A smart collision recovery receiver for RFIDs
- Jelena Kaitovic^{1}Email author,
- Robert Langwieser^{1} and
- Markus Rupp^{1}
https://doi.org/10.1186/1687-3963-2013-7
© Kaitovic et al.; licensee Springer. 2013
Received: 14 November 2012
Accepted: 21 March 2013
Published: 30 April 2013
Abstract
In this work, we focus on framed slotted Aloha (FSA) and passive ultra high-frequency radio frequency identification multi-antenna systems with physical layer collision recovery. We modify the tags slightly by adding a so-called ‘postpreamble’ that facilitates channel estimation. Furthermore, we investigate the throughput performance of advanced receiver structures in collision scenarios. More specifically, we analyse the throughput of FSA systems with up to four receive antennas that can recover from a collision of up to eight tags on the physical layer and acknowledge all tags involved in that collision. Due to the higher collision recovery capabilities, the frame sizes can be significantly reduced, and thus, the throughput can be increased. We also derive analytically optimal frame sizes, given that a certain number of collisions can be resolved. We further study the constraints to the throughput due to the structure of our receiver and channel estimation for different collision scenarios. Furthermore, we propose a novel collision recovery method with two phases: first, a successive interference cancellation and, second, a projection of the constellation into the orthogonal subspace of the interference. Additionally, the inventory time, i.e. the number of slots necessary to successfully decode all tags in the reader range, is calculated and compared for different receiver types. A validation of our theoretical predictions is achieved by means of simulations. We show that by our proposed methods, we can realistically achieve more than ten times higher throughput or, equivalently, a reduction of the inventory time by more than 90%.
1 Introduction
Usually, several radio frequency identification (RFID) tags operate within a coverage area of an RFID reader. For the efficient scheduling of tag transmissions, framed slotted Aloha (FSA) or binary tree protocols are used on the medium access control layer. Our focus is on passive ultra high-frequency (UHF) RFID systems and FSA as defined in the EPCglobal standard [1]. If multiple tags respond simultaneously, a collision at the air interface occurs. The standard collision detection mechanism regards this as a destructive event and discards the information. Thus, only slots in which one tag is active can be decoded successfully [2]. This determines the maximal throughput per slot for an FSA system. The maximum throughput value of 0.368 is achieved when the inventory frame size F is equal to the tag population size N.
1.1 Related work
To overcome such limitations, different research groups are working on collision arbitration protocols and collision recovery procedures. Knerr et al. in [3] formulated a maximum likelihood estimator to yield the estimated number of tags on a slot-wise basis. Their method can be applied for an immediate update of the frame size, during the frame duration, according to the probability level of the current slot-by-slot estimate. Yu et al. in [4] proposed an anti-collision algorithm based on smart antenna technology, which leads to the use of the space division multiple access in RFID systems. They divided the reader coverage area into several subspaces and used an FSA or a binary tree search in each sector, but they did not recover from collisions. If readers with collision recovery (CR) features are available, slots with colliding tags can also be decoded successfully, and the throughput increases further. Knowing the maximum number of collisions that can be resolved by a certain receiver architecture, the frames can be reduced which results in further throughput enhancement and smaller inventory times. A practically working CR on a physical layer with a single antenna reader receiver with two colliding tags in one slot is demonstrated in [5]. With such reader, Angerer et al. obtained an expected throughput increase of approximately 60%. In [6, 7], the authors derived a single antenna detection scheme for the simultaneous transmission of two tags using a memory-assisted detection of collided FM0 signals. Furthermore, they calculated an inventory time reduction of 8% to 17% when a two-tag detection and collision recovery is utilized. In [8], De Donno et al. showed, by experiments, that performances of conventional RFID systems can be considerably enhanced by using collision recovery in case of two colliding tags. The authors achieved an inventory time reduction of 26% in actual measurements taken with a software-defined RFID reader and off-the-shelf programmable tags. In [9], Kim et al. presented an improved binary tree collision arbitration protocol that decreases the number of retransmissions and reduces the identification delay by exploiting multiple antennas at the reader. Theoretical calculations of the FSA system throughput for the reader with physical layer collision recovery were performed in [10], and a significant increase is shown. Additionally, the authors proved a single antenna receiver with a channel estimation procedure for recovering from a two-tag collision to work in practice. Moreover, they have shown that multiple antenna receivers with perfect channel knowledge are capable of recovering from a collision of R ≤ M tags. Here, M denotes the so-called collision recovery factor, that is the maximum number of colliding tags a reader can resolve under best circumstances. It is directly related to the number of receive antennas N_{RA}. In [10], it was conjectured that M = N_{RA}. In [11], the single antenna receiver was further extended, and a 2.6-fold throughput increase compared to a conventional reader was achieved with four receiving antennas. Such reader is capable of recovering from a collision of R ≤ M = 2N_{RA} tags in a slot and to acknowledge one out of them. Such perfect CR scheme comes with a caveat, though: at least a moderate channel estimate for each tag is required. Since a tag signal, modelled according to EPCglobal, is not suitable for channel estimation in collision scenarios, in [12], we have proposed a modified tag response that can be used for channel estimation. This modification requires minor changes in the standard by adding a so-called ‘postpreamble’ sequence. A collision recovery from a scenario in which all tags involved in the collision have different, unique ‘postpreambles’ is considered, and excellent channel estimation results are obtained. Moreover, in [12], we have identified a potential throughput increase of more than five times in the case of a reader that can recover from a collision of up to eight tags in one slot and acknowledge two of them. Fyhn et al. showed that channel fading, the difference in delay and the tag frequency dispersion can be used for easier separation of colliding signals in a multipacket receiver in [13]. In [14], Ricciato et al. achieved a 20% to 25% gain in throughput by applying inter-frame successive interference cancellation (ISIC) with respect to traditional intra-frame SIC. Myung et al. elaborated frameless binary splitting methods in [15]. Their results show that adaptive binary splitting reduces delay and tag communication overhead for the tag reading process. In [16], a theoretical study on collision recovery binary tree algorithm is proposed, and a closed form for calculating system efficiency is derived.
1.2 Contribution
This work is focused on the analysis of the theoretical throughput of an FSA system and its associated constraints. In this paper, we investigate the influence of a tag signal modification by adding postpreambles, we analyse the receiver structure and CR properties and compare obtained results to their theoretical throughput. The collision recovery is performed with receivers that perform channel estimation using a small (C = 8) set of postpreambles. Since the distribution of the postpreamble in the colliding tags is random, different collision scenarios need to be considered. In this contribution, we deviate from some optimal prior assumptions and study the performance on more feasible constraints, including a fixed set of postpreambles, additive noise impacting the channel estimation and collision recovery as well as collision detection algorithms with limited quality. We compare our results with the performance of an EPC protocol compliant reader (so-called conventional reader).
The remainder of the paper is organized as follows: Section 2 provides a brief introduction into the mathematical modelling of RFID transmissions and provides a basis for our advanced algorithms. The theoretical throughput of FSA systems and its associated constraints are analysed in Section 3. In Section 4, we introduce a recovery procedure from a collision in which two tags use the same postpreamble and explain our two-step recovery approach. Section 5 provides a performance analysis by means of simulations where we validate our previous predictions, and the last section concludes the paper.
2 RFID multi-antenna reader
where r_{c,i}(t) is the complex-valued received signal, n_{ i }(t) is the noise at the i th antenna, and a_{ j }(t) denotes the modulation signal of tag j. Here, we assume that the transmit and receive parts of a reader are perfectly isolated (there is no carrier leakage). Since all signals, except the tag modulation signal, are complex values, we can double the number of equations by splitting Equation (1) in real $\mathfrak{\Re}\{\xb7\}$ and imaginary part $\mathfrak{T}\{\xb7\}$. This allows the recovery from a collision of R ≤ M tags, where M = 2N_{RA} denotes the collision recovery factor.
Most commonly used symbols and parameters
Variable | Description |
---|---|
N _{RA} | Number of receiving antennas |
M = 2N_{RA} | Collision recovery factor / number of |
tags the reader is capable of resolving | |
J | Maximum number of tags |
the reader acknowledges | |
J _{ C } | Maximum number of tags with |
colour C the reader acknowledges | |
R∈[0..N] | Number of tags active in the same slot |
${R}_{C}\in \left[0\u2025\frac{N}{C}\right]$ | Number of tags per slot |
with colour C | |
j∈[1..R] | Tag index per slot for R>0 |
i∈[1..N_{RA}] | Receive antenna index |
r_{ c }(t) | Received signal vector $\in {\mathbb{C}}^{{N}_{\text{RA}}\times 1}$ |
H _{ c } | Channel matrix $\in {\mathbb{C}}^{{N}_{\text{RA}}\times R}$ |
a(t) | Modulation vector $\in {\mathbb{R}}^{R\times 1}$ |
N | Number of tags within the reader range |
F | Number of slots in a frame |
r_{ i }[k] | Sample of the received signal from i th antenna |
taken within duration of the first preamble bit t_{1bit} | |
s _{ l } | Collision scenario l = 1,2,…,S(R) |
Set of postpreambles [[12]], with permission of the IEEE
Sequence | Postpreamble |
---|---|
p _{1} | 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 |
p _{18} | 1 0 1 0 1 0 1 1 0 1 0 1 0 1 0 0 |
p _{69} | 1 0 1 1 0 1 0 1 0 1 0 0 1 0 1 0 |
p _{86} | 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 0 |
p _{171} | 1 1 0 1 0 0 1 0 1 1 0 1 0 0 1 0 |
p _{188} | 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 0 |
p _{239} | 1 1 0 0 1 1 0 1 0 0 1 1 0 0 1 0 |
p _{256} | 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 |
Here, ${\mathbf{r}}^{\text{pp}}\left(t\right)\in \mathbb{C}$ denotes the part of the received signal containing the postpreamble.
3 FSA with CR
FSA is an interrogation scheme, and it is used for scheduling the transmission of tags. Our focus is on FSA as defined in the second-generation EPCglobal standard for passive UHF RFID [1]. Through the Query command, the reader announces the beginning of the frame and the frame duration (number of slots in a frame). Tags randomly choose slots for transmission. For a conventional reader without CR, only slots without a collision can be decoded successfully, and it is well known that the maximal throughput is achieved when the frame size F is the same as the tag population size N. If more than one tag is active in one slot, a collision at the air interface occurs and the entire slot is discarded. With CR capable readers, and some changes in the protocol, it is possible to use the information from slots with a collision to increase the throughput together with shorter frame sizes.
In order to evaluate the performance of FSA systems with CR, theoretical bounds are calculated in the following. These bounds are determined by the receiver structure, the tag signal modification and the channel estimation. Furthermore, we denote the number of simultaneously acknowledged tags as J. The maximum number of J is given by M, but J can also be limited by the standard (the current standard only allows for J = 1) and/or the capabilities of the receiver technique. By introducing such a variable J, we can study beforehand the expected throughput improvements and later compare with the true achievable values of J based on our receiver capabilities.
3.1 Throughput constrained with receiver structure
Maximal theoretical throughput per slot constrained with receiver structure [[21]], with permission of the IEEE
System | F_{opt}/N | Tps | R _{Tps} |
---|---|---|---|
M = 1 J = 1 | 1 | 0.368 | 1.000 |
M = 2 J = 2 | 0.618 | 0.841 | 2.285 |
M = 4 J = 4 | 0.339 | 1.944 | 5.283 |
M = 8 J = 8 | 0.173 | 4.479 | 12.171 |
By assuming an optimal receiver structure and a tag population of N = 1,000, the maximal theoretical throughput per slot is 4.479, achieved for a frame that contains only 173 slots. However, the values obtained here are in the case of perfect channel knowledge, which is much higher than we can expect to achieve with a feasible receiver. In order to recover from a collision when applying an MMSE receiver (Equation (2)), we need to estimate the channel. For channel estimation, we introduce additional postpreambles. In the following paragraph, we investigate the influence of the tag signal modification to the system throughput.
3.2 Throughput constrained with postpreambles
where R_{ C }denotes the number of tags per slot with identical colour.
Maximal theoretical throughput per slot constrained with postpreambles
System | F_{opt}/N | Tps | R _{Tps} | R _{Tpf} |
---|---|---|---|---|
C = 1 J = 1 | 1 | 0.368 | 1.000 | 1.000 |
C = 1 J = 2 | 0.618 | 0.841 | 2.285 | 3.697 |
C = 8 J_{ C } = 1 | 0.125 | 2.955 | 8.030 | 47.096 |
C = 8 J_{ C } = 2 | 0.077 | 6.757 | 18.361 | 174.824 |
Here, we take into account shorter frames (F_{opt}) and the stretching of the frames by an additional postpreamble (G) that is required for C > 1 colour. The signal of a tag consists of a preamble (6 bits), a postpreamble (8 bits) and an RN16 (16 bit), and each bit is encoded with FM0. Thus, the frame stretching factor is $G=\frac{6+8+16}{6+16}=1.364$. In spite of the small loss due to G, the relative improvement R_{Tpf} can climb up to 174.8. However, such considerations are too optimistic as the following example shows. For N_{RA} receive antennas, only R ≤ M = 2N_{RA} tags can be resolved. Consider, for example, a scenario in which each of the C = 8 colours appears twice. Then, there are in total R = C·R_{ C } = 16 tags in this slot, but with N_{RA} = 4, only eight tags can be resolved. Practically, Equation (5) needs at least to be constrained by C·J_{ C }≤M. Furthermore, the channel cannot be estimated in all collision scenarios. We thus derive tighter bounds in the following.
3.3 Expected throughput for covered scenarios
Collision scenarios for up to eight colliding tags per slot
Scenarios | R = 1 | R = 2 | R = 3 | R = 4 | R = 5 | R = 6 | R = 7 | R = 8 |
---|---|---|---|---|---|---|---|---|
Unique | P_{s 1} = 1 | P_{s 1} = 0.875 | P_{s 1} = 0.656 | P_{s 1} = 0.410 | P_{s 1} = 0.205 | P_{s 1} = 0.077 | P_{s 1} = 0.019 | P_{s 1} = 0.002 |
1 | 1 + 1 | 1 + 1 + 1 | 1 + 1 + 1 + 1 | 1 + 1 + 1 + 1 | 1 + 1 + 1 + 1 | 1 + 1 + 1 + 1 | 1 + 1 + 1 + 1 | |
1 | 1 + 1 | 1 + 1 + 1 | 1 + 1 + 1 + 1 | |||||
Mixed scenario | P_{s 2} = 0.125 | P_{s 2} = 0.328 | P_{s 2} = 0.492 | P_{s 2} = 0.513 | P_{s 2} = 0.385 | P_{s 2} = 0.202 | P_{s 2} = 0.067 | |
2 | 2 + 1 | 2 + 1 + 1 | 2 + 1 + 1 + 1 | 2 + 1 + 1 | 2 + 1 + 1 | 2 + 1 + 1 | ||
1 + 1 | 1 + 1 + 1 | 1 + 1 + 1 + 1 | ||||||
P_{s 3} = 0.016 | P_{s 3} = 0.041 | P_{s 3} = 0.154 | P_{s 3} = 0.288 | P_{s 3} = 0.337 | P_{s 3} = 0.252 | |||
3 | 2+2 | 2+2+1 | 2+2+1 | 2+2+1 | 2+2+1 | |||
1 | 1 + 1 | 1 + 1 + 1 | ||||||
P_{s 4} = 0.055 | P_{s 4} = 0.103 | P_{s 4} = 0.019 | P_{s 4} = 0.084 | P_{s 4} = 0.168 | ||||
3+1 | 3+1 + 1 | 2 + 2 + 2 | 2 + 2 + 2 | 2 + 2 + 2 | ||||
1 | 1 + 1 | |||||||
P_{s 5} = 0.002 | P_{s 5} = 0.017 | P_{s 5} = 0.128 | P_{s 5} = 0.112 | P_{s 5} = 0.011 | ||||
4 | 3 + 2 | 3 + 1 + 1 | 3 + 1 + 1 | 2 + 2 + 2 | ||||
1 | 1 + 1 | 2 | ||||||
P_{s 6} = 0.009 | P_{s 6} = 0.077 | P_{s 6} = 0.168 | P_{s 6} = 0.067 | |||||
4 + 1 | 3 + 2 + 1 | 3 + 2 + 1 | 3 + 1 + 1 + 1 | |||||
1 | 1 + 1 | |||||||
P_{s 7} = 2·10^{-4} | P_{s 7} = 0.002 | P_{s 7} = 0.017 | P_{s 7} = 0.224 | |||||
5 | 3 + 3 | 3 + 2 + 2 | 3 + 2 + 1 | |||||
1 + 1 | ||||||||
P_{s 8} = 0.019 | P_{s 8} = 0.112 | P_{s 8} = 0.084 | ||||||
4 + 1 + 1 | 3 + 3 + 1 | 3 + 2+ 2 | ||||||
1 | ||||||||
P_{s 9} = 0.003 | P_{s 9} = 0.028 | P_{s 9} = 0.028 | ||||||
4 + 2 | 4 + 1 + 1 | 3 + 3 + 1 | ||||||
1 | 1 | |||||||
P_{s 10} = 0.001 | P_{s 10} = 0.017 | P_{s 10} = 0.006 | ||||||
5 + 1 | 4 + 2 + 1 | 3 + 3 + 2 | ||||||
P_{s 11} = 3·10^{-5} | P_{s 11} = 0.001 | P_{s 11} = 0.028 | ||||||
6 | 4 + 3 | 4 + 1 + 1 | ||||||
1 + 1 | ||||||||
P_{s 12} = 0.003 | P_{s 12} = 0.042 | |||||||
5 + 1 + 1 | 4 + 2 + 1 | |||||||
1 | ||||||||
P_{s 13} = 6·10^{-4} | P_{s 13} = 0.004 | |||||||
5 + 2 | 4 + 2 + 2 | |||||||
P_{s 14} = 2·10^{-4} | P_{s 14} = 0.006 | |||||||
6 + 1 | 4 + 3 + 1 | |||||||
P_{s 15} = 4·10^{-6} | P_{s 15} = 1·10^{-4} | |||||||
7 | 4 + 4 | |||||||
P_{s 16} = 0.006 | ||||||||
5 + 1 + 1 + 1 | ||||||||
P_{s 17} = 0.003 | ||||||||
5 + 2 + 1 | ||||||||
P_{s 18} = 2·10^{-4} | ||||||||
5 + 3 | ||||||||
P_{s 19} = 6·10^{-4} | ||||||||
6 + 1 + 1 | ||||||||
P_{s 20} = 9·10^{-5} | ||||||||
6 + 2 | ||||||||
P_{s 21} = 3·10^{-5} | ||||||||
7 + 1 | ||||||||
P_{s 22} = 5·10^{-7} | ||||||||
8 |
Take for example, six tags transmitting in one slot; then, R = 6 and just one tag is having a distinct colour U = 1, two tags are using the same colour ${R}_{1}^{\mathit{\text{cc}}}=2$, and three tags have an identical but different colour ${R}_{2}^{\mathit{\text{cc}}}=3$. Thus, the number of colliding colours is D = 2. In Table 5, this is scenario 6 (3 + 2 + 1).
Each column of Table 5 lists various collision scenarios given a collision of R tags, and each row of Table 5 represents a different collision scenario. In the first row of the table, scenario 1 is listed. Here, all tags involved in a collision have a different postpreamble. In the second row, we find scenario 2, where two out of all colliding tags have the same postpreamble while others have a different one, and so on. Thus, for R = 2 tags active in one slot, we can differentiate S(R = 2) = 2 scenarios; for R = 3, the number of scenarios is S(R = 3) = 3; for R = 4, the number is S(R = 4) = 5, and so on. The numbers in Table 5 represent the combination of tags with the same postpreamble. Indicated by the italic digit ‘1’ are tags that can be successfully decoded due to their occurrence of a unique colour. Furthermore, the italic digit ‘2’ denotes those tags with a single occurrence of the same postpreamble that can be decoded by the projection method (scenario 2) as explained in [21].
and represents the probability that exactly R tags are active in one slot.
Maximal theoretical throughput for covered scenarios
System | F_{opt}/N | Tps | R _{Tps} |
---|---|---|---|
M = 1 J = 1 | 1 | 0.368 | 1.000 |
M = 2 J = 2 | 0.618 | 0.841 | 2.285 |
M = 4 J = 4 | 0.345 | 1.879 | 5.106 |
M = 8 J = 8 | 0.207 | 3.073 | 8.351 |
Comparing Tables 3 and 6, we observe that for higher values of the collision recovery factor M, the loss in Tps performance increases because the number of unresolved tags becomes much higher.
4 Collision recovery procedure
where ${\mathbf{r}}_{1}^{\mathit{\text{pp}}}\left(t\right)$ and ${\mathbf{r}}_{2}^{\mathit{\text{pp}}}\left(t\right)$ are parts of the received signals containing the postpreamble from antennas 1 and 2, respectively.
In this scenario, tags 3 and 4 share the same postpreamble, p_{ c }, and we cannot use an LS channel estimation technique from [12]. To overcome this situation, we propose a collision recovery procedure that consists of two phases. The first phase is performed by a successive interference cancellation (SIC), and the second is a projection of the constellation into the orthogonal subspace of the interference.
4.1 Successive interference cancellation
Through this procedure, the received signal is cleaned from the influence of the strongest tag with its unique postpreamble, and the channel coefficients that correspond to this tag are stored. The new signal, $\stackrel{\u0304}{\mathbf{r}}\left(t\right)$, together with the new set S_{ M } of postpreambles without the postpreamble that corresponds to the strongest tag signal, is used as an input signal for the next iteration of the SIC.
4.2 Channel estimation with projections
After SIC, the remaining signal is composed of signals that originate from two tags. Thus, theoretically, we should be able to differentiate 2^{R = 2} = 4 states in the IQ diagram of Figure 8: the state when both tags are absorbing ${\u0108}_{i}^{a,a}$, the state when both tags are reflecting ${\u0108}_{i}^{r,r}$ and the states in which one tag is absorbing and one is reflecting ${\u0108}_{i}^{a,r},{\u0108}_{i}^{r,a}$[21].
Here, r_{ i }[k] is the sample of the received signal from i th antenna taken within the duration of the first preamble bit t_{1bit}.
The absorbing state is determined by averaging the received signal over the time period T before the tag response ${\u0108}_{i}^{a,a}=E{\left\{{r}_{i}\right[k\left]\right\}}_{T}$.
where r_{i⊥}[k] is the signal component located in the orthogonal subspace.
With this, we have finished the channel estimation process, and the tag signals are extracted by the MMSE receiver from Equation (2).
Generally, the remaining signal after SIC is composed of the signals from tags with the same postpreambles. However, this signal is disturbed by the channel, noise and accumulated errors during the SIC process. As the disturbances are higher, there are more intersections, leading to a less accurate channel estimation.
5 Performance analysis
The performance analysis is achieved through Monte Carlo simulations. In the simulated system, the RFID reader has one transmitting and up to four receiving antennas N_{RA}. In a first experiment to validate our predicted performance metrics, the number R of tags that are active in one slot is kept fixed and can be set from one, i.e. transmission without collision, to up to eight, when eight tags are colliding in one slot. The channel between the reader’s transmit antenna, the tag and the receiving antenna of the reader is modelled as a double Rayleigh fading channel as in [10]. Furthermore, imperfections like additive noise, an imperfect channel estimation, errors accumulated during successive interference cancellation and a non-ideal projection of the constellation into the orthogonal subspace of interference are assumed in this simulator. Additionally, we assume that colliding tags are perfectly synchronized and that the reader can exactly determine the size of the tag population. The influence of such parameters is left to be investigated in the future work.
As a performance measure, we observe the bit error ratio (BER) and the average number of successfully received packets (NSRP) per slot for different levels of average signal-to-noise ratios (SNRs). The SNR is averaged over the receiving antennas as explained in [11]. In NSRP calculations, the part of the signal that contains the RN16 number is considered as one packet. The NSRP is averaged over ${N}_{\text{iter}}=50\xb71{0}^{\frac{\overline{\text{SNR}}\left[\mathit{\text{dB}}\right]}{10}}+50$ iterations [21], guaranteeing approximately the same quality (confidence interval) in the results. Around each point in the BER figures, a confidence interval that contains 95% of the obtained results is plotted to evaluate the quality of the simulations.
Results obtained with the receivers that apply an LS channel estimation method instead are shown in Figures 10 and 13, for BER and NSRP, respectively. It can be observed that since two out of eight colliding tags have the same postpreamble, the channel cannot be estimated correctly by a standard LS estimator, and the MMSE receiver cannot recover from this collision. The BER curves are saturating at high values. Nevertheless, some packets are decoded correctly as the NSRP curves show that in average more than four packets can be correctly received with four antenna receivers (N_{RA} = 4). Hence, the errors are mostly concentrated in packets from tags with the same postpreamble, while the packets from the other six tags are less affected.
In Figures 11 and 14, the results obtained from the proposed smart receiver with the two-phase channel estimation and collision recovery are presented. Even though the BER values are significantly higher when compared to the reader with perfect channel knowledge, the performances in NSRP are comparable. It can be observed that a reader with four receiving antennas can successfully recover from this collision and in average can successfully receive almost seven packages. Corresponding BER and NSRP figures in the case of four tags transmitting simultaneously (2 + 1 + 1) are presented and discussed in [21].
where ${\text{Sd}}_{i,R}^{{s}_{l}}$(SNR) denotes the average number of successfully decoded tags in a system with i receive antennas in scenario s_{ l },l = 1,2,..,S(R). Variable ${\text{Sd}}_{i,R}^{{s}_{l}}$(SNR) represents the average number of packets in a slot that are correctly received, and at best, it is close to ${R}_{{s}_{l}}^{\text{sol}}\left(R\right)$. The values of ${\text{Sd}}_{i,R}^{{s}_{l}}$(SNR) are taken from simulations and are thus dependent on the SNR. In Equation (16), P_{ R }represents the probability that exactly R tags are active in one slot, and this probability is calculated based on Equation (11) for the optimal value F_{opt} taken from Table 6. The probabilities of scenarios ${P}_{{s}_{1}},\dots ,{P}_{{s}_{S\left(R\right)}}$ are taken from Table 5.
Here, the probability P_{ R }is calculated according to Equation (11) for F_{opt} taken from Table 3, and the values of Sd_{i,R}(SNR) correspond to those of ${\text{Sd}}_{i,R}^{{s}_{l}}$(SNR) but are now obtained from simulations with perfect channel knowledge.
Based on Figure 15, we observe the Tps for the different values of SNR, and according to that, we recalculate how many tags are left for the next frame in the same inventory round. For a receiver with collision recovery factor M = 8, for example, the Tps value at the SNR = 15 dB is Tps^{15 dB} = 2.805. The theoretically expected maximal throughput per slot is Tps_{ f } = 3.073 for F_{opt}/N = 0.207 (Table 6). Taking into account the optimal frame duration, the average number of tags that are successfully decoded within the duration of the first frame is N^{dec} = round(Tps^{15 dB}·F_{opt}) = 581. Thus, for the next inventory round, N^{left} = 419 tags are left. On the other hand, a conventional receiver has a maximal throughput per slot Tps = 0.368 for a frame size equal to the tag population size F_{opt}/N = 1, and at the SNR = 15 dB, Tps^{15 dB} = 0.212. Accordingly, within the first frame duration, a conventional receiver successfully reads out N^{dec} = 212 tags, and N^{left} = N-N^{dec} = 788 tags are left for the next round.
The number of residual tags, tags that still have not been decoded, versus the number of elapsed slots is shown in Figure 16. For the reader with collision recovery factor M = 1, a number of 4,693 slots (22 frames) are necessary to decode 99.5% of the tags in the reader range. A reader with collision recovery factor M = 2 needs 2,447 slots (19 frames) to decode 99.6%, while the readers with higher collision recovery factors are much faster. The reader that is capable of recovering from a collision of up to four tags active in a slot M = 4 and acknowledges all of them spends 775 slots (19 frames) for successfully decoding 99.6%, and the reader with M = 8 decodes 99.7% of tags in just 355 slots (7 frames).
Number of decoded tags and optimal frame duration at SNR = 15 dB
M = 1 | M = 2 | M = 4 | M = 8 | ||||
---|---|---|---|---|---|---|---|
F _{opt} | N ^{dec} | F _{opt} | N ^{dec} | F _{opt} | N ^{dec} | F _{opt} | N ^{dec} |
1,000 | 212 | 618 | 252 | 345 | 455 | 207 | 581 |
788 | 167 | 462 | 188 | 188 | 248 | 87 | 244 |
621 | 131 | 346 | 141 | 102 | 134 | 36 | 101 |
490 | 104 | 259 | 105 | 56 | 74 | 15 | 42 |
386 | 82 | 194 | 79 | 31 | 41 | 7 | 20 |
304 | 64 | 145 | 59 | 17 | 22 | 2 | 6 |
240 | 51 | 109 | 44 | 9 | 12 | 1 | 3 |
Number of slots spent for decoding 95%, 98% and 99.5% and relative improvement at SNR = 15 dB
Slot | M = 1 | M = 2 | M = 4 | M = 8 |
---|---|---|---|---|
Relative improvement | ||||
95% | 4 481 | 2 334 | 720 | 338 |
1 | 1.920 | 6.224 | 13.257 | |
98% | 4 623 | 2 408 | 743 | 349 |
1 | 1.920 | 6.222 | 13.246 | |
99.5% | 4 693 | 2 445 | 754 | 354 |
1 | 1.920 | 6.224 | 13.257 |
6 Conclusion
In this work, we have analysed the theoretical throughput of an FSA RFID system. We have studied the influence of several parameters on the system throughput, and we found the maxima of the theoretically expected throughput for receivers with different collision recovery factors and for different receiver architectures. We have investigated the benefits of an additional postpreamble to the throughput, and we observed that without taking into account the receiver structure and the channel estimation method, it is possible to increase the system throughput by more than 17 times. On the other hand, if the receiver structure is taken into account, then a throughput increase of more than 12 times can still be achieved for a reader capable of successfully reading and acknowledging up to eight tags per slot. In these calculations, it is assumed that the readers have perfect channel knowledge. However, in order to recover from a collision, a reader needs to perform channel estimation. For the channel estimation procedure, the tags are augmented by postpreambles. Based on this, we can differentiate several collision scenarios, and if we include the probability of scenarios that can be resolved and the number of tags that can be successfully decoded, the maximal theoretical throughput is still about eight times the throughput of a conventional system at 30 dB SNR. For theoretical calculations, it is assumed that the reader can successfully decode all tags with unique postpreambles, regardless of the scenario, and also all tags colliding in scenario 2, where exactly two of colliding tags share an identical postpreamble.
Practically, for recovering from scenario 2 collisions, we propose a two-phase collision recovery procedure. In the first phase, the signal part from the tags with unique postpreambles is taken out during a successive interference cancellation process, while in the second phase, the remaining signal, originating from the tag pair with the same postpreambles, is resolved using the projection of the constellation into the orthogonal subspace of the interference. The so obtained results show that the proposed method provides satisfactory results.
Moreover, the necessary time to read out a high tag population is investigated. We showed that at the average SNR of 15 dB, a smart reader with collision recovery factor M = 8 successfully decodes all tags in the reader range, more than 13 times faster than a conventional reader, and performances are considerably enhanced.
Appendix 1
Approximation of Tps_{ M }
Thus, the entire expression is a function of F/N.
which offers them to differentiate with respect to x and to find the maxima for throughput and thus the optimal F/N ratio.
The obtained optimal ratios F/N for maximal throughput are [1;0.618;0.441;0.340;0.275;0.230;0.197;0.172] for R = 1,2,…,8. When compared with simulation results, this approximation shows an almost perfect agreement.
Appendix 2
Approximation of Tps_{ C }
This allows to differentiate with respect to x and to find the maxima for throughput and thus the optimal F/N ratio. When compared with simulation results, this approximation shows an almost perfect agreement.
Appendix 3
Approximation of Tps_{ f }
Now we can differentiate with respect to x and find the optimal F/N ratio that corresponds to the throughput maxima. When compared with simulation results, this approximation shows an almost perfect agreement.
Declarations
Acknowledgements
This work has been funded by the Christian Doppler Laboratory for Wireless Technologies for Sustainable Mobility and its industrial partner Infineon Technologies. The financial support by the Federal Ministry of Economy, Family and Youth and the National Foundation for Research, Technology and Development is gratefully acknowledged. We finally like to thank Christoph Mecklenbräuker for his fruitful discussions and stimulative thoughts.
Authors’ Affiliations
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