Abstract
This paper discusses the spacetime coding (STC) problem for RFID MIMO systems. First, a mathematical model for this kind of system is developed from the viewpoint of signal processing, which makes it easy to design the STC schemes. Then two STC schemes, namely Scheme I and Scheme II, are proposed. Simulation results illustrate that the proposed approaches can greatly improve the symbolerror rate (SER) or biterror rate (BER) performance of RFID systems, compared to the non spacetime encoded RFID system. The SER/BER performance for Scheme I and Scheme II is thoroughly compared. It is found that Scheme II with the innate realsymbol constellation yields better SER/BER performance than Scheme I. Some design guidelines for RFIDMIMO systems are pointed out.
Introduction
Radio frequency identification (RFID) is a contactless, usually short distance, wireless data transmission and reception technique for identification of objects. It is believed that RFID can substitute, in the notfar future, the widely used optical barcode technology due to the limitations of the latter in i) the barcode cannot read nonlineofsight (NLOS) tag; ii) each barcode needs personal care to be read; and iii) limited informationcarrying ability of the barcode. Currently, a single antenna is usually used at the reader and tag of RFID in the market. However, RFID research community recently started to pay attention on using multiple antennas at either the reader side or the tag side [1,2]. The reason is that using multiple antennas is an efficient approach to increasing the coverage of RFID, solving the NLOS problem, improving the reliability of data communications between the reader and tag, and thus further extending the informationcarrying ability of RFID. Besides, some advanced technology in multiple transmit and receive antennas (MIMO) can be used to solve the problem of detecting multiple objects simultaneously, see e.g., [3].
There have been several studies about RFIDMIMO. In general, these studies are somehow scattered in different topics. It is difficult to find the logical relationship among these studies. Therefore, the state of the art of the studies will be reviewed in a large degree in a chronological order. The work [4] first showed the idea of using multiple antennas at the reader for both transmission and reception. In [1], the authors first proposed to use multiple antennas at the tag and showed the performance gain by equipping multiple antennas at the reader (for both transmission and reception) and the tag. In [5], the multipath fading for both singleantenna based RFID channel and RFIDMIMO channel was measured and compared. The improvement on the fading depth by using MIMO can be clearly seen from the measured power distribution (see, e.g., Figure Ten therein). In [6], the authors first proposed to apply the Alamouti spacetime coding (STC) technique, which is now popularly used in wireless communication systems, to the RFID systems. The reference [6] presented a closedform expression for the biterror rate (BER) of the RFID system with the nonecoherent frequency shift keying modulation and multiple transmit antennas at the tag and single transmit/receive antenna at the reader, where the double Rayleigh fading is assumed at the forward and backward links. In [7], the interrogation range of ultrahighfrequencyband (UHFband) RFID with multiple transmit/receive antennas at the reader and single antenna at the tag was analyzed, where the forward and backward channels are assumed to take the Nakagamimdistribution. In [3], the blind source separation technique in antenna array was used to solve the multiple tag identification problem, where the reader is equipped with multiple antennas. The work [8] applied the maximal ratio combining technique to the RFID receiver, where the channel of the whole chain, including forward link, backscattering coefficient, and backward link, was estimated and used as the weighting coefficient for the combining branches. In [9], a prototype for the RFIDMIMO in the UHFband was reported. In [10], both MIMObased zeroforcing and minimummeansquareerror receivers were used to deal with the multipletag identification problem, where the channel of the whole chain was estimated, similar to the approach in [8]. It is reported in [11] that four antennas are fabricated in a given fixed surface at the reader. The measurement results showed that an increase of 83% in area gave a 300% increase in available power to turn on a given tag load and the operational distance of the powered device is increased to 100 cm by the fourantenna setup from roughly 40 cm for the singleantenna setup. The result in [11] suggests that the MIMO technique can be very promising to the RFID technology.
In the aforementioned reports, the Alamouti STC technique has been shown to be able to extend to RFIDMIMO systems. However, it can only apply to the case where the tag has two antennas. Since implementing four antennas at the tag have been shown to be possible in experiments, it is necessary to investigate the possibility of applying other STC techniques to RFIDMIMO systems. In this paper, we will study how to apply the real orthogonal design (ROD) technique, proposed by Tarokh et al. in [12], to RFIDMIMO systems. This technique is suitable for the case where the tag is equipped up to eight antennas, which should be sufficient for the RFID technology in the near future.
The paper is organized as follows. A modified MIMORFID channel model will be developed in Section “Channel Modeling of RFID MIMO Wireless Systems”. The ROD in [12] and the companion of the ROD (CROD) proposed in [13] are briefly introduced in Section “A SpaceTime Coding Scheme for RFID MIMO Systems”. Two spacetime decoding approaches for RFID MIMO systems will be discussed in Section “Two SpaceTime Decoding Approaches for RFID MIMO Systems”. Section “Simulation Results” presents the simulation results and discussions, and Section “Conclusions” concludes the paper.
Channel Modeling of RFID MIMO Wireless Systems
In this paper our discussion is confined only on narrowband RFID systems. The block diagram of the RFID MIMO system is illustrated in Figure 1, where both the reader and tag are equipped with multiple antennas.
Figure 1. A block diagram of the RFID MIMO system.
In terms of equation (1) of [1], the narrowband RFID MIMO wireless channel can be expressed as
where the reader and tag are equipped with N_{rd} and N_{tag} antennas, respectively, x (an N_{rd} × 1 vector) is the transmitted signal at the reader, y (an N_{rd} × 1 vector) is the received signal at the reader, n is the receiver noise, H^{f} (an N_{tag} × N_{rd} matrix) is the channel matrix from the reader to the tag, H^{b} (an N_{rd}×N_{tag} matrix) is the channel matrix from the tag to the reader, and Sis the backscattering matrix, which is also called signaling matrix. It is assumed that the N_{rd} antennas at the reader are used for both reception and transmission. This assumption is just for brevity of the notation. It is straightforward to extend the approach presented in this paper to the case where the reader has different numbers of antennas for reception and transmission. The channels H^{f} and H^{b} are assumed to be complex Gaussian distributed, H^{f} and H^{b} are mutually independent, and all the entries of either H^{f} or H^{b} are independent of each other. It is also assumed that Re(H^{f}), Im(H^{f}), Re(H^{b}), Im(H^{b}) are mutually independent and of the same distribution.
In most general case where the modulated backscatter signals at the tag are transferred between the antennas, the signaling matrix Sis a full matrix [1]. However no application of the full signalling matrix has been identified up to now [1]. Therefore, we will consider the situation where the RF tag antennas modulate backscatter with different signals and no signals are transferred between the antennas. In this case, the signaling matrix is a diagonal matrix [1]
where Γ_{i}(t) is the backscattering coefficient of ith antenna at the tag. The ith tag identity (ID) is contained in the coefficient Γ_{i}(t).
Note that in the RFID system, the transmitted signal xis mainly used to carry the transmit power, while the information data (i.e., tag ID) is carried out by S. Therefore, the central issue for the RFID is to decode Γ_{1}, …, from the received signal. Next we transform equation (1) to the conventional form in signal processing. Let us define
Then equation (1) can be rewritten as
where
Equation (3) converts the original system model (1) to the conventional form in signal processing: the signal to be estimated or decoded is packed in a vector, whose entries are independent of each other.
A SpaceTime Coding Scheme for RFID MIMO Systems
Let us first review the real orthogonal design proposed by Tarokh et al. in [12].
Definition 1
[12] A real orthogonal design of size m is an m × k matrix with entries 0, , , …, such that , where D is a diagonal matrix with diagonal entries being , i = 1,2,…,m, and the coefficients l_{i1}, l_{i2}, …, l_{ik}are strictly positive integers.
In some cases, we need to explicitly specify the arguments of . In these cases, the ROD will be denoted as ( , …, , where , …, are the arguments of .
The construction of general RODs can be found in [12]. For completeness, the RODs for the cases of m = 2,3,4, denoted as , , respectively, are listed as follows:
For the construction of , readers are referred to [12].
To formulate the decoding algorithm for the ROD, let us define the companion of the ROD as follows.
Definition 2
A companion of a real orthogonal design , denoted as , is a matrix satisfying the following equation
For the RODs as shown in equations (4)(6), their CRODs are
For a given ROD, the calculation of its CROD is given in [13].
For the CRODs as defined in equations (7)(9), it can be easily shown that the following equality
holds true, where the superscript ^{T} stands for the transpose (without conjugate!) of a matrix or vector. As can be seen from the discussion in Section “Simulation Results”, one can remove the intersymbol interference (ISI) by using the above property of CROD, but the diversity gain thus obtained from the multiple channels is limited when the channel is complex instead of real.
To find the decoding scheme, let us consider the property of , where the superscript ^{H} stands for the conjugate transpose of a matrix or vector. We have
where the entry marked with ★ means that its value can be inferred from the value of its corresponding symmetric entry. It can be checked that the structural property as shown in equations (11)(13) also holds true for higher dimensional CRODs.
Using RODs and the corresponding CRODs, a general spacetime encoding scheme and two decoding approaches for RFIDMIMO systems can be developed as follows.
Consider the equivalent RFIDMIMO channel (3). Denote by T_{f} a symbol period. Suppose that the channels of both forward and backward links do not change with time during a coding block period KT_{f}. The transmit signal x at the reader is also fixed during one coding block period KT_{f}. Therefore, the equivalent composite channel will not change with time when we only consider the signal processing for one coding block. Let us define
Let (of dimension N_{tag} × K) be a ROD in variables , , …, , where , , …, are the symbols to be transmitted at the N_{tag} transmit antennas in one STC frame. Define
where w(t)is the baseband waveform of the transmit signal at the tag. The transmitted signal across the N_{tag} transmit antennas at the tag can be expressed as
where E_{0} is the total power used for the transmission of one symbol per time slot. The scaling coefficient is to normalize the overall energy consumption per time slot at the tag side to be E_{0} no matter how many antennas are deployed at the tag.
Two SpaceTime Decoding Approaches for RFID MIMO Systems
The received signal after sampling can be expressed as
where is the receiver noise (a matrix) at the corresponding time instant. Notice that is of dimension N_{rd} × K, since one frame of the transmitted signal contains the pulses of K time slots.
Denote by [M]_{j} the jth row of a matrix M. Let us consider the jth row of the matrix which is the received signal at the jth antenna of the reader for the time instants 1, …, K respectively. Let
Since the transmitted signal is spacetime coded, the entries in [y]_{j} should be related with each other somehow. Righthand multiplying both sides of equation (15) with the matrix , , we have
From equation (17) we can see that the transmitted symbols are decoupled from each other in the processed signal z_{j} through the processing algorithm (16). However, it is not efficient to decode the symbols directly from (17) since the complex channel makes the phase of randomly change over [0, 2Π]. Define
Multiplying both sides of (17) by will remove the phase ambiguity of the equivalent channel. This gives
where
To collect all the diversities provided by multiple receive antennas at the reader, we sum up all ’s. This gives
The symbols can be easily decoded from equation (20).
For the convenience of exposition in next section, we call the encoding and decoding scheme discussed above as Scheme I.
Another decoding scheme (hereafter it is referred to as Scheme II) is to exploit the property of the matrix , as shown in equations (11)(13). Righthand multiplying both sides of equation (15) with the matrix , we have
From equations (21) and (11)(13) we can see that, if the symbols are real, the symbol to be decoded, say for some k, and the ISI caused by other symbols, are projected into different subspaces in the complex plane: the desired signal is in the real subspace, while the ISI is in the imaginary subspace. Therefore, a very simple decoding method for this case works in the following way: From kth entry of u_{j} (denoted as u_{j,k}), get the real part of u_{j,k} [denoted as Re (u_{j,k})], and then decode in terms of Re (u_{j,k}).
The diversities provided by multiple receive antennas at the reader can be collected in the following way:
Simulation Results
In this section, we investigate the symbolerror rate (SER) or biterror rate (BER) performance of both Schemes I and II. In Scheme I, the quadrature phase shift keying (QPSK) modulation is used and the constellation of transmitted symbols is . In Scheme II, the binary phase shift keying (BPSK) modulation is used and the constellation of transmitted symbols is ±1. Therefore, the SER in Scheme II reduces to BER. At the transmitter of the reader, the signal x takes the form of a random vector whose entry is uniformly distributed among . It is seen that x is of unity power. Each entry of the channels H^{f} and H^{b} is of mean zero and variance unity.
In the figures to be shown, the signaltonoise power ratio (SNR) is defined as the , where is the variance of the each entry of noise vector .
Figure 2 shows the SER of Scheme I for different cases: Figures 2(a) and (b) illustrate how the SER changes with N_{tag} for fixed N_{rd}, i.e., when N_{rd} = 1 and 4 respectively; while Figures 2(c) and (d) demonstrate how the SER changes with N_{rd} for fixed N_{tag}, i.e., when N_{tag} = 1 and 4 respectively.
Figure 2. SER of RFID MIMO systems for Scheme I with QPSK modulation.(a)SER vs N_{tag} for N_{rd} = 1(b)SER vs N_{tag} for N_{rd} = 4(c)SER vs N_{rd} for N_{tag} = 1(d) SER vs N_{rd} for N_{tag} = 4.
Figure 3 shows the BER of Scheme II for different cases: Figures 3(a) and (b) illustrate how the BER changes with N_{tag} for fixed N_{rd}, i.e., when N_{rd} = 1 and 4 respectively; while Figures 3(c) and (d) demonstrate how the BER changes with N_{rd} for fixed N_{tag}, i.e., when N_{tag} = 1 and 4 respectively.
Figure 3. BER of RFID MIMO systems for Scheme II with BPSK modulation.(a)BER vs N_{tag} for N_{rd} = 1(b)BER vs N_{tag} for N_{rd} = 4(c)BER vs N_{rd} for N_{tag} = 1(d)BER vs N_{rd} for N_{tag} = 4.
From Figures 2 and 3 the following phenomena can be observed:
Claim 1
Comparing the dashed curves, which corresponds to the performance of the non spacetime encoded RFID system with single antenna at both reader and tag sides, and the solid curves in Figures 2(b), (d), and Figures 3(b), (d), we see that deploying multiple antennas at both reader and tag can greatly improve the SER/BER performance of RFID systems.
Claim 2
When N_{rd} is fixed to be one, increasing N_{tag }considerably decreases the BER of the system in Scheme II, but only marginally decreases the SER of the system in Scheme I. For example, when SNR=18 dB and N_{rd} = 1, the BER of Scheme II decreases from 1.6 × 10^{−2} at N_{tag} = 1 to 2.0 × 10^{−3} at N_{tag} = 2 and 8.8 × 10^{−5} at N_{tag} = 4, respectively. For the same SNR and N_{rd}, the SER of Scheme I decreases from 4.7 × 10^{−2} at N_{tag} = 1 to 2.9 × 10^{−2} at N_{tag} = 2 and 3.0 × 10^{−2} at N_{tag} = 4 respectively. The reason for this phenomenon is that the channel diversity provided by N_{tag} antennas at the tag side is harvested by Scheme II [as seen from equations (11)(13)], but not harvested by Scheme I [as seen from equation (17)].
Claim 3
When N_{tag} is fixed to be one, increasing N_{rd }noticeably and monotonically decreases the SER or BER of the system. This phenomenon can be clearly seen from Figure 2(c) and Figure 3(c). The reason is that only the array gain is provided by the system when N_{tag} = 1 and it is indeed collected by both Scheme I and Scheme II. Due to the double Rayleigh fading channel, the system performance cannot be improved conspicuously by only exploiting this array gain.
Claim 4
When N_{rd} (or N_{tag}) is fixed and greater than one, increasing N_{tag} (or N_{rd}) greatly decreases the SER or BER of the system, especially for Scheme II. For example, when SNR=18 dB and N_{tag} = 4, the SER of Scheme I decreases from 3.0 × 10^{−2} at N_{rd} = 1 to 2.7 × 10^{−3} at N_{rd} = 2 and 7.5 × 10^{−5} at N_{rd} = 4, respectively. For the same SNR and N_{tag}, the BER of Scheme II decreases from 8.8 × 10^{−5} at N_{rd} = 1 to 1.2 × 10^{−6} at N_{rd} = 2 and 2.4 × 10^{−8} at N_{tag} = 4 respectively. To achieve the BER=8.8 × 10^{−5} for the case of Scheme II and N_{tag} = 4, the SNR gain is about 7.5 dB and 10 dB, respectively, by deploying N_{rd} = 2 and N_{rd} = 4 antennas at the reader, compared to the singleantenna setup at the reader. On the other side, to achieve the BER=1.3 × 10^{−3} for the case of Scheme II and N_{rd} = 4, the SNR gain is about 9 dB and 13.5 dB, respectively, by deploying N_{tag} = 2 and N_{tag} = 4 antennas at the tag, compared to the singleantenna setup at the tag. This is dramatic improvement for the system performance.
Claim 5
Scheme II yields much better SER performance than Scheme I. There are two reasons. The first reason, which is obvious, is that different symbol constellations are used in Schemes I and II. In the above simulations, one symbol in Scheme I actually carries two bit information, while one symbol in Scheme II carries only one bit information. The second reason, which is somewhat subtle to see, is that the diversity gain harvested by Scheme I is lower than that harvested by Scheme II, even though Scheme II throw away the signal in another half signal space. This observation can be seen by comparing equations (11)(13) and (22) (for Scheme II) and equations (17), (18) and (20) (for Scheme I). For Scheme I, it is seen from (17) and (18) that the N_{tag} independent channels are not coherently summed. In (20), the N_{rd} independent summedchannels are further summed. Thus Scheme I yields a diversity order of N_{rd} and the systeminherited diversity order N_{tag} is sacrificed. For Scheme II, it is seen from (11)(13) that the N_{tag} independent channels are first coherently summed, yielding a diversity order of N_{tag}. From (22), the N_{rd} independent summedchannels are further summed, yielding a diversity order of N_{rd}. Thus a total diversity order of N_{rd} × N_{tag} is obtained in Scheme II.
Claim 6
Comparing Figure 2 and Figure 3, we can conclude that it is better to deploy as many antennas as possible at the reader. At least the number of antennas at the reader side should be not less than the number of antennas at the tag side. In this way, the full channel diversity generated by multiple antennas at the tag can be maximally exploited.
It may be argued that it is not fair to compare the SER performance of Scheme I and Scheme II, since the former uses QPSK modulation, while the latter uses BPSK modulation. To make the comparison complete, the BER performance of Scheme I with BPSK modulation is shown in Figure 4 for the corresponding cases. Figure 2, Figure 4 and Figure 3 show that the BER performance of Scheme I is much worse than that of Scheme II, even though the BER of Scheme I with BPSK modulation is lower than the SER of Scheme I with QPSK modulation for the same configuration of antenna numbers at the reader and tag. By comparing Figure 4 and Figure 3 we can see that Claims 16 obtained based on the comparison between Figure 2 and Figure 3 also holds true qualitatively.
Figure 4. BER of RFID MIMO systems for Scheme I with BPSK modulation.(a)BER vs N_{tag} for N_{rd} = 1(b) BER vs N_{tag} for N_{rd} = 4(c) BER vs N_{rd} for N_{tag} = 1(d) BER vs N_{rd} for N_{tag} = 4.
From the above phenomena, the following conclusions can be drawn: if the required data rate is not high, it is better to use realsymbol constellation for the transmitted symbols at the tag and correspondingly to use Scheme II decoding policy at the reader receiver; by keeping the cost of the system under constraint, it is better to deploy multiple tag antennas and reader antennas, and the number of reader antennas should be at least equal to the number of tag antennas.
It is interesting to compare the ROD based STC and Alamouti STC. Figure 5 shows the comparison. It can be seen that Scheme II and Alamouti STC yield the same BER performance, both are better than Scheme I. This is due to the fact that both Scheme II and Alamouti STC collect all the available channel diversities, while Scheme I does not.
Figure 5. A comparison among Scheme I, Scheme II and the Alamouti STC. For the curves marked with “Scheme I”, “Scheme II” and “Alamouti”, N_{tag} = 2 and N_{rd} = 1.
Finally, let us compare the complexity of Scheme I and Scheme II. Both Scheme I and Scheme II perform the same processing, as shown in equations (4)(6), for the transmitted symbols at the tag. As seen from (4)(6), the symbol processing at the tag is quite simple: only the sign of the symbols to be transmitted needs to be changed at some time slots for some antennas. For the processing of a block of spacetime decoding at the reader, Scheme I needs N_{rd}(K^{2} + K + N_{tag}) complex multiplications and N_{rd}K(K − 1) + (N_{rd} − 1)K + N_{rd}(N_{tag}−1) = N_{rd}(K^{2} + N_{tag} − 1) − K complex additions, and Scheme II needs N_{rd}K^{2} complex multiplications, N_{rd}K(K − 1) complex additions, and (N_{rd} − 1)K real additions. Therefore, the computational burden of Scheme II is a little less than that of Scheme I. With regard to the hardware cost of the proposed STC technique, the main increase in the cost arises from the deployment of multiple antennas. The cost increase for the involved signal processing unit is negligible at either tags or readers, since the spacetime encoding is very simple, which can be easily dealt with by the embedded chip at tags, and the required computational burden for the spacetime decoding at readers is also negligible compared to the relatively strong computation power of readers.
Conclusions
In this paper, we have discussed the spacetime encoding and decoding problem for RFID MIMO systems. First, a mathematical model for this kind of system is developed from the viewpoint of signal processing, which makes it easy to design the STC schemes. Two STC schemes, namely Scheme I and Scheme II, are proposed. Simulation results illustrate that the proposed approaches can greatly improve the SER/BER performance of RFID systems, compared to non spacetime encoded RFID systems. Besides, the SER/BER performance for Scheme I and Scheme II is thoroughly compared and it is found that Scheme II with the innate realsymbol constellation yields better SER/BER performance than Scheme I.
As is commonly assumed in the STC technique, the channel state information (CSI) is required to be available at the receiver side of the reader to adopt the technology of Scheme I and Scheme II. The channel estimation problem for RFID systems has been discussed in [8,10], where a method for estimating the channel of the whole chain, including forward link, backscattering coefficient, and backward link, is presented. However, to estimate the forward and backford channels H^{f} and H^{b} separately remains an open issue. On the other hand, if the CSI is also available at the transmitter side of the reader, we can combine the design for the reader transmit signal and STC for the tag to further improve the system performance. For the first step towards the optimal transmit signal design at the reader side, readers are referred to the reference [14].
Competing interests
The authors declare that they have no competing interests.
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