94
3 Physical Theory of RFID System Physical Anti-Collision
the study of multi parameter estimation [46, 47]. Considering the parameter estimation of the MIMO system, Cramer–Rao bound (CRB) determines a lower limit for
any unbiased variance of estimator, which means that it is impossible to obtain the
unbiased estimator when the variance is less than the lower limit. Meanwhile, the
CRB provides a standard of comparing the performance of unbiased estimator. In
[48], Wang studied the CRB for joint RSS/DoA-Based Primary-User localization
in cognitive radio networks. Bekkerman studied the CRB for estimating parameters of coherently distributed targets (CDT) using MIMO radars [49]. Jagannatham
discussed the Cramer–Rao bound based mean-squared error and throughput analysis
of superimposed pilots for semi-blind multiple input multiple output wireless channel
estimation [50]. In [51], Kalkan calculated the CRB for target position and velocity
estimations for widely separated MIMO radar. However, at present, the research
on CRB in the MIMO system is mainly focused on the study of the beam and the
estimated CRB. There are fewer reports on the RFID-MIMO system, especially the
impact of the size of CRB on the reading performance of the RFID- MIMO system.
Therefore, on the basis of the above research, this paper introduces the MIMO system
into the field of RFID, and constructs a channel model of the RFID-MIMO system.
Besides that, in the paper, CRB will be applied to the field of parameter estimation in
the RFID-MINO system. The CRB of different tag numbers is simulated by computer
to obtain the CRB corresponding to the number of different tags in the case of orthogonal and coherent signals. Finally, by studying the relationship between multi-tag
distribution CRB and reading performance, the paper analyzes the effect of multi-tag
distribution on reading performance in RFID-MIMO system based on CRB.
3.3.1 Channel Model
Consider a RFID-MIMO system composed of M antennas coordinate of Z m =
(x m ,y m )
T (m = 1,…,M). Let antenna azimuth angle θ denotes the angle between
the tag and the vertical plane of the antenna arrays. The space between two tags is d a
times of wavelength, and the space between two antennas is d b times of wavelength.
The schematic diagram of the structure of RFID-MIMO system is shown in Fig. 3.23.
Let the column vector s[n] represents the baseband signal transmitted by antenna
unit when n represents the time. So a echo signal of the target received by the receiving
array is given by
y[n] = αA(θ )s[n] + w[n](n = 1, 2, . . . N )
(3.53)
where α is the complex amplitude corresponding to the tag, A(θ ) is the corresponding
response matrix, w[n] is the noise matrix, and A(θ ) can be defined as
A(θ ) = a(θ )a
T
(θ )
(3.54)
3 Physical Theory of RFID System Physical Anti-Collision
the study of multi parameter estimation [46, 47]. Considering the parameter estimation of the MIMO system, Cramer–Rao bound (CRB) determines a lower limit for
any unbiased variance of estimator, which means that it is impossible to obtain the
unbiased estimator when the variance is less than the lower limit. Meanwhile, the
CRB provides a standard of comparing the performance of unbiased estimator. In
[48], Wang studied the CRB for joint RSS/DoA-Based Primary-User localization
in cognitive radio networks. Bekkerman studied the CRB for estimating parameters of coherently distributed targets (CDT) using MIMO radars [49]. Jagannatham
discussed the Cramer–Rao bound based mean-squared error and throughput analysis
of superimposed pilots for semi-blind multiple input multiple output wireless channel
estimation [50]. In [51], Kalkan calculated the CRB for target position and velocity
estimations for widely separated MIMO radar. However, at present, the research
on CRB in the MIMO system is mainly focused on the study of the beam and the
estimated CRB. There are fewer reports on the RFID-MIMO system, especially the
impact of the size of CRB on the reading performance of the RFID- MIMO system.
Therefore, on the basis of the above research, this paper introduces the MIMO system
into the field of RFID, and constructs a channel model of the RFID-MIMO system.
Besides that, in the paper, CRB will be applied to the field of parameter estimation in
the RFID-MINO system. The CRB of different tag numbers is simulated by computer
to obtain the CRB corresponding to the number of different tags in the case of orthogonal and coherent signals. Finally, by studying the relationship between multi-tag
distribution CRB and reading performance, the paper analyzes the effect of multi-tag
distribution on reading performance in RFID-MIMO system based on CRB.
3.3.1 Channel Model
Consider a RFID-MIMO system composed of M antennas coordinate of Z m =
(x m ,y m )
T (m = 1,…,M). Let antenna azimuth angle θ denotes the angle between
the tag and the vertical plane of the antenna arrays. The space between two tags is d a
times of wavelength, and the space between two antennas is d b times of wavelength.
The schematic diagram of the structure of RFID-MIMO system is shown in Fig. 3.23.
Let the column vector s[n] represents the baseband signal transmitted by antenna
unit when n represents the time. So a echo signal of the target received by the receiving
array is given by
y[n] = αA(θ )s[n] + w[n](n = 1, 2, . . . N )
(3.53)
where α is the complex amplitude corresponding to the tag, A(θ ) is the corresponding
response matrix, w[n] is the noise matrix, and A(θ ) can be defined as
A(θ ) = a(θ )a
T
(θ )
(3.54)