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Reverse-Link Interrogation Range of a UHF MIMO-RFID System in Nakagami-m Fading Channels Do-Yun Kim, Student Member, IEEE, Han-Shin Jo, Student Member, IEEE, Hyungoo Yoon, Member, IEEE, Cheol Mun, Member, IEEE, Byung-Jun Jang, Member, IEEE, and Jong-Gwan Yook, Member, IEEE

Abstract—In this paper, the reverse-link interrogation range (RIR) of ultrahigh-frequency-band passive radio-frequency identification (RFID) is analyzed for single-input and single-output (SISO) and multiple-input and multiple-output (MIMO) systems with maximal-ratio combining in the pinhole channel, where each channel is modeled as an arbitrarily correlated Nakagami-m distribution. Under the assumptions of perfect channel estimation and no interference, the closed-form expression of average RIR is derived, involving various parameters, such as the number of antennas, correlation, reader structure, and Nakagami-m shaping factor. The results show that the employment of multiple antennas at a reader causes the received SNR to change favorably and contributes to the improvement of the average RIR. Particularly, for the bistatic structure and Rayleigh fading (m = 0 dB), a 3 × 3 MIMO-RFID system can achieve 60% gain in the average RIR compared to the SISO-RFID system. In order to consider more realistic environments, finally, we investigated the influence of interference and imperfect channel estimation on the average RIR of the MIMO-RFID system in the uncorrelated Rayleigh fading channel. Index Terms—Arbitrarily correlated Nakagami-m fading, pinhole channel, reverse-link interrogation range (RIR), single-input and single-output (SISO)/multiple-input and multiple-output (MIMO) radio-frequency identification (RFID).

I. I NTRODUCTION

R

ECENTLY, ultrahigh-frequency (UHF)-band radiofrequency identification (RFID) systems that operate in the 860–960-MHz range have received a great deal of attention. It is generally accepted that UHF RFID systems connected to an intelligent sensor network can revolutionize commercial processes, such as supply-chain management [1]–[6]. Indeed, several influential retail organizations, such as Wal-Mart, Manuscript received March 17, 2009; revised August 7, 2009. First published September 1, 2009; current version published March 10, 2010. This work was supported by the Ministry of Knowledge Economy, Korea, under the Information Technology Research Center support program supervised by the Institute of Information Technology Assessment (IITA) (IITA-2009-C10900902-0038 and IITA-2009-C1090-0904-0002). D.-Y. Kim, H.-S. Jo, and J.-G. Yook are with the Department of Electrical and Electronic Engineering, Yonsei University, Seoul 120-149, Korea (e-mail: [email protected]). H. Yoon is with the Department of Computer and Electronic Engineering, Myongji College, Seoul 120-848, Korea. C. Mun is with the Department of Electronic Communications Engineering, Chungju National University, Chungbuk 380-702, Korea. B.-J. Jang is with the Department of Electrical Engineering, Kookmin University, Seoul 136-702, Korea. Digital Object Identifier 10.1109/TIE.2009.2030134

Tesco, Metro, Procter & Gamble, etc., have adopted UHF RFID systems in their supply chains. Other retailers, such as Zara and Prada, are using RFID technology to enhance their fashion supply-chain management and thus respond faster to consumer preferences. Pfizer, a leading pharmaceutical company, is also using UHF RFID tags on bottles, cases, and pallets [7]. In order to support the rapid growth rate of RFID devices and their use in mass-market applications, various works have been studied for RFID performances, including interrogation range [8]–[10], bit-error rate (BER) [11]–[14], data rate [13], [14], and anticollision [15]–[21]. Among them, the interrogation range is one of the most important characteristics of UHF RFID system design, like coverage in cellular systems. The actual interrogation range is determined by considering forward- and reverse-link interrogation ranges (FIR and RIR, respectively). In general, an FIR is defined as the maximum distance at which the tag receives just enough power to turn on, and then, it is calculated by the time-averaged absorption power at the input of the tag’s voltage rectifier. An RIR is also indicated as the maximum distance at which the reader can detect the tag’s backscattered signal and is calculated through the signal-tonoise (SNR) required to correctly receive the tag’s data at the demodulation output signal of the reader. In [10], the actual interrogation range of a single-input and single-output (SISO) system with reader-to-reader interferences was mathematically derived under perfect line-of-sight (LOS) environments with no fading. The RIR is much more significant than the FIR in determining the actual interrogation range in some environments, such as warehouses and manufacturing facilities, because of interference from other readers [10]. There is also some research in which the use of multiple antennas at the reader or RF tag is proposed to improve RFID performance without the additional spectrum usage. In [11] and [12], it was shown that pinhole diversity is available in a rich scattering environment caused by the modulating backscatter with multiple RF-tag antennas—no diversity combining and channel knowledge. Pinhole diversity can lead to the reduction in the power required to maintain a certain BER under a Rayleigh fading channel. According to [13], the use of multiple antennas at both the reader and RF tag enhances the BER performance and communication capacity due to transmit diversity and spatial multiplexing, respectively. In [22], it was

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KIM et al.: RIR OF A UHF MIMO-RFID SYSTEM IN NAKAGAMI-m FADING CHANNELS

shown that the use of multiple RF-tag antennas increases the power available to the RF-tag integrated circuit. Instead of conventional solutions based on a collision-avoidance scheme using medium-access-control protocols (e.g., slotted-ALOHA and binary-tree algorithms), [23] used the multiple antennas at the reader with blind-source-separation techniques in order to separate overlapping tag signals. Although a number of studies related to the interrogation range or the multiple antennas of a UHF RFID system have been conducted, there are few mathematical models that posit the effects of the multiple antennas at the reader on the interrogation range. Therefore, this paper investigates the RIR of a multipleinput and multiple-output (MIMO) RFID system in a pinhole channel where the fading of each link is modeled as an arbitrarily correlated Nakagami-m distribution. First, under the assumptions of perfect channel estimation and no interference, the closed-form expression of the average RIR of the MIMORFID system with maximal-ratio combining (MRC) is derived. Second, from the equations, the pure gain of the average RIR will be analyzed according to various parameters, such as the number of antennas at a reader, correlation, reader structure, and Nakagami-m shaping factor. Finally, in order to extend the derived equations for the average RIR of the MIMORFID system to more realistic environments, the reader-toreader interference and imperfect channel estimation are taken into consideration in uncorrelated Rayleigh fading. These approaches will contribute quantitatively to the analysis of the performance gain due to the utilization of multiple antennas at the reader and give design guidelines for actual MIMO-RFID system deployments. The rest of this paper is organized as follows. In Section II, the system model and the pinhole channel are described. Under Nakagami-m fading channels, the received SNR is calculated, and the closed-form equations for the average RIR are then derived according to the SISO/MIMO-RFID systems in Section III. Then, the influence of interference and imperfect channel estimation are presented in Section IV. This is followed by analytical and numerical results of the RIR in Section V. Finally, Section VI presents the conclusions of our work. II. S YSTEM M ODEL In a UHF RFID system, the channel can be assumed by a pinhole channel [24], [25]. The hallmark of this channel is that it is modeled by the cascade of two channels, such as the forward and reverse links. Here, the forward channel coefficient hf,D describes signal propagation from the reader transmit antenna to a tag antenna, and the reverse channel coefficient hb,D propagates the signals scattered from the tag antenna to a receive antenna at the reader. As LOS propagation dominates in the UHF RFID system, the literature on the fading problem frequently uses the Rician model to represent the strength of a received signal. While the Rician distribution spans the range of the fading distributions from Rayleigh fading to nonfading, the Nakagami-m distribution spans the range from one-sided Gaussian fading to nonfading. Moreover, the Nakagami-m distribution is much more convenient for mathematical analysis compared to the Rician distribution because the Nakagami-m

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Fig. 1. RFID system configurations. (a) Monostatic system with transmit and receive antennas to be colocated at the reader (hT f,D = hb,D ). (b) Bistatic system with reader transmit and receive antennas to be spaced far apart (hT f,D and hb,D are independent).

distribution is a central distribution [26]. Thus, it is assumed that the forward and reverse links follow the Nakagami-m fading channels in this paper. In addition, two cases of a reader are considered, with mono- and bistatic structures at the reader, as shown in Fig. 1. In the former case, the reader transmit and receive antennas may be closely spaced or colocated, giving rise to potentially high link correlation. In the latter case, however, the antennas of the transmitter at the reader are spaced far apart from those of the receiver. It is then assumed that fading is independent between the transmit and receive ends. For the remainder of this paper, we assume that the reader knows the channel information of all the links, and the transmit and receive weight vectors are obtained by MRC. III. A NALYSIS OF RIR A. SISO-RFID In Fig. 1, a reader transmits a continuous-wave (CW) signal to activate a tag. For a tag, the received signal at the distance of d[m] from a reader and time t is given as  z(d, t) = PTX GTX GTAG P0 d−γ hf,D (t)wf,D (t)xcw (t)+n(t) (1) where PTX denotes the total transmit power, P0 is the reference path loss at the distance of 1 [m], and GTX and GTAG are the gain of the transmit antenna at the reader and the gain of the tag antenna, respectively. Furthermore, wf,D (t) is the weight of a matched filter at the transmitter, hH f,D (t)/|hf,D (t)|, xcw (t) is a CW signal from a reader, n(t) is an additive white Gaussian noise (AWGN) signal, and (·)H represents the complex-conjugate transpose function. Therefore, the instantaneous received power at the tag PTAG (d, t) gives the following result: PTAG (d, t) = PTX GTX GTAG P0 d−γ |hf,D (t)|2 .

(2)

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If the power supplied from the reader is sufficient to operate the tag, a backscattered signal from the tag is received by the desired reader. The received signal at the reader is given by  y(d, t) = PTAG (d, t)αF ETAG GTAG GRX P0 d−γ × hb,D (t)xTAG (t) + n(t)

(3)

where ETAG is the effective power reflection coefficient of a tag, GRX is the gain of the receive antenna at the reader, and αF denotes the fractional power ratio in the bandwidth that is used, which can be expressed using the power spectral density function Φ(f ) of the backscattered signal of the tag, as expressed as follows:  Φ(f )df . (4) α = BW ∞ −∞ Φ(f )df Therefore, for the reader, the instantaneous SNR at the output of the matched filter with wb,D (t) = hH b,D (t)/|hb,D (t)| is calculated by SN R(d, t) =

αFPTX GTX GRX G2TAG ETAGP02 d−2γ |hf,D (t)|2 |hb,D (t)|2 . N0 (5)

To evaluate the RIR of the reader R(t), it is assumed that the SNR at the reader receiver is greater than a certain value RTH . Here, RTH , the threshold value, can be determined by a combination of the data-encoding schemes of the tag and its target-BER values. Thus, R(t) is defined as the following criterion: R(t) = arg min SN R(d, t), d≥0

such that SN R(d, t) ≥ RTH (6)

and then

On the other hand, when considering a bistatic structure with propagations in the forward and reverse links to experience independent Nakagami-mf and Nakagami-mb fading channels, the average RIR Rb.av.si can be obtained by 1   2γ   1 1 ξ Rb.av.si = · E |hf,D (t)| γ E |hb,D (t)| γ N0

⎞ ⎛

⎞ ⎛ 1 1 1   2γ Γ m Γ m + + t r 2γ 2γ ξ ⎠⎝ ⎠. = ·⎝ 1 1 N0 2γ 2γ m Γ(m ) m Γ(m ) t

=ξ

1 2γ

1   2γ |hf,D (t)|2 |hb,D (t)|2 · N0

r

B. MIMO-RFID In Fig. 1, it is assumed that the Mt × 1 × Mr pinhole channel matrix is generated by a UHF RFID system with Mt reader transmit antennas, one RF-tag antenna, and Mr reader receive antennas [11], [12]. The channel coefficient of the path from the ith transmit antenna to an RF-tag antenna is denoted by hf,D,i , and that of the path from the RF-tag antenna to the jth receive antenna is represented by hb,D,j . Thus, the received signal at a tag is represented by  z(d, t) = PTX GTX GTAG P0 d−γ hf,D (t)wf,D (t)xcw (t)+n(t) (10) where hf,D = [hf,D,1 , . . . , hf,D,Mt ] denotes the channel vecH tor of the forward link and wf,D = hH f,D /hf,D  means the transmit-MRC weight vector. Therefore, the instantaneous received power at the tag PTAG (d, t) is calculated by PTAG (d, t) = PTX GTX GTAG P0 d−γ hf,D (t)2 .

(11)

Thus, the Mr × 1 received-signal vector at the reader is given by  y(d, t) = PTAG (d, t)αF ETAG GTAG GRX P0 d−γ × hb,D (t)xTAG (t) + n(t) (12)

1 2γ

(7)

where ξ = αF PTX GTX GRX G2TAG ETAG P02 /RTH . If a monostatic structure is assumed, i.e., the forward- and reverse-link channels are fully correlated Nakagami-m fadings, hD (t), the average RIR, Rm.av.si , can be calculated by 1   2γ  2 ξ · E |hD (t)| γ Rm.av.si = N0

⎞ ⎛ 1   2γ Γ m + γ1 ξ ⎠ = ·⎝ (8) 1 N0 m γ Γ(m) where Γ(·) is the standard gamma function.

r

(9)

R(t)   αFPTX GTX GRX G2TAG ETAG P02 |hf,D (t)|2 |hb,D (t)|2 = RTH N0

t

where hb,D = [hb,D,1 , . . . , hb,D,Mr ]T denotes the channel vector of the reverse link and n is the Mr × 1 AWGN vector. Therefore, the instantaneous SNR at the output of MRC is calculated by SN R(d, t) =

αFPT X GTX GRX G2TAG ETAGP02 d−2γhf,D (t)2hb,D (t)2 . N0 (13)

From the criterion in (6), R(t) becomes 1   2γ 2 2 1 (t) h (t) h f,D b,D R(t) = ξ 2γ · N0  M 1  r t |hf,D,i (t)|2 · M |hb,D,j (t)|2 2γ 1 i=1 j=1 = ξ 2γ · . N0 (14)

KIM et al.: RIR OF A UHF MIMO-RFID SYSTEM IN NAKAGAMI-m FADING CHANNELS

The average RIRs of mono- and bistatic structures can be calculated, respectively, by ⎧  γ1 ⎫ 1   2γ Mt ⎨  ⎬ ξ 2 ·E |hf,D,i (t)| Rm.av.mi = (15) ⎩ ⎭ N0 i=1

 Rb.av.mi =

ξ N0

1  2γ

·E

⎧ Mt ⎨  ⎩

|hf,D,i (t)|2

1 ⎫  2γ ⎬

⎭

i=1

⎫ ⎧⎛ 1 ⎞ 2γ ⎪ ⎪ Mr ⎬ ⎨  . |hb,D,j (t)|2 ⎠ ·E ⎝ ⎪ ⎪ ⎭ ⎩ j=1

The two parameters ΩXM and mXM are derived from the first two moments of the exact distribution by the statistical properties of complex random vectors of quadratic form as follows: λk

(19)

k=1

mX M =

2

2



M k=1

⎞ ⎠

(22)

(16)

where m and Ω are the fading parameter and average received SNR, respectively. Thus, the distribution of XMt or XMr can be approximated to a gamma distribution, with the first two moments being identical to those of the exact distribution, as in [27]    mX M γ mXM −1 mX M mX exp − M γ . (18) PXM (γ) = ΩXM Γ(mXM ) ΩXM

M 

1 2γ

where ΩXMt , ΩXMr , mXMt , and mXMr are calculated by (19) and (20). When Mt = Mr = 1, (21) and (22) are equal to (8) and (9), respectively.

To derive the closed-form expressions from and (16), we  (15) t 2 have to know the distributions of XMt = M |h f,i (t)| and i=1 Mr 2 XMr = j=1 |hb,j (t)| . Now, if the envelope of the channel is the Nakagami-m random variable, then the square of the envelope of the channel represents gamma-distributed random variables with probability density function (pdf) m m m γ m−1 exp − γ (17) P|h|2 (γ) = Ω Γ(m) Ω

ΩXM =Tr(R) =

and for the bistatic structure 1   2γ  1 ΩXMt ΩXMr 2γ ξ · Rb.av.mi = N0 mX M t mX M r

⎛ 1 Γ mXMt + 2γ Γ mX M r +     ·⎝ Γ mX M t Γ m X M r

1471

λk

2

(Tr(R)) E XM  = m· = m· M 2 Var{XM } Tr(R2 ) k=1 λk

(20)

where Tr(G) denotes the trace of matrix G, R is a normalized covariance matrix of the channel defined as E{hH f,D hf,D } or }, and λ represents the kth eigenvalue of R. The E{hb,D hH k b,D verification of our approximated distribution is shown in [28], in which our approximated pdf derived by the corresponding correlation matrix agrees closely with the exact pdf. From (18), the average RIR for mono- and bistatic structures in (15) and (16) can be derived as the following closed-form expressions. For the monostatic structure

⎞ ⎛ 1 1   2γ   γ1 Γ m + X M Ω γ ξ t X Mt  ⎠  · ·⎝ Rm.av.mi = N0 mX M t Γ mX M t (21)

IV. I NFLUENCE OF I NTERFERENCE AND C HANNEL E STIMATION E RROR ON AVERAGE RIR In the previous section, in order to analyze the pure gain of the MIMO-RFID system with MRC weight, it was assumed that there was no interference and that the reader can perfectly estimate the channel information of all the links. Because the aforementioned assumptions may not be realistic in actual deployments, we now study the influence of interference and imperfect channel estimation on the average RIR of the MIMORFID system. In the following, it is assumed that the channels are Rayleigh fading (m = 0 dB) and that the correlations between antennas are uncorrelated. A. Influence of Interference There are three types of UHF RFID interference: multipletag-to-reader interference, multiple-reader-to-tag interference, and reader-to-reader interference [15], [18]. In general, the multiple-tag-to-reader interference can be solved by anticollision algorithms, such as tree-based, ALOHA, and beamforming algorithms. The second type of interference, namely, multiplereader-to-tag interference, can also be settled by simply separating the reader interrogation ranges. On the other hand, the reader-to-reader interference can occur, even when many algorithms have been applied to mitigate it and when the reader interrogation ranges contain no overlapping zones. This type of interference can be magnified in actual environments, which can involve many readers in one warehouse or manufacturing facility [10]. Among the three types of interference, therefore, we need to bring into focus the effect of reader-to-reader interference on the average RIR. Assume that there are MI independent interferers in the MIMO-RFID systems, the instantaneous signal-tointerference-plus-noise ratio (SINR) is given by (23), shown at the bottom of the next page, where I¯0 is the average H power from a single interferer, wb,D (t) = hH b,D (t)/hb,D (t) means the 1 × Mr receive-MRC weight vector of a desired reader, HI(k) (t) is the Mr × Mt channel matrix between the transmitter of the kth interferer and the receiver of the desired reader, and wf,I(k) (t) is the Mt × 1 transmit-MRC weight vector of the kth interferer. When interferers are subjected to independent and identically distributed (i.i.d.) Rayleigh fading, HI(k) (t)wf,I(k) (t) is the i.i.d. complex Gaussian vector with zero mean and covariance matrix I (identity matrix). Thus, each term

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of wb,D (t)HI(k) (t)wf,I(k) (t), k = 1, . . . , MI , is a complex Gaussian random variable with zero mean, with variance H (t) = 1, and is independent of being given by wb,D (t)wb,D 2 hb,D (t) [29]. Therefore, if we define z=

MI 

2  I¯0 wb,D (t)HI(k) (t)wf,I(k) (t) + N0

k=1

= I¯0 y + N0

(24)

then y ∼ Γ(1, MI ) (i.e., y is a gamma random variable with parameters 1 and MI ) and fy (y) = y MI −1 /Γ(MI )e−y . Also, the pdf of z is given by   0 (z − N0 )MI −1 − z−N e |I¯0 | . (25) fz (z) = ¯ M |I0 | I Γ(MI ) Next, substituting (23) and (24) into (6), the average RIR for RFID systems with MI interferers can be written as   1

2γ  1 1 E{R(t)} = ξ 2γ · E hf,D (t)2 hb,D (t)2 · E z − 2γ (26) where an expectation for the function of hf,D (t) and hb,D (t) was already derived in Section III-B, and when an interference-limited environment (z  I¯0 y) is assumed,1 E{z −1/2γ } can be calculated by ignoring the thermal noise power in (25), as in the following closed-form expression:

1  1 Γ MI − 2γ . (27) E z − 2γ = ¯ 1/2γ |I0 | Γ(MI ) Consequently, the average RIR for mono- and bistatic structures can be derived, respectively, by

⎞ ⎛

⎞ ⎛ 1 1 Γ M Γ M + − t I 1 γ 2γ ⎠·⎝ ⎠ (28) Rm.av.mi = ξ 2γ · ⎝ 1/2γ ¯ Γ(Mt ) |I0 | Γ(MI )

Rb.av.mi

⎛ 1 Γ M + t 1 2γ Γ Mr + = ξ 2γ · ⎝ Γ(Mt )Γ(Mr )

⎞ 1 Γ MI − 2γ ⎠. · ⎝ ¯ 1/2γ |I0 | Γ(MI )

1 2γ

⎞ ⎠

⎛

how to determine the average power from a single interferer I¯0 and a number of interferers MI . The authors have attempted to calculate these values by using the reader-to-reader interference model based on interference statistics [10]. When the interferers are uniformly randomly distributed over an area in two dimensions and γ > 2, the average interference power from a single interfering reader is given by I¯0 =

r γ   Imax LD min 2 rmin − D2 2 2 (γ/2 − 1) (D − rmin ) D

(30)

−γ where Imax = PTX βGT GR P0 rmin denotes the maximum interference power that would be received from an interfering reader and LD is the antenna discrimination loss [30].2 If there are MA interfering readers with two states (active and inactive) and only readers in the active state can interfere with the desired reader, then the number of readers in the active state is determined by a binomial distribution, with the probability of a reader being in the active state denoted as pact . Therefore, the average number of interfering readers MI can be expressed as pact · MA , where x denotes the smallest integer that exceeds x.

B. Influence of Channel Estimation Error So far, many algorithms to estimate channel information have been conducted. There are two types of channel estimation algorithms: the algorithm based on the reference signal (pilot or training sequences) [31] and the blind-channel-estimation algorithm [32]. For the former case, a tag transmits a pilot signal with frequency or time separation from the data signal to assist the desired reader in estimating the channel information. On the other hand, for the latter case, the reader obtains the channel characteristics from the received data signal only. However, the channel estimates cannot be perfect in fading channels, and thus, the adverse effect of imperfect channel estimation on the average RIR must be taken into account in the MIMO-RFID system. Considering the channel estimation error, the instantaneous SINR μ(d, t) is given by

(29)

Φ(d) |hf,D (t)wf,D (t)|2 |wb,D (t)hb,D (t)|2 μ(d, t) = M 2  I ¯   + N0 k=1 I0 wb,D (t)HI(k) (t)wf,I(k) (t) (31)

In addition, to properly evaluate the influence of reader-toreader interference on the average RIR, the important point is

where Φ(d) = αF PTX GTX GRX G2TAG ETAG P02 d−2γ . When Qf = |hf,D (t)wf,D (t)|2 and Qb = |wb,D (t)hb,D (t)|2 , the pdf

1 When z = I¯ y + N , the closed-form equation in (27) cannot be derived. 0 0 Fortunately, the reader-to-reader interference is much more than the thermal noise power in actual RFID deployments, such as multiple-reader and densereader environments. Thus, it is a reasonable assumption of an interferencelimited system.

2 In [10], I¯ was calculated in the worst case, where the antenna of a desired 0 reader and the antennas of all interferers were put face to face. Thus, the authors adjust I¯0 to a more realistic environment by considering the antenna discrimination loss LD .

μ(d, t) =

αF PTX GTX GRX G2TAG ETAG P02 d−2γ hf,D (t)2 hb,D (t)2 2 M I ¯   + N0  k=1 I0 wb,D (t)HI(k) (t)wf,I(k) (t)

(23)

KIM et al.: RIR OF A UHF MIMO-RFID SYSTEM IN NAKAGAMI-m FADING CHANNELS

of Qi |i=f,b is given by M −1−n 2n  M −1   ρi n −q M − 1 1 − ρ2i q e fQi (q) = n n! n=0

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TABLE I S YSTEM PARAMETERS [34], [35]

(32)

√ where ρi = Qi /hi,D (t) denotes the magnitude of the normalized correlation coefficient between the actual channel vector and its estimate [33]. Under imperfect channel estimation, therefore, the average RIR for mono- and bistatic structures can be expressed, respectively, by Rm.av.mi 1

= ξ 2γ

⎞ 1 Γ MI − 2γ ⎠ · ⎝ ¯ 1/2γ |I0 | Γ(MI ) ⎛

⎛

M t −1 

⎜ ·⎝

n=0

M −1−n

⎞ 1  1 − ρ2 t 2n ρ Γ n + f f γ ⎟ Mt − 1 ⎠ n Γ(n) (33)

Rb.av.mi

⎞ 1 Γ MI − 2γ ⎠ · ⎝ ¯ 1/2γ |I0 | Γ(MI ) ⎛

1

= ξ 2γ ⎛

M t −1 

⎜ ·⎝

n=0

⎛

1 2γ

 1 − ρ2Mr −1−n ρ2n Γ n + b b Mr − 1 Γ(n) n

1 2γ

M r −1 

·⎝

n=0

⎞

M −1−n  1 − ρ2 t 2n ρ Γ n+ f f Mt − 1 Γ(n) n

⎟ ⎠

⎞ ⎠. (34)

V. N UMERICAL R ESULTS In this section, the RIR of a UHF RFID system is presented under the Nakagami-m fading channel. First, the comparison of different reader structures is shown in SISO RFID. Second, the benefits of multiple antennas at the transmit or receive ends are discussed, and then, the average RIR will be shown in two cases of reader structures (mono- and bistatic), the correlation between antennas (fully correlated and uncorrelated), and the number of antennas in a MIMO-RFID system. Third, relative increments of average RIR are depicted according to the number of antennas. Finally, under uncorrelated Rayleigh fading, the influences of reader-ro-reader interference and imperfect channel estimation on the average RIR are shown in the MIMORFID system with MRC. In these numerical results, it is assumed that the reader supports a 50-kb/s data rate using FM0 encoding [34] and the 600-kHz channel bandwidth specified by South Korean regulations [35]. Moreover, P0 and γ in the pathloss model are set to −31.6 dB and 3.0 [36], [37], respectively. All other parameters used in the analysis are summarized in Table I.

Fig. 2(a) shows the average RIR results according to the shaping factor m in the Nakagami fading channel for both mono- and bistatic structures. The results show that the average RIR can increase as the Nakagami shaping factor m increases and that the monostatic structure has a longer average RIR than the bistatic one. The gap for the different structures is expected to decrease at higher m. Here, when m = 1 (0 dB), Nakagami fading becomes Rayleigh fading, and when m → ∞, the channel becomes an impulse (no fading). From this characteristic of Nakagami fading, it was found that a ratio of the LOS component leads to the important influence to the change of the average RIR and that the lower bound of the average RIR is formed during Rayleigh fading. On the other hand, Fig. 2(b) shows the cumulative distribution function (cdf) of the instantaneous RIR in (7) under Rayleigh fading (m = 0 dB). In this result, it was shown that the change of an interrogation range according to the randomness of channels for the monostatic structure was larger than that for the bistatic one. This is attributed to the increased tightening of the cdf of interrogation range due to the diversity gain for the separation between the transmit and receive antennas. Thus, it is known that the bistatic structure retains a more reliable performance in rich scattering environments. To study the influence of multiple antennas on the RIR of RFID systems, we examined two cases of dual transmit antennas and dual receive antennas at the reader. Fig. 3(a) shows the average RIR for the bistatic reader with the transmit and receive arrays as a function of m-shaping factor. In the results, it is shown that the transmit array gain is consistently equal to the receive array gain in environments involving different antenna correlations and m parameters. In addition, the average RIR of the system with dual transmit or receive antennas is clearly preferred at all ranges of m. To assess the impact of correlation, Fig. 3(a) shows the average RIR according to the antenna correlation at the reader, i.e., uncorrelated and fully correlated. It can be seen that the array gain for dual antennas is smaller in the fully correlated case than in the uncorrelated case, and the impact is less significant in the large-m region.

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Fig. 2. Plots of the characteristics for the interrogation range in Nakagami-m fading channels according to the different structures at the reader. In (a), each curve represents the average RIR as a function of m. In (b), cdf curves are plotted against the instantaneous RIR of (7), where channels are assumed by Rayleigh fading (m = 0 dB).

As expected, the average RIR of the reader with multiple antennas is much more sensitive to the correlation at low m than that at high m. In Fig. 3(b), the average RIRs for SISO- and M × M MIMO-RFID systems (M = 2, 3) are shown as a function of m. The result shows that the reader structures, antenna correlation, and randomness of the fading channel have influence on the average RIR as a whole. For the bistatic structure and Rayleigh fading (m = 0 dB), a 2 × 2 MIMO-RFID system has a maximum of 36% and 26% gains for the average RIR in uncorrelated and fully correlated channels, respectively. For these environments, moreover, the results show that a 3 × 3 MIMO-RFID system can achieve a 60% larger gain for the average RIR compared to the SISO-RFID system. As mentioned before, the employment of multiple antennas at the reader causes the received SNR to change favorably and contributes to the improvement of RIR. However, the results

Fig. 3. Plot of the average RIR as a function of m for the different array antennas at the reader. (a) Comparison of the average RIR between SISO (Mt = 1, Mr = 1) and dual transmit or receive array (Mt = 2, Mr = 1 or Mt = 1, Mr = 2). (b) Plot of the average RIR of the MIMO-RFID system with MRC as a function of m.

in Fig. 3 depend very much on the operating environments, such as the system parameters in Table I. To get a sense of this, Fig. 4 shows the average RIR for multiple antennas as a fraction of that for SISO RFID under Rayleigh fading channels (m = 0 dB). In the results, the M × M MIMO-RFID system can achieve a much larger gain in the average RIR than the 1 × M or M × 1 array RFID system. The most significant change is seen as the antennas are added at the reader in an uncorrelated environment, and the gain for the average RIR is shown to reduce as multiple antennas are closely spaced. When M = 3, the transmit or receive array RFID systems have a 26% gain in uncorrelated channels and a 20% gain in fully correlated channels. For the 3 × 3 MIMO-RFID system, however, the uncorrelated and fully correlated channels show up to 60% and 44% gains with respect to the SISO-RFID system.

KIM et al.: RIR OF A UHF MIMO-RFID SYSTEM IN NAKAGAMI-m FADING CHANNELS

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Fig. 4. Average RIR for RFID with multiple antennas as a fraction of that for SISO-RFID under Rayleigh fading channels (m = 0 dB).

So far, we have compared the average RIR of MIMORFID systems with one of a SISO-RFID system under the assumptions of perfect channel estimation and no interference. Now, reader-to-reader interference and imperfect channel estimation are taken into consideration in analyzing the average RIR. The adverse effect of reader-to-reader interference on the average RIR of UHF RFID systems with MRC is shown in Fig. 5(a), where uncorrelated Rayleigh fading channels are assumed. The result shows that the reduction of average RIR occurs gradually as the number of interferers MA increases. When MA = 50, particularly, its value decreases to 54% of the average RIR of UHF RFID systems without reader-to-reader interference (MA = 0). Moreover, given MA , the reduction ratio (= average RIR with MA interferers/average RIR without interferers) of the average RIR has a fixed value for the arbitrary number of antennas M . Mathematically, this can be explained as follows. Under the assumption of uncorrelated Rayleigh fading channels, the interference power is independent of the channels between the desired reader and a tag, and thus, the influence of interference on the average RIR is only related to MA , not M , as shown in (27). This means that the use of multiple antennas at the transmitter and receiver cannot lead to changes in the average interference power. Fig. 5(b) shows the influence of imperfect channel estimation on the average RIR of UHF RFID systems with MRC, where the x-axis is the correlation coefficient ρ. From the results, it is observed that the presence of decorrelation between an actual channel vector and its estimate deteriorates the average RIR of MIMO-RFID systems. Particularly, when a true channel and its estimate are independent (ρ = 0), the M × M MIMO-RFID system with MRC can no longer contribute to an increase in the average RIR, and thus, their average RIRs equal to the average RIR of the SISO-RFID system for any M . It was also found that the average RIR is not concerned with ρ in the SISO-RFID system. This result is expected because both interference and noise experience the same weighting factors, so there is no change in the SINR results.

Fig. 5. Influence of reader-to-reader interference and imperfect channel estimation on the average RIR of UHF RFID systems with MRC in uncorrelated Rayleigh fading channels. (a) Comparison of the average RIR between SISOand M × M MIMO-RFID systems as a function of the number of interferers. (b) Comparison of the average RIR as a function of the normalized correlation coefficient between the actual channel vector and its estimate, ρ(= ρf = ρb ).

VI. C ONCLUSION In the pinhole channel composed of two Nakagami-m distributed links, the average RIRs have been derived for SISOand MIMO-RFID systems. The use of multiple antennas can improve the received SNR at the reader, which results in an increment of average RIR according to the number of antennas, correlation, and system structures. The results have demonstrated that the gain of the average RIR for a MIMO-RFID system leads to its maximum value in the uncorrelated Rayleigh environment and improves as the number of antennas increases. For the average RIR of the 3 × 3 MIMO-RFID system, the uncorrelated and fully correlated channels show up to 60% and 44% gains with respect to the SISO-RFID system. Despite the high complexity and cost of implementation of the antenna array and channel estimation, it can finally be concluded that the

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MIMO-RFID system with MRC provides noteworthy improvement for the statistical characteristics of RIR. Future research on this topic could include measurement of the average RIR of the M × M MIMO-RFID system with MRC and analysis of the influence of reader-to-reader interference and imperfect channel estimation in an arbitrarily correlated Nakagami-m fading channel. R EFERENCES [1] K. Finkenzeller, RFID Handbook: Fundamentals and Applications in Contactless Smart Cards and Identification. Chichester, U.K.: Wiley, 2003. [2] V. Vyatkin, Z. Salcic, P. S. Roop, and J. Fitzgerald, “Now that’s smart!,” IEEE Ind. Electron. Mag., vol. 1, no. 4, pp. 17–29, 2007. [3] Y. Bendavid, E. Lefebvre, L. A. Lefebvre, and S.F. Wamba, “B-to-B E-Commerce: Assessing the impacts of RFID technology in a five layer supply chain,” in Proc. IEEE HICSS, Waikoloa, HI, 2007, p. 143. [4] L. L. Bello, O. Mirabella, and A. Raucea, “Design and implementation of an educational testbed for experiencing with industrial communication networks,” IEEE Trans. Ind. Electron., vol. 54, no. 6, pp. 3122–3133, Dec. 2007. [5] M. Niitsuma, H. Hashimoto, and H. Hideki, “Spatial memory as an aid system for human activity in intelligent space,” IEEE Trans. Ind. Electron., vol. 54, no. 2, pp. 1122–1131, Apr. 2007. [6] S. Park and S. Hashimoto, “Autonomous mobile robot navigation using passive RFID in indoor environment,” IEEE Trans. Ind. Electron., vol. 56, no. 7, pp. 2366–2373, Jul. 2009. [7] C. Linda and S. F. Wamba, “An inside look at RFID technology,” J. Technol. Manag. Innovation, vol. 2, no. 1, pp. 114–128, Jan. 2007. [8] D. Y. Kim, B. J. Jang, H. G. Yoon, J. S. Park, and J. G. Yook, “Effects of reader interference on the RFID interrogation range,” in Proc. 37th EuMC, Oct. 2007, pp. 728–731. [9] D. Y. Kim, H. G. Yoon, B. J. Jang, and J. G. Yook, “Interference analysis of UHF RFID systems,” Prog. Electromagn. Res. B, vol. 4, pp. 115–126, 2008. [10] D. Y. Kim, H. G. Yoon, B. J. Jang, and J. G. Yook, “Effects of reader-toreader interference on the UHF RFID interrogation range,” IEEE Trans. Ind. Electron., vol. 56, no. 7, pp. 2337–2346, Jul. 2009. [11] J. D. Griffin and G. D. Durgin, “Link envelope correlation in the backscatter channel,” IEEE Commun. Lett., vol. 11, no. 9, pp. 735–737, Sep. 2007. [12] J. D. Griffin and G. D. Durgin, “Gains for RF tags using multiple antennas,” IEEE Trans. Antennas Propag., vol. 56, no. 2, pp. 563–570, Feb. 2008. [13] M. A. Ingram, M. F. Demirkol, and D. Kim, “Transmit diversity and spatial multiplexing for RF links using modulated backscatter,” in Proc. ISSSE, Tokyo, Japan, Jul. 2001. [14] M. Buettner and D. Wetherall, “An empirical study of UHF RFID performance,” in Proc. MobiCom, San Francisco, CA, Sep. 2008, pp. 223–234. [15] D. W. Engels and S. E. Sarma, “The reader collision problem,” in Proc. IEEE Int. Conf. Syst., Man, Cybern., 2002, vol. 3, pp. 92–97. [16] J. Waldrop, D. W. Engels, and S. E. Sarma, “Colorwave: An anticollision algorithm for the reader collision problem,” in Proc. IEEE Wireless Commun. Netw. Conf., Mar. 2003, pp. 1206–1210. [17] J. Ho, D. W. Engels, and S. E. Sarma, “HiQ: A hierarchical Q-learning algorithm to solve the reader collision problem,” in Proc. Int. SAINTW, 2006, pp. 88–91. [18] B. Carbunar, M. K. Ramanathan, M. Koyuturk, C. Hoffman, and A. Grama, “Redundant reader elimination in RFID systems,” in Proc. 2nd Annu. IEEE Commun. Soc. Conf. Sens. and Ad Hoc Commun. Netw., 2005, pp. 176–184. [19] D. R. Hush and C. Wood, “Analysis for tree algorithms for RFID arbitration,” in Proc. ISIT, Cambridge, MA, 1998, p. 107. [20] Y. Cui and Y. Zhao, “Mathematical analysis for binary tree algorithm in RFID,” in Proc. IEEE Veh. Technol. Conf., May 2008, pp. 2725–2729. [21] J.-B. Eom, S.-B. Yim, and T.-J. Lee, “An efficient reader anticollision algorithm in dense RFID networks with mobile RFID readers,” IEEE Trans. Ind. Electron., vol. 56, no. 7, pp. 2326–2336, Jul. 2009. [22] M. Mi, M. H. Mickle, C. Capelli, and H. Swift, “RF energy harvesting with multiple antennas in the same space,” IEEE Antennas Propag. Mag., vol. 47, no. 5, pp. 100–106, Oct. 2005. [23] A. F. Mindikoglu and A.-J. van der Veen, “Separation of overlapping RFID signals by antenna arrays,” in Proc. IEEE ICASSP, Apr. 2008, pp. 2737–2740.

[24] D. Chizhik, G. J. Foschini, and R. A. Valenzuela, “Capacities of multielement transmit and receive antennas: Correlations and keyholes,” Electron. Lett., vol. 36, no. 13, pp. 1099–1100, Jun. 2000. [25] D. Kim, M. A. Ingram, and W. W. Smith, “Measurements of small-scale fading and path loss for long range RF tags,” IEEE Trans. Antennas Propag., vol. 51, no. 8, pp. 1740–1749, Aug. 2003. [26] M. Nakagami, “The m distribution—A general formula of intensity distribution of rapid fading,” in Reprint from Statistical Methods of Radio Wave Propagation. New York: Pergamon, 1960. [27] S. Kotz and J. W. Adams, “Distributions of sum of identically distributed exponentially correlated gamma variables,” Ann. Math. Stat., vol. 35, no. 1, pp. 277–283, 1964. [28] C. Mun, C. H. Kang, and H. K. Park, “Approximation of SNR statistics for MRC diversity in arbitrarily correlated Nakagami fading channels,” Electron. Lett., vol. 35, no. 4, pp. 266–267, Feb. 1999. [29] M. Kang and M.-S. Alouini, “A comparative study on the performance of MIMO MRC with and without cochannel interference,” in IEEE Trans. Commun., Aug. 2004, vol. 52, no. 8, pp. 1417–1425. [30] H.-S. Jo, H.-G. Youn, J. Lim, W.-G. Chung, and J.-G. Yook, “The coexistence of OFDM-based systems beyond 3G with fixed service microwave systems,” J. Commun. Netw. (KICS), vol. 8, no. 2, pp. 187–193, Jun. 2006. [31] J. K. Cavers, “An analysis of pilot symbol assisted modulation for Rayleigh fading channels,” IEEE Trans. Veh. Technol., vol. 40, no. 4, pp. 686–693, Nov. 1991. [32] D. Boss, K. D. Kammeyer, and T. Petermann, “Is blind channel estimation feasible in mobile communication systems? A study based on GSM,” IEEE J. Sel. Areas Commun., vol. 16, no. 8, pp. 1479–1492, Oct. 1998. [33] M. J. Gans, “The effect of Gaussian error in maximal ratio combiners,” IEEE Trans. Commun. Technol., vol. COM-19, no. 4, pp. 492–500, Aug. 1971. [34] EPCglobal, EPCglobal Standard Specification EPC Radio-Frequency Identity Protocols Class-1 Generation-2 UHF RFID Protocol for Communications at 860 MHz–960 MHz Version 1.0.92004. [35] Korea Communication Commission (KCC), KCC Announcement, no. 2008-137, part 99, Regulations for Radio Communications Facilities, Dec. 2008. [36] T. S. Rappaport, Wireless Communications: Principles and Practice, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, 2002. [37] K. Tang, K. Man, and S. Kwong, “Wireless communication network design in IC factory,” IEEE Trans. Ind. Electron., vol. 48, no. 2, pp. 452– 459, Apr. 2001.

Do-Yun Kim (S’05) was born in Seoul, Korea, on November 13, 1979. He received the B.S. and M.S. degrees in electrical and electronics engineering from Yonsei University, Seoul, in 2002 and 2004, respectively, where he is currently working toward the Ph.D. degree in the Department of Electrical and Electronic Engineering. His current research interests include the capacity of wireless channels and networks, space–time processing in multiple-input–multiple-output systems, and channel modeling.

Han-Shin Jo (S’05) was born in Korea. He received the B.S., M.S., and Ph.D. degrees in electrical and electronics engineering from Yonsei University, Seoul, Korea, in 2001, 2004, and 2009, respectively. He is currently a Postdoctoral Research Fellow in the Department of Electrical and Computer Engineering, The University of Texas at Austin. His research interests include capacity analysis and resource optimization in femtocell and wireless ad hoc networks, and coexistence of mobile communication systems beyond the third generation and mobile radio propagation channels.

KIM et al.: RIR OF A UHF MIMO-RFID SYSTEM IN NAKAGAMI-m FADING CHANNELS

Hyungoo Yoon (S’95–M’02) was born in Seoul, Korea, on February 6, 1972. He received the B.S., M.S., and Ph.D. degrees in electronics engineering from Yonsei University, Seoul, in 1995, 1997, and 2002, respectively. He is currently an Associate Professor in the Department of Computer and Electronic Engineering, Myongji College, Seoul. His main research interests include wireless communication systems, radio resource management, and channel modeling.

Cheol Mun (S’97–M’01) was born in Mokpo, Korea. He received the B.S., M.S., and Ph.D. degrees in electronics engineering from Yonsei University, Seoul, Korea, in 1995, 1997, and 2001, respectively. From March 2001 to February 2002, he was with Samsung Electronics Company, Ltd., Suwon, Korea, as a Research Engineer. He is currently an Assistant Professor in the Department of Electronic Communications Engineering, Chungju National University, Chungbuk, Korea. His main research interests include the design and analysis of communication systems, such as multiple-input–multiple-output and cooperative communication systems.

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Byung-Jun Jang (S’90–M’96) received the B.S., M.S., and Ph.D. degrees in electronic engineering from Yonsei University, Seoul, Korea, in 1990, 1992, and 1997, respectively. From 1995 to 1999, he was with LG Electronics, Seoul, where he developed code-division multipleaccess and digital enhanced cordless telecommunication RF modules. From 1999 to 2005, he was with the Electronics and Telecommunications Research Institute, Daejeon, Korea, where he performed research in the fields of satellite RF components and monolithic microwave integrated circuits. In 2005, he joined Kookmin University, Seoul, where he is currently with the Department of Electrical Engineering. He is currently interested in the areas of RF circuit design and system analysis, radio-frequency-identification interference modeling, and biosensor design.

Jong-Gwan Yook (S’89–M’97) was born in Seoul, Korea. He received the B.S. and M.S. degrees in electronics engineering from Yonsei University, Seoul, in 1987 and 1989, respectively, and the Ph.D. degree from the University of Michigan, Ann Arbor, in 1996. He is currently a Professor in the Department of Electrical and Electronic Engineering, Yonsei University. His main research interests are in the areas of theoretical/numerical electromagnetic modeling and characterization of microwave/millimeter-wave circuits and components, very large scale integration and monolithic-microwave integrated-circuit interconnects, RF MEMS devices using frequency- and time-domain full-wave analysis methods, space–time processing in multipleinput–multiple-output systems, channel modeling, and development of numerical techniques for the analysis and synthesis of high-speed high-frequency circuits for wireless communication applications, with emphasis on parallel/ super computing.