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International Journal of Distributed Sensor Networks
Volume 2013 (2013), Article ID 681386, 10 pages
TPMS Interference Suppression Based on Beamforming Technology
1Junsung E&R Inc., Gwangju, Republic of Korea
2Department of Advanced parts and Materials Engineering, Chosun University, Gwangju, Republic of Korea
3Department of Mechatronics Engineering, Chosun University, Gwangju, Republic of Korea
Received 8 February 2013; Revised 27 June 2013; Accepted 29 July 2013
Academic Editor: Jose Ramiro Martinez-de Dios
Copyright © 2013 Cheol Park et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The Tire Pressure Monitoring System (TPMS) displays the state of a tire on a display to inform a driver of the relevant information, by means of a sensor installed on the tire of the vehicle. When the data measured from the tire are wirelessly transmitted to a receiving antenna located in the center of the vehicle, the exact transmission of data is affected by the interference from various external electronic and electrical devices. In this paper, we suggest a minimum variance distortionless response (MVDR) beamformer based on the angle-of-arrival (AOA) vector for suppressing external interference and receiving accurate data. Although the MVDR beamformer effectively suppresses the interference, it has high computational complexity because of the calculation of an autocorrelation matrix. In order to address this issue, we also suggest a generalized sidelobe canceler (GSC) beamformer which does not have the same performance of the interference suppression to MVDR but also has low computational complexity. Since the signal from each tire can cause interference to others, we consider utilizing a unique Gold Code to each tire to minimize intertire interference and reduce power consumption of a battery installed in each tire.
If air pressure of a tire is too high or low compared with a reference pressure, it is likely to cause a serious accident. The TPMS is a system for measuring the temperature and pressure of each tire by means of the installed sensor to transmit the measured data to the central processing unit (CPU) in the vehicle in order to prevent the accident [1–3]. The TPMS sensor unit (SU) installed on each tire transmits the data measured in real time to the driver’s console to enable the driver to check tire pressure and temperature. Since the TPMS transmits and receives data through wireless communication between the transmitting antenna on the tire and the receiving antenna in the center of the vehicle, the transmission module installed on the tire needs a battery for supplying power, and it is thus currently required to develop compact battery technology and the technology for prolonging the life span of the TPMS through a low-power consuming device [4–7]. Since TPMS wirelessly transmits data from SU installed in tire of a vehicle to CPU installed in the center of a vehicle, it is the typical example of the machine-to-machine communication system.
Since September, 2007, it is compulsory to install the TPMS on vehicles produced in the USA and imported from other countries by the act on compulsory TPMS installation in the USA . The EU is promoting an act for compulsory installation of the TPMS on vehicles from 2012 to 2014. The Korean government is also promoting enforcement of compulsory installation of the TPMS on vehicles since 2013, and the introduction and development of vehicle safety devices in addition to the TPMS are underway in Korea. The TPMS uses communication frequency of 433.92 MHz in the USA and Europe and 433.92 MHz and 447 MHz in Korea . The interference signal with the high power from external devices should interfere with exact transmission and reception of the TPMS data. For suppressing such interference, we suggest AOA vector-based MVDR beamformer with excellent performance. While the precedent switch beamforming technology  cannot create null in the AOA direction of interference, which results in the low performance for the interference suppression, the MVDR beamforming technology creates null in the relevant AOA to implement highly effective performance of interference suppression. However, the MVDR uses the autocorrelation matrix, which results in very high complexity. In order to address this issue, the generalized sidelobe canceler (GSC) beamforming technology is also suggested in this paper. While the GSC beamforming technology has similar performance of interference suppression to the MVDR beamformer, its complexity is significantly low . For applying the beamformer suggested in this paper to the TPMS, a transmission antenna and a sensor are installed in each tire, and antennas are arranged in the center of the vehicle in a line. In this paper, we also consider utilizing the unique Gold code  given to each tire in order to suppress interference caused by transmission signals of other tires.
This paper is organized as described below. Section 2 defines a received signal model which includes TPMS signals, interference signals, and additive white Gaussian noise (AWGN). Section 3 describes the suggested beamformers for suppressing TPMS interference signals. Section 4 describes a method of calculating the complexity of the GSC and the MVDR beamformer. Section 5 examines the performance of beamformers suggested in this paper, including beamformer complexity, output signal-to-interference and noise ratio (SINR), and beam patterns, by means of computer simulation. Finally, the conclusion is given in Section 6.
2. Received Signal Model
For applying the beamformer suggested in this paper to the TPMS, antennas are arranged in a line in the center of the vehicle in order to receive data from each tire as shown in Figure 1. Based on the uniform linear array (ULA), the received signal at the sample index is given by where is an array response vector (size ) for the th tire, is the cyclostationary Gold code for the th tire with length , and is a measured data bit for the th tire, which remains constant over the length of one cycle of Gold code. is the array response matrix, is the number of interference signals, and is an interference signal vector (sized ) composed of interference signals. is AWGN vector (size ) with independent and identically distributed components, each with zero mean and variance . The array response matrix [13, 14] is defined by where and is an incident angle to the receiving antenna, is the interelement spacing, and is a wavelength of a signal, all for the th interferer. The th column of in (2) corresponds to the array response vector of the th interference signal .
SINR  of the beamformer output, used in computer simulation, is given by In (4), S. Power (signal power) is signal power transmitted by each tire, N. Power is noise power, and I. power is interference power.
3. Beamformer for Wireless Communication of TPMS
The TPMS wireless communications for the accurate data transmission suffer from various external devices. In this section, the beamforming technology is suggested for the TPMS receiver with the high performance of the interference suppression for accurately receiving the desired signals.
3.1. MVDR Beamformer for TPMS
A beamformer shown in Figure 2 calculates a weight vector for minimizing the power of the beamformer output while maintaining the power of the desired signal, by using the AOA vector of the desired signal. The AOA of the TPMS signal can be determined when the TPMS is installed in a vehicle. The MVDR weight vector based on AOA is calculated by  where is an autocorrelation matrix of the received signal and denotes a complex conjugate transpose. The weight vector [18, 19] satisfying (5) is given by [20, 21] The weight vector generates a beam factor of one for the th tire and creates nulls to the unwanted interference signals, at the same time. The beamformer output increasing the signal-to-interference ratio (SIR)  is given by
This output contains the TPMS signal, residual interference, and noise.
3.2. GSC Beamformer for TPMS
Although the MVDR has excellent performance of the interference suppression, it has high computational complexity due to the calculation of an autocorrelation matrix. In order to address this issue, in this paper, we suggest a TPMS receiver based on GSC beamformer, shown in Figure 3. The GSC beamformer has similar performance of interference suppression to that of MVDR, and it also has low computational complexity compared to MVDR because it does not require autocorrelation matrix calculation. The GSC weight vector is calculated based on the adaptive algorithm like the least mean square (LMS) algorithm. The LMS algorithm is robustness to the environmental change and it has simple equation form which results in simple calculation.
The LMS weight vector of GSC is given by [23, 24] where is a weight vector adapted by the LMS algorithm, is a step-size parameter, is an input signal vector, and is an estimation error, calculated by has a function the same as the reference signal of LMS, defined by
In (10), is an LMS output value, calculated by Here, includes the interference signal and noise except the TPMS signal, defined by In (13), is a matrix defined as where the columns of span the left null space of. The weight vector of GSC based on the LMS algorithm is calculated by [25, 26] The GSC weight vector given in (14) generates the beam factor sized one for the th tire and nulls the interference signal, thus it improves signal-to-interference ratio (SIR). The beamformer output for the th tire by means of the weight vector of a given GSC is given by The output of the TPMS GSC beamformer in (15) includes the transmitted th TPMS signal, residual interference signal from the external electronics or electrical devices, and additive Gaussian noise (AGN) [27, 28].
3.3. Gold Code for TPMS Signal
The signal from other tires in different directions acts as interference when receiving data from a uniform direction. In order to suppress the interference from other tires and to reduce the consumed power, the Gold code with the length of is employed to each tire. A unique Gold code (length ) is given to each tire to transmit data. The transmitted signal is spread by means of the Gold code in SU, and the received signal is despread by means of the same Gold code in CPU located in the center of a vehicle to detect the desired data. The despread signal is given by where and the Gold code for the th tire are defined by respectively.
4. Computational Complexity of Beamformer
In this section, we describe a method of calculating the complexity of the proposed TPMS beamformers to compare and analyze the performance of the computational complexity of each beamformer.
4.1. MVDR Beamformer
The temporal average used to calculate the autocorrelation matrix required for beamforming of MVDR is defined by For each sample , the number of multiplications/divisions and additions/subtractions required in (19) is and , respectively. Because the number of multiplications/divisions and additions/subtractions required for calculating the inverse matrix of a correlation matrix is and , respectively, total complexity of multiplication/division required to use the MVDR beamforming to estimate the TPMS data is roughly Assuming that (19) in the th sample converges, total complexity of addition/subtraction is
4.2. GSC Beamformer
In consideration of complexity calculation for the GSC beamformer, the number of multiplication/division and addition/subtraction to obtain of (11) and of (13) is given by and , respectively, for the sample . Assuming that (9) converges on the th sample, complexity of multiplication/division for estimating TPMS data by using GSC beamforming is approximately described by The complexity of addition/subtraction for estimating the TPMS data by using GSC beamforming is described below. Consider Since MVDR beamformer requires calculating the autocorrelation matrix unlike the GSC beamformer, its computational complexity is much higher than that of the GSC beamformer.
5. Computer Simulations
In this section, the results of computer simulation are described to verify the performances of the proposed beamforming technologies.
5.1. Computer Simulations for Computational Complexity
For computational complexity simulation of two TPMS beamformers, the complexity of multiplication/division and addition/subtraction of each beamformer is considered. The results are compared through complexity simulation of each beamformer for variables , , and . Figures 4 and 5 show complexity comparisons of multiplication/division and addition/subtraction, respectively, depending on the number of samples for convergence, assuming that the length of the Gold code is and the number of antenna elements is . From the figures, we observe that the MVDR beamformer has higher complexity than the GSC beamformer, as increases.
Figures 6 and 7 show complexity comparisons of multiplication/division and addition/subtraction, respectively, depending on the length of Gold code, assuming that and . The length of Gold code considered in this paper is usually much shorter than the number of samples for converging adaptive algorithms, because we need to consider only four signals from four tires and at least four unique gold codes and enough samples are required for converging adaptive weights. In Figures 6 and 7, we assume that and is varied from 1 to 50 to show the extreme case. From two figures, we observe that the GSC beamformer has lower complexity than the MVDR beamformer, as increases. If is greater than 30, the difference of the computational complexities of them should be increased.
5.2. Computer Simulations for Interference Suppression
For the computer simulation, we consider two cases with four and six receiving antennas in the center of the vehicle. The incidence angles of the TPMS transmission signal from each tire to the receiving antennas are assumed 60°, 120°, 240°, and 300°, respectively, and the number of the Gold code is . Another assumption is that three interference signals are received to the receiving antennas at the angles of 87°, 165°, and 268°, respectively.
Figure 8 shows the beam patterns of the MVDR beamformer with four receiving antennas. In Figure 8(a), the MVDR forms two beams to 60° (right front) and 300° (left rear) direction, and it created nulls for three directions of 87°, 165°, and 268°, at the same time. Similarly, we can find two beams for 120° (right front) and 240° (right real) directions and three nulls for 87°, 165°, and 268° in Figure 8(b). Figure 9 shows the beam patterns of the GSC beamformer with four receiving antennas. It is seen that the GSC beam patterns in Figure 9 are very similar to the beam pattern of MVDR. Figures 8 and 9 show concurrent beamforming for the front tire and the rear tire directions, because the beam is simultaneously formed at angles of and in beamformer by means of the array response vector structure with the cosine function given in (2). That is, we need calculating two weight vectors for four tires instead of four weight vectors. Figures 10 and 11 show the beam patterns of MVDR and GSC beamformers, respectively, with six receiving antennas. Beam patterns of Figures 10 and 11 are similar to those of Figures 8 and 9, respectively, except the width of beams and the size of the side lobe. Since Figures 10 and 11 employ more antenna elements than Figures 8 and 9, the width of those beams are narrower and the sizes of those side lobes are smaller than those in Figures 8 and 9.
Figures 12, 13, and 14 show the simulation results for the output SINR of the MVDR and GSC beamformers with four and six antennas and without a beamformer, with respect to SNR for dB, 10 dB, and 20 dB, respectively, where ISR means interference-to-signal ratio. From the figures, we observe that interference signals are not suppressed to result in low output SINR for any beamformer which is not employed. However, the MVDR and the GSC beamformer with four and six antennas hold uniform values in all figures because interference signals are almost perfectly suppressed. We also observe that the performance of the interference suppression using six antennas is better than using four antennas. In the figures, the SINR curves of the MVDR and GSC beamformers are almost identical because both beamformers have very similar interference suppression performance and the range of the input SNR is too wide to compare them. In order to observe their difference, we examined the input SINR (in case of dB) from −0.15 to 0.15 dB for four antennas and from −0.06 to 0.06 dB for six antennas as shown in Figures 15(a) and 15(b), respectively, illustrating that the adaptive GSC output SINR is slightly lower than the MVDR output SINR because weights may not have converged to the optimal solution in these simulations. From results of the simulation, we observe that the GSC TPMS beamformer has similar performance of the interference suppression to the MVDR TPMS beamformer, while it has lower computational complexity than that of MVDR beamformer.
As more vehicle accidents occur, research on auxiliary safety devices are underway across the globe to prevent the accidents. The TPMS is designed to prevent the vehicle accident due to the abnormal tire air pressure in advance and to reduce greenhouse gas discharged from vehicles and fuel consumption. Since TPMS utilizes wireless communication technology, the serious interference occurs from the external electrical and electronic devices using the similar frequency to the TPMS frequency. The switching beamformer with the low computational complexity does not have excellent performance of the interference suppression because it does not create null to the AOA direction of the interference signal. In this paper, we suggested an MVDR beamformer for TPMS, which has excellent performance of interference suppression. Although the MVDR beamformer has excellent performance of the interference suppression, it has very high computational complexity due to the calculation of an autocorrelation matrix. In order to overcome this drawback, we also proposed a GSC beamformer for the TPMS, which has similar performance of interference suppression to that of the MVDR and does not require calculating the autocorrelation matrix to result in the relatively low computational complexity. Through computer simulation results, we verified that the TPMS GSC beamformer has better performance compared with the TPMS MVDR beamformer if the GSC weight is closely converged to optimal weight vector, because interference suppression performance of GSC is comparable to that of MVDR and its computational complexity is lower than that of MVDR. Currently, we are investigating the hybrid TPMS beamformer based on a switching and MVDR beamformers for selecting an efficient algorithm depending on circumstances in order to suppress the interference signals.
This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (no. 2012-0008837). This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (no. 2011-0024811).
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