Independent Eavesdroppers 上浒充通大学 SHANGHAI JIAO TONG UNIVERSITY Capacity for Eavesdroppers Lemma 1:When a legitimate node t is transmitting to a legitimate receiver r,the maximum rate that an independent eavesdropper e can obtain is upper-bounded by R,≤min( No Bd+d) Received Power where d is the Euclidean distance between legitimate node t and node r and de is the distance between legitimate node t and eavesdropper e. Asymptotic Analysis on Secrecy Capacity in Large-Scale Wireless Networks 11
11 Independent Eavesdroppers ❑ Capacity for Eavesdroppers Lemma 1: When a legitimate node t is transmitting to a legitimate receiver r, the maximum rate that an independent eavesdropper e can obtain is upper-bounded by 0 min( , (1 ) ) t te t e tr r Pd P R d N P − + where is the Euclidean distance between legitimate node t and node r and is the distance between legitimate node t and eavesdropper e. tr d te d Received Power Asymptotic Analysis on Secrecy Capacity in Large-Scale Wireless Networks
Independent Eavesdroppers 上浒充通大￥ SHANGHAI JIAO TONG UNIVERSITY Case 1:when d andd both greater 1, PI(x,x) SINR,=N+∑r于 (xx)+egpl(xx) PI(xx)_pd Pl(x,x.)pd-a Case 2-4: die <l,dre>1;die <1,dre <l;d>1,dre<1. Asymptotic Analysis on Secrecy Capacity in Large-Scale Wireless Networks 12
12 Independent Eavesdroppers 0 \{ } ( , ) ( , ) ( , ) ( , ) ( , ) (1 ) ) t t e e t k e r k e k T i k R t t e t te e re t te t tr rt te r Pl x x SINR N Pl x x Pl x x Pl x x P Pl x x P P P d P d P − − − − = + + + + ｒ ｒ ｒ ｒ ｄ ＝ ｄ ｄ (ｄ Case 1: when and both greater 1, te d re d 1, 1; 1, 1; 1, 1. te re te re te re d d d d d d Case 2-4: Asymptotic Analysis on Secrecy Capacity in Large-Scale Wireless Networks