Physical layer secure communication against an eavesdropper with arbitrary number of eavesdropping antennas

Abstract

A method for physical layer secure transmission against an arbitrary number of eavesdropping antennas includes: S1: communication between legitimate transmitter Alice and legitimate receiver Bob is confirmed; S2: Alice randomly generates a key bit b.sub.k with M.sub.S bits, maps the key bit b.sub.k into a key symbol K, and performs an XOR on the key bit b.sub.k and to-be-transmitted confidential information b to obtain an encrypted bits b.sub.s; S3: Bob transmits a pilot sequence to Alice, and Alice calculates a candidate precoding space W and transmits modulated symbol streams s=(s.sub.1, . . , s.sub.N) by using precoding W(e); S4: 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; S5: Bob performs an XOR on observed key bits and the demodulated ciphertext bits to obtain the confidential information.

Claims

1. A method for physical layer secure transmission against a number of eavesdropping antennas, comprising the following steps: S1: confirming a communication between a legitimate transmitter Alice and a legitimate receiver Bob; S2: randomly generating, by the legitimate transmitter Alice, a key bit b.sub.k with M.sub.S bits, mapping, by the legitimate transmitter Alice, the key bit b.sub.k into a key symbol K, and performing, by the legitimate transmitter Alice, an XOR on the key bit b.sub.k and to-be-transmitted binary confidential bit information b to obtain an encrypted ciphertext bits b.sub.s, and modulating, by the legitimate transmitter Alice, the encrypted ciphertext bits b.sub.s into modulated symbols s=(s.sub.1, . . . , s.sub.N); S3: 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.sub.1, . . . , s.sub.N) by using a precoding W(e); S4: 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; S5: 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 S6: repeating steps S2-S5; 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 S1 comprises the following steps: S11: dividing, by the legitimate transmitter Alice, the to-be-transmitted binary confidential bit information b=(b.sub.1, b.sub.2, . . . , b.sub.N) into N parts, wherein each part b.sub.i, i=1, 2, . . . , N of the N parts contains bits; and S12: determining, by the legitimate receiver Bob, a number N.sub.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.sub.B−1: $N_K=\left(\begin{array}{c}N\\ N_B\end{array}\right),M_S={\log }_2\left(N_K\right);$ wherein M.sub.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.sub.s is calculated as follows:
b.sub.s=(b.sub.s,1, b.sub.s,2, . . . , b.sub.s,N)=(b.sub.1⊕b.sub.k,b.sub.2⊕b.sub.k, . . . , b.sub.N⊕b.sub.k).

4. The method according to claim 2, wherein, after receiving the pilot sequence, the legitimate transmitter Alice estimates an uplink channel H.sub.BA and transposes the uplink channel H.sub.BA to obtain a downlink channel H.sub.AB=H.sub.BA.sup.T; and the candidate preceding space W is calculated as follows: $\tilde{W}={H_{\mathrm{AB}}^H\left(H_{\mathrm{AB}}{H}_{\mathrm{AB}}^H\right)}^{-1}=\left({\tilde{w}}_1,{\tilde{w}}_2,.Math.{\tilde{w}}_{N_B}\right);\mathrm{and}W=\left(\frac{{\tilde{w}}_1}{.Math.{\tilde{w}}_1.Math.},\frac{{\tilde{w}}_2}{.Math.{\tilde{w}}_2.Math.},.Math.\frac{{\tilde{w}}_{\mathrm{NB}}}{.Math.{\tilde{w}}_{\stackrel{\_}{N}}.Math.}\right)=\left(w_1,w_2,.Math.w_{N_B}\right).$

5. The method according to claim 2, wherein, the key symbol corresponds to different receive antennas K={0, 1, 2, . . . , N.sub.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.sub.1, . . . , s.sub.N) by using the precoding W(e), and received signals are expressed as: $y=\sqrt{\frac{P_T}{N}}{H}_{\mathrm{AB}}W\left(e\right)s+n=\sqrt{\frac{P_T}{N}}\underset{k=1}{\overset{N}{.Math.}}{H}_{\mathrm{AB}}{w}_i{s}_k+n,i\in ℐ\left(e\right),$ 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 S2 further comprises: S21: modulating the encrypted ciphertext bits b.sub.s into the modulated symbols s=(s.sub.1, . . ., s.sub.N) to be transmitted.

10. The method according to claim 1, wherein, a number of receive antennas of the legitimate receiver Bob is N.sub.B; after receiving a signal y∈.sup.N.sup.B.sup.×1[y.sub.1, y.sub.2, . . . , y.sub.N.sub.B].sup.T, the legitimate receiver Bob measures an intensity of signal-plus-noise (SPN) of the each antenna as: α.sub.i=|y.sub.i|.sup.2, i=1, 2, . . . N.sub.B.

11. The method according to claim 10, wherein, step S4 comprises the following steps: S41: selecting, by the legitimate receiver Bob, N maximum values of α.sub.i, and obtaining observed e according to a subscript of the α.sub.i; S42: obtaining the observed key symbols K and the observed key bits {circumflex over (b)}.sub.k according to the observed e; and S43: 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)}.sub.s; wherein ŝ.sub.1=arg min.sub.s.sub.1.sub.∈S∥y.sub.i−s.sub.1∥.sup.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)}.sub.k and the demodulated ciphertext bits {circumflex over (b)}.sub.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)}.sub.s,1⊕{circumflex over (b)}.sub.k,{circumflex over (b)}.sub.s,2⊕{circumflex over (b)}.sub.k, . . . , {circumflex over (b)}.sub.s,N⊕{circumflex over (b)}.sub.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.sub.1, . . . , s.sub.N) by using the precoding W(e), and received signals are expressed as: $y=\sqrt{\frac{P_T}{N}}{H}_{\mathrm{AB}}W\left(e\right)s+n=\sqrt{\frac{P_T}{N}}\underset{k=1}{\overset{N}{.Math.}}{H}_{\mathrm{AB}}{w}_i{s}_k+n,i\in ℐ\left(e\right),$ wherein I (e) denotes a subscript position of a non-zero element in the E(:, K 1).

Description

BRIEFDESCRIPTION OF DRAWINGS

(1) FIG. 1 is a schematic diagram of a communication system model of the present invention;

(2) FIG. 2 is a flow chart of the method of the present invention;

(3) FIG. 3 is a schematic diagram of mapping key symbols to different antenna. vectors of Bob under the condition of N.sub.B=2 according to the present invention; and

(4) FIG. 4 is a graph showing the bit error rate performance of Bob and the lower bound BER of Eve when Eve sequentially increases the number of eavesdropping antennas according to the present invention.

DETAILED DESCRIPTION OF THE EMBODIMENTS

(5) In order to facilitate a clearer understanding of the technical features, objectives and effects of the present invention, the specific embodiments of the present invention will be described hereinafter with reference to the drawings.

(6) In order to facilitate a deeper understanding of the present invention, the physical layer where the method is implemented is explained below. Those skilled in the art should understand that the scope of protection of the present invention is not limited thereto.

(7) The legitimate transmitter Alice and receiver Bob each employs a protected zone with a radius R to surround themselves. The radius R of the protected zone must be greater than the uncorrelated distance of the channel to prevent eavesdropper Eve from entering the protected zone for eavesdropping. Namely, the distances from Eve to Alice and Bob are both larger than R, thereby ensuring that Eve's channel is independent from the channel of Alice and the channel of Bob, respectively. The radius R is determined by the channel propagation environment and carrier frequency, and is generally 10 cm-100 cm in a rich scattering environment.

(8) The legitimate transmitter Alice and the legitimate receiver Bob each need to be equipped with at least 2 antennas. N.sub.A and N.sub.B below denote the number of antennas of Alice and the number of antennas of Bob, respectively, where N.sub.A>N.sub.B>1. A downlink communication is taken as an example for illustration, where Alice transmits confidential binary information b=(b.sub.1, b.sub.2, . . . ), (b.sub.i∈{0,1}) to Bob, and the eavesdropper Eve eavesdrops from her received signals. The eavesdropper Eve employs arbitrary number of receive antennas as N.sub.E.

(9) As shown in FIG. 1, the legitimate transmitter Alice communicates with the legitimate receiver Bob through the downlink channel H.sub.AB, and the eavesdropper's channel is H.sub.AE.

(10) As shown in FIG. 2, a method for physical layer secure transmission against an eavesdropper with arbitrary number of eavesdropping antennas includes the following steps:

(11) S1: The legitimate transmitter Alice and the legitimate receiver Bob confirm communication parameters. The parameters include N, which is the stream number of the transmitted symbols where 1≤N≤N.sub.B−1. The modulation order M.sub.S and the total number of constellation symbols M.

(12) S2: First, Alice independently generates random bits b.sub.k to encrypt (exclusive-OR: XOR) the binary confidential information b to obtain b.sub.s. Alice modulate b.sub.s=(b.sub.s,1, b.sub.s,2, . . . , b.sub.s,N) to modulated symbols (s.sub.1, s.sub.2, . . . , s.sub.N), s.sub.i denotes the specific constellation symbol. Alice maps the key bits b.sub.k into the key symbol K.

(13) S3: Bob transmits a pilot sequence to Alice, Alice estimates channel H.sub.AB, and processes it to get a precoding weights space matrix W. According to K, Alice obtains the corresponding antenna index vector e. According to e, Alice chooses different column vectors from W to construct the precoding matrix W(e). Then Alice transmits s=(s.sub.1, . . . , s.sub.N) by multiplying precoding W(e);

(14) S4: Bob measures the received signal plus noise strength (SPN) of each receive antenna, estimates the antenna index vector, inversely mapping the antenna index vector to obtain key symbols K and key bits b.sub.k. Bob demodulates the received modulated symbol s=(s.sub.1, . . . , s.sub.N) at each activated antenna to obtain b.sub.s=(b.sub.s,1, b.sub.s,2, . . . , b.sub.s,N);

(15) S5: Bob performs XOR on the observed key bits b.sub.k and the demodulated bits b.sub.s=(b.sub.s,1, b.sub.s,2, . . . , b.sub.s,N) to obtain the confidential information bits b; and

(16) S6: repeating steps S2-S5.

(17) Further, step S1 includes the following steps:

(18) S11: Alice presents the confidential bits as b=(b.sub.1, b.sub.2, . . . , b.sub.N), where each b.sub.i, i=1, 2, . . . , N, contains M.sub.S=log.sub.2 M independent bits (M.sub.S and M denote the modulation order and the total number of constellation symbols in the modulation set); and

(19) S12: Alice and Bob confirm parameters: the number of symbol streams N and receive antennas N.sub.B, such that

(20) $N_K=\left(\begin{array}{c}N\\ N_B\end{array}\right),M_S={\log }_2\left(N_K\right);$

(21) Where M.sub.S denotes the order of a constellation signal of the modulation type used by the communication. For example, for binary phase-shift keying (BPSK), M.sub.S=1.

(22) Further, in Step S2, Alice obtains b.sub.s as
b.sub.s=(b.sub.s,1, b.sub.s,2, . . . , b.sub.s,N)=(b.sub.1⊕b.sub.k, b.sub.2⊕b.sub.k, . . . , b.sub.N⊕b.sub.k).

(23) Further in Step S2, each key symbol K corresponds to different receive antennas
K={0, 1, 2, . . . , N.sub.k−1}.

(24) As shown in FIG. 3, the key symbols are mapped to different antenna vectors of Bob. For example, under the condition of N.sub.B=2, if N.sub.B=2, N=1 then K∈{0,1}, and all possible antenna combinations E are denoted as:

(25) $K\in \left(\begin{array}{c}0\\ 1\end{array}\right)\iff E=\left(\begin{array}{cc}1& 0\\ 0& 1\end{array}\right);$
wherein, “1” in the first column vector e.sub.1 of E denotes Bob's first antenna that is activated, “0” in the first column vector e.sub.1 of E denotes Bob's second antenna that is non-activated, and so on.

(26) Further, according to the value of K, Alice selects the (K+1)-th column in E as e=E(:, K+1) and used it as a selection criterion for constructing the precoding. Further, Alice selects N column vectors from W corresponding to the subscript position of N non-zero elements in e to construct precoding W(e) to transmit s=(s.sub.1, . . . , s.sub.N).

(27) Further, step S3 includes the following steps:

(28) After receiving the pilot sequence, Alice estimates an uplink channel H.sub.BA and transposes the uplink channel H.sub.BA to obtain a downlink channel H.sub.AB=H.sub.BA.sup.T; and the precoding weights space W is calculated as follows:

(29) $\tilde{W}={H_{\mathrm{AB}}^H\left(H_{\mathrm{AB}}{H}_{\mathrm{AB}}^H\right)}^{-1}=\left({\tilde{w}}_1,{\tilde{w}}_2,.Math.{\tilde{w}}_{N_B}\right);\mathrm{and}W=\left(\frac{{\tilde{w}}_1}{.Math.{\tilde{w}}_1.Math.},\frac{{\tilde{w}}_2}{.Math.{\tilde{w}}_2.Math.},.Math.\frac{{\tilde{w}}_{\mathrm{NB}}}{.Math.{\tilde{w}}_{\stackrel{\_}{N}}.Math.}\right)=\left(w_1,w_2,.Math.w_{N_B}\right).$

(30) Further in Step S3, Alice transmits s=(.sub.1, . . . , s.sub.N) by multiplying the precoding W(e), and the received signals are expressed as:

(31) $y=\sqrt{\frac{P_T}{N}}{H}_{\mathrm{AB}}W\left(e\right)s+n=\sqrt{\frac{P_T}{N}}\underset{k=1}{\overset{N}{.Math.}}{H}_{\mathrm{AB}}{w}_i{s}_k+n,i\in ℐ\left(e\right),$
wherein I (e) denotes the subscript position of a non-zero element in e=E(:, K+1).

(32) Step S4 includes the following sub steps:

(33) Further, the number of the receive antennas of Bob is N.sub.B; after receiving a signal y∈.sup.N.sup.B.sup.×1=[y.sub.1, y.sub.2, . . . y.sub.N.sub.B].sup.T, Bob measures the strength of signal-plus-noise (SPN) of each antenna as:
α.sub.i=|y.sub.i|.sup.2, i=1, 2, . . . N.sub.B.

(34) S41: Bob selects N maximum values of α.sub.i, wherein the subscript of α.sub.i denotes the position corresponding to the non-zero elements in e and then obtaining the observed e according to the subscripts,

(35) For example, when N=1,

(36) $\stackrel{\_}{E}\left(i,:\right)=\underset{\mathrm{antenna}\mathrm{index}\mathrm{with}\mathrm{the}\mathrm{maximum}\mathrm{SPN}}{\left(0,0,.Math.,\underset{\bigvee }{1}.Math.0\right)}\mathrm{Max}\left({\alpha }_i\right)=i.Math.\tilde{E}\left(i,:\right){\tilde{k}}_i$

(37) S42: Bob accordingly obtains his own observed ê, and then obtains the observed key symbols {circumflex over (K)} and key bits {circumflex over (b)}.sub.k according to the observed ê; and

(38) In Step S5 Bob independently demodulates the symbols ŝ at the activated antennas corresponding to N non-zero elements in the observed e to obtain the demodulated bits {circumflex over (b)}.sub.s; wherein ŝ.sub.i=arg min.sub.s.sub.1.sub.∈S∥y.sub.i−s.sub.1∥.sup.2, i=1, 2, . . . N.

(39) Further in Step S5, an XOR is performed by Bob on the observed key bits {circumflex over (b)}.sub.k and the decrypted bits {circumflex over (b)}.sub.s to obtain the confidential bit information transmitted by Alice:
{circumflex over (b)}=({circumflex over (b)}.sub.s,1⊕{circumflex over (b)}.sub.k,{circumflex over (b)}.sub.s,2⊕{circumflex over (b)}.sub.k, . . . {circumflex over (b)}.sub.s,N⊕{circumflex over (b)}.sub.k).

(40) Steps S2 to S5 are repeated to securely transmit confidential information between legitimate transmitter and receiver.

(41) FIG. 4 shows the final bit error rate performance of Bob and the lower bound of BER of Eve, where Eve uses 1 (labeled as “Eve NK”), 2 (labeled as “Eve OK”), 4, 8, and 100 antennas, respectively, and she processed the signals by using optimal-ratio combining(MRC).

(42) The basic principles and main features and advantages of the present invention have been shown and described above. Those skilled in the art should understand that the present invention is not limited by the foregoing embodiments. The foregoing embodiments and the description in the specification only illustrate the principle of the present invention. The present invention may have various changes and improvements without departing from the spirit and scope of the present invention, and these changes and improvements shall fall within the scope claimed by the present invention. The scope of protection claimed by the present invention is defined by the appended claims.