Physical layer secure communication against an eavesdropper with arbitrary number of eavesdropping antennas
A method for physical layer secure transmission against an arbitrary number of eavesdropping antennas includes: S 1 : communication between legitimate transmitter Alice and legitimate receiver Bob is confirmed; S 2 : Alice randomly generates a key bit b k with M S bits, maps the key bit b k into a key symbol K, and performs an XOR on the key bit b k and to-be-transmitted confidential information b to obtain an encrypted bits b s ; S 3 : Bob transmits a pilot sequence to Alice, and Alice calculates a candidate precoding space W and transmits modulated symbol streams s=(s 1 , . . , s N ) by using precoding W(e); S 4 : Bob measures received signal strength of each antenna, estimates the corresponding antenna vector e, inversely maps the vector e to obtain key symbols and key bits, and demodulates the received symbol streams in sequence at each activated antenna to obtain demodulated ciphertext bits; S 5 : Bob performs an XOR on observed key bits and the demodulated ciphertext bits to obtain the confidential information.
1. A method for physical layer secure transmission against a number of eavesdropping antennas, comprising the following steps:
S 1 : confirming a communication between a legitimate transmitter Alice and a legitimate receiver Bob;
S 2 : randomly generating, by the legitimate transmitter Alice, a key bit b k with M S bits, mapping, by the legitimate transmitter Alice, the key bit b k into a key symbol K, and performing, by the legitimate transmitter Alice, an XOR on the key bit b k and to-be-transmitted binary confidential bit information b to obtain an encrypted ciphertext bits b s , and modulating, by the legitimate transmitter Alice, the encrypted ciphertext bits b s into modulated symbols s=(s 1 , . . . , s N );
S 3 : transmitting a pilot sequence to the legitimate transmitter Alice by the legitimate receiver Bob, calculating a candidate precoding space W by the legitimate transmitter Alice, and transmitting, by the legitimate transmitter Alice, the modulated symbols s=(s 1 , . . . , s N ) by using a precoding W(e);
S 4 : independently measuring, by the legitimate receiver Bob, a received signal strength of each receive antenna, estimating, by the legitimate receiver Bob, a vector of the each receive antenna, inversely mapping, by the legitimate receiver Bob, the vector of the each receive antenna to obtain observed key symbols and observed key bits, and demodulating, by the legitimate receiver Bob, the modulated symbols in sequence at each activated antenna to obtain demodulated ciphertext bits;
S 5 : performing, by the legitimate receiver Bob, an XOR on the observed key bits and the demodulated ciphertext bits to obtain the to-be-transmitted binary confidential bit information b; and
S 6 : repeating steps S 2 -S 5 ;
wherein, the legitimate transmitter Alice and the legitimate receiver Bob are each surrounded by a protected zone with a radius R to prevent an eavesdropper Eve from entering the protected zone for eavesdropping, and a channel of the eavesdropper Eve is independent from a channel of the legitimate transmitter Alice and a channel of the legitimate receiver Bob, respectively.
2. The method according to claim 1 , wherein,
step S 1 comprises the following steps:
S 11 : dividing, by the legitimate transmitter Alice, the to-be-transmitted binary confidential bit information b=(b 1 , b 2 , . . . , b N ) into N parts, wherein each part b i , i=1, 2, . . . , N of the N parts contains bits; and
S 12 : determining, by the legitimate receiver Bob, a number N B of receive antennas and a number N of streams of the modulated symbols, wherein the legitimate transmitter Alice transmits the streams of the modulated symbols simultaneously, wherein 1≤N≤N B −1:
N
K
=
(
N
N
B
)
,
M
S
=
log
2
(
N
K
)
;
wherein M S denotes an order of a constellation signal of a modulation type used by the communication.
3. The method according to claim 2 , wherein,
the encrypted ciphertext bits b s is calculated as follows:
b s =( b s,1 , b s,2 , . . . , b s,N )=( b 1 ⊕b k ,b 2 ⊕b k , . . . , b N ⊕b k ).
4. The method according to claim 2 , wherein,
after receiving the pilot sequence, the legitimate transmitter Alice estimates an uplink channel H BA and transposes the uplink channel H BA to obtain a downlink channel H AB =H BA T ; and the candidate preceding space W is calculated as follows:
W
~
=
H
AB
H
(
H
AB
H
AB
H
)
-
1
=
(
w
~
1
,
w
~
2
,
…
w
~
N
B
)
;
and
W
=
(
w
~
1
w
~
1
,
w
~
2
w
~
2
,
…
w
~
NB
w
~
N
_
)
=
(
w
1
,
w
2
,
…
w
N
B
)
.
5. The method according to claim 2 , wherein,
the key symbol corresponds to different receive antennas K={0, 1, 2, . . . , N k −1} activated at the legitimate receiver Bob, and antenna combinations are denoted by a vector E.
6. The method according to claim 5 , wherein,
the key symbols K∈κ, according to a value of the key symbol K, a (K+1)-th column in the vector E is selected as E(:, K+1) and used as a selection criterion for transmitting the precoding W(e).
7. The method according to claim 6 , wherein,
N non-zero column vectors corresponding to the E(;. K+1) are selected, from the candidate precoding space W, as the precoding W(e).
8. The method according to claim 4 , wherein,
the legitimate transmitter Alice transmits the modulated symbols s=(s 1 , . . . , s N ) by using the precoding W(e), and received signals are expressed as:
y
=
P
T
N
H
AB
W
(
e
)
s
+
n
=
P
T
N
∑
k
=
1
N
H
AB
w
i
s
k
+
n
,
i
∈
ℐ
(
e
)
,
wherein I (e) denotes a subscript position of a non-zero element in E(:, K+1).
9. The method according to claim 1 , wherein,
step S 2 further comprises:
S 21 : modulating the encrypted ciphertext bits b s into the modulated symbols s=(s 1 , . . ., s N ) to be transmitted.
10. The method according to claim 1 , wherein,
a number of receive antennas of the legitimate receiver Bob is N B ; after receiving a signal y∈ N B ×1 [y 1 , y 2 , . . . , y N B ] T , the legitimate receiver Bob measures an intensity of signal-plus-noise (SPN) of the each antenna as: α i =|y i | 2 , i=1, 2, . . . N B .
11. The method according to claim 10 , wherein,
step S 4 comprises the following steps:
S 41 : selecting, by the legitimate receiver Bob, N maximum values of α i , and obtaining observed e according to a subscript of the α i ;
S 42 : obtaining the observed key symbols K and the observed key bits {circumflex over (b)} k according to the observed e; and
S 43 : independently demodulating, by the legitimate receiver Bob, symbols ŝ at antennas corresponding to N non-zero elements in the observed e to obtain the demodulated ciphertext bits {circumflex over (b)} s ; wherein ŝ 1 =arg min s 1 ∈S ∥y i −s 1 ∥ 2 , i=1, 2, . . . N.
12. The method according to claim 11 , wherein,
an XOR is performed on the observed key bits {circumflex over (b)} k and the demodulated ciphertext bits {circumflex over (b)} s to obtain the to-be-transmitted binary confidential bit information to be transmitted by the legitimate transmitter Alice as follows:
{circumflex over (b)}= ( {circumflex over (b)} s,1 ⊕{circumflex over (b)} k ,{circumflex over (b)} s,2 ⊕{circumflex over (b)} k , . . . , {circumflex over (b)} s,N ⊕{circumflex over (b)} k ).
13. The method according to claim 1 , wherein,
the radius R of the protected zone is larger than a channel uncorrelated distance, and the radius R is determined by a channel propagation environment and a carrier frequency.
14. The method according to claim 6 , wherein,
the legitimate transmitter Alice transmits the modulated symbols s=(s 1 , . . . , s N ) by using the precoding W(e), and received signals are expressed as:
y
=
P
T
N
H
AB
W
(
e
)
s
+
n
=
P
T
N
∑
k
=
1
N
H
AB
w
i
s
k
+
n
,
i
∈
ℐ
(
e
)
,
wherein I (e) denotes a subscript position of a non-zero element in the E(:, K 1).