Computer Science Mathematics
Computer Science-2021.gz:143355
Computer Science
da222dc1f3cb400ade6b259361cfff7656c999dc
Nonlinear RF Fingerprints Authentication for OFDM Wireless Devices based on Demodulated Symbols

Radio Frequency fingerprints (RFF) authentication is one of the methods for the physical-layer information security, which uses the hardware characteristics of the transmitter to identify its real identity. In order to improve the performance of RFF based on preamble with fixed duration, a nonlinear RFF authentication method based on payload symbols is proposed for the wireless OFDM devices with the bit mapping scheme of QPSK. The communication system is modeled as a Hammerstein system containing the nonlinear transmitter and wireless multipath fading channel. A parameter separation technique based on orthogonal polynomial is presented for the estimation of the parameters of the Hammerstein system. The Hammerstein system parameter separation technique is firstly used to estimate the linear parameter with the training signal, which is used to compensate the adverse effect of the linear channel for the demodulation of the successive payload symbols. The demodulated payload symbols are further used to estimate the nonlinear coefficients of the transmitter with the Hammerstein system parameter separation technique again, which is used as the novel RFF for the authentication of the QPSK-OFDM devices. Numerical experiments demonstrate that the proposed method is feasible. The novel method can also be extended to the OFDM signals with other bit mapping schemes.


Introduction
of a radio device is determined by the power amplifier and digital to analog converter etc. of the transmitter, which includes the coefficient estimation of the nonlinear model of the transmitter [11][12][13] and mode decomposition or entropy transform [14][15][16] of the received signal etc. The nonlinear coefficients related RFF is normally estimated with the priori preamble and the corresponding received analog signal. In [11], the amplifier is modeled as a Taylor

System Model
The system model of the proposed nonlinear RFF authentication method for QPSK-OFDM wireless devices is shown in Fig. 1.

The Hammerstein System Parameter Separation Technique
The nonlinearity of the OFDM transmitter is with memories.
The QPSK-OFDM wireless transmitter and the channels are modeled as a Hammerstein system which contains a static nonlinear and a successive dynamic linear sub-system. The discrete equivalent model of the Hammerstein system is depicted in Fig. 2. ( ) x n is the emitted signal of the transmitter; ( ) v n is the AWGN, and ( ) d n denotes the received wireless signal.

Linear vector model of the Hammerstein system
After the QPSK-OFDM signal u(n) passes the static nonlinearity, it becomes where P is an odd integer, z  denotes the unit delay, the linear vector model for the Hammerstein system is depicted as Fig. 3.

Fig. 3. The linear vector model for the Hammerstein system
Similar to [20], define the vector of QPSK-OFDM signal

Hammerstein system parameter separation based on orthogonal polynomial
As the inversion of matrix H Φ Φ will often incur numerical instability caused by conventional polynomial, we use the orthogonal polynomial basis function in [19] to U is an upper triangular matrix in [19] for orthogonal basis.
With Eq. (4), the LS estimation of h is  h and  b are the separated linear and nonlinear parameters of the Hammerstein system.

The Proposed Nonlinear RF Fingerprints Authentication Method
Suppose the pilot arrangement of the QPSK-OFDM system is block type, which means FD symbols at all sub-carriers of the first OFDM symbol of a frame is the pilot symbols and the subsequent OFDM symbols of the frame are the payload symbols.

Numerical Experiments
The numerical experiments with two nonlinear transmitters and a multipath fading channel are done to verify the feasibility of the proposed method.
The number of sub-carriers of an OFDM symbol is set to 2048 and the bit mapping scheme for FD symbols on all sub-carriers is QPSK. The length of CP is set to 512, and no virtual sub-carriers are employed. The number of the training OFDM symbol of a frame is 1, and the number of the payload OFDM symbols in the frame is set to p = 1, 2, 4, and 8, respectively. The static nonlinear parameters of the two transmitters [12] to be authenticated are shown in Table 1.   Fig. 6 where k = 3, the number of the preamble OFDM symbol is 1, and the number of the payload OFDM symbols is p = 1, 2, 4, and 8, respectively. On the other hand, it can be seen from Fig. 6 that the classification performances based on one payload symbol are near to that based on the preamble symbol. And the correct classification rates with the two kinds of RFF are greater than the random guess probability of the two transmitters even when Eb/N0 is 0dB. When the number of payload symbols is 8, the correct rates reach 80% when Eb/N0 remains 0dB. When Eb/N0 is greater than 10dB and the number of payload symbols is 8, the correct classification rates are close to 100%. And when Eb/N0 is 20dB and the number of payload symbols is one, the correct classification rates are also near to 100%.

Conclusion
In this paper, we have proposed a nonlinear RFF authentication method for QPSK-OFDM wireless devices based on the demodulated payload symbols, rather than the known training symbols. A Hammerstein system parameter separation technique has also been presented, which is used twice for the proposed method. Numerical simulations show that the longer the length of the payload symbols, the better the correct classification performance of the proposed nonlinear RFF, which is not limited by the duration of the preamble signal any more. The novel method can also be extended to the OFDM signals with other bit mapping schemes.