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k k 1 use none none writer toaccess none for noneasp.net code for barcode generation p( )d ,. Visual Studio 2008 k = 1, . . . , K . (10.11). In a Raylei gh fading channel, is exponentially distributed with probability density function p( ) = 1/ 0 exp( / 0 ), where 0 is the average channel gain. 2. State transition probabilities: k = 1, .

. . , K 1, (10.

12) k = 2, . . .

, K , k )Tp / k , where N ( ) is the level-crossing function given by N ( ) = 2 / 0 f D exp( / 0 ), Tp is the packet transmission time and f D is the maximum Doppler frequency. pc (k, k + 1) = N ( pc (k, k 1) = N (. k+1 )Tp / k ,. Reinforcement learning for energy-aware communications p12 1 p21 p11 p23 2 p32 p22 p33 3 p34 p43 pk 1,k K pk,k 1 pk,k An FSMC with K states. Construction of the state-transition probability We construc none for none t the system state as the aggregate of the number of packets in the buffer, n b , and the channel gain, , that is s (n b , ). The control space consists of the modulation level and transmit power, i.e.

a (m, pt ). The state transition probability maps (n b , ) (n b , ) (m, pt ) [0, 1]. In particular, the state transition probability depends on the probability of packet arrival, the channel transition probability and the probability of successful packet transmission.

We model the packet arrival process as a Poisson process with mean packet arrival rate . The channel is modeled as an FSMC and the channel gain state transition probability is calculated according to Section 10.4.

3.1. The probability of successful packet transmission, S( ( , pt ), m), depends on the targeted SIR, ( , pt ), which is represented as ( , pt ) = W pt A t , R 2 (10.

13). where , m odeled as the FSMC, is the variation in channel gain between the transmitter and the receiver, W denotes the total bandwidth of the transmission, R is the transmission rate (W/R is also known as the processing gain in CDMA literature), At 1/d 4 is the attenuation factor resulting from the path loss, d is the distance between the transmitter and the receiver, and 2 is the variance of the thermal noise. Denote the number of packet arrivals as n a = 0, 1, . .

., the probability of packet arrival as pa (n a ), the probability of successful packet transmission as S( ( , pt ), m), and the channel-transition probability as pc ( k , k+1 ). Here, pc ( k , k+1 ) indicates the transition probability of the channel gain from state k at time instant k to state k+1 at the next time instant.

Suppose that the current state is sk = (n b,k , k ), where n b,k is the number of packets in the buffer at time k and k is the channel gain that is fed back. The action taken at time k is ak = (m k , pt,k ), where m k and pt,k denote the modulation level and the transmit power employed at time k. Assuming that the events of packet arrival, successful transmission, and channel transition are all mutually independent, the corresponding system state transition probability is determined as follows.

1. Transmission failure: sk+1 = (n b,k + n a , k+1 ), Psk ,sk+1 (ak ) = pa (n a )(1 S( , m k )) pc ( k , k+1 ). (10.

14). 10.4 Throughput maximization in point-to-point communication Table 10.2. Single-node simulation parameters Packet size System parameters Channel gain Buffer cost Modulation level Packet success probability Transmit power SNR range L b = 64, L = 80 W = 10 MHz, R = 100 kbits/s, Tp = 0.

8 ms 2 = 5 10 15 W f D = 50 Hz, = [ 8, 6, ...

, 8] dB At = 1.916 10 14 f (n b ) = 0.05(n b + 4) if n b = max(n b ) max(n b ) = 7, f (max(n b )) = 3 m = 1, 2, 3, 4 (BPSK, QPSK, 8PSK, 16PSK), S( ( , pt ), m) = (1 P( ( , pt ), m)) L P( , m) = erfc sin( /2m ) pt = [0, 0.

2, ...

, 2] W = [0, 1, ...

, 24] dB. 2. Successf none none ul transmission: sk+1 = (n b,k + n a m k , k+1 ), Psk ,sk+1 (ak ) = pa (n a )S( , m k ) pc ( k , k+1 ). (10.

15). The formula tion of the MDP has the following interpretation. Before transmission of a packet, the transmitter is in some state (obtained from the previous history of transmission, i.e.

buffer content and channel condition, see Figure 10.2). The transmitter uses this information to determine what modulation and transmit power should be used to maximize the average throughput relative to the total energy consumed.

At the end of a packet transmission, the transmitter obtains feedback information from the receiver containing the quantized channel gain and ACK/NACK. The quantized channel gain is used to track the channel evolution k . The ACK/NACK is used to update the buffer content.

When an ACK signal is received, the transmitter will send the following packet at the next transmission time. Otherwise, it retransmits the packet. The number of successfully transmitted packets relative to the energy consumed during one transmission time is recorded as the reward, R(sk , ak ) = R((n b,k , k ), (m k , pt,k )).

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