comi
16、ng into the buff er and sn= C(n)TB data leaving the buff er. Defi ne B(n) is the length of data in the buff er during the time interval n, then B(n) = B(n 1) + a0 sn,0 B(n 1) + a0 sn L 0,B(n 1) + a0 sn L (2) Defi ne S(n) is the sum of data which has transmitted over the channel. S(n) = n X k=1 sk Defi ne T is the time when the length of data fi rst be 0 or L. T = minn : B(n) = 0 or B(n) = L 3 Simplifi ed Channel Model I
