Tham khảo tài liệu 'mobile and wireless communications network layer and circuit level design 2012 part 3', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | RSS Based Technologies in Wireless Sensor Networks 51 The vector representation of the above is I 1 f- r 1 R 19 I J where 1n is the unity matrix and ã Rị. As proposed by Zander in Zander 1992 we can derive the optimal value as follows see Remark 1 n - 1 Vn nmax 20 which results Rt R V .n . the received power values of the signals from every client measured at the server should be equal. Here R is the target received power. This reduces the CIR balancing problem to a simple power control problem as presented in the next section. Using the Perron-Froebenius theorem see Varga 1962 the largest real eigenvalue of the matrix 1n can be found as n . Selecting Rf Rm n results in maintaining the CIR at the optimal value of------- while gaining the maximum energy saving in the network. b Transmission Power Control In this section we propose a power control scheme to maintain the variable CIR presented above. Since we proved that maintaining a constant received power at the base station satisfies the optimal CIR condition the ultimate target of the power control algorithm is to maintain R at R m. c Iterative Controller The iterative power control algorithm is proposed as follows pT f R - R m . 21 Here the f is defined as any function satisfying the Lipschitz condition f a - b 11 a - b 22 where k1 e 0 1 is the Lipschitz constant for the function f . Proposition 1 The controller converges the R m starting from any arbitrary value to R 1 if the transceiver gains remain constant. Proof. From the path loss model between the client 15 and the server 16 nodes we have Rm PT - PT Rm and since pT is a constant in our problem the received power at the client node remains a constant. Then the controller becomes PT f R - PT PT - Rm 23 resulting PT f C - PT ut 52 Mobile and Wireless Communications Network layer and circuit level design where C R P T - Rm is a constant for the time interval. Here the Uj is the random noise in the Rm . Rị Rị Vị . Let p C - pi then p -pi . The equation .