Estimation and Equalization of Fiber-Wireless Uplink for ... - IEEE Xplore

IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 58, NO. 6, JUNE 2010

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Estimation and Equalization of Fiber-Wireless Uplink for Multiuser CDMA 4G Networks Stephen Z. Pinter, Student Member, IEEE, and Xavier N. Fernando, Senior Member, IEEE

Abstract—Fiber-wireless (Fi-Wi) access fronts can support 100s of Mb/s envisioned by 4G networks. However, a major issue associated with Fi-Wi links is the nonlinear distortion of the radio-over-fiber (ROF) link coupled with the multipath dispersion of the wireless channel. Estimation and subsequent equalization of the concatenated fiber-wireless channel needs to be done, especially at high bit rates. The uplink is severely affected due to large fluctuations in the radio signal. This paper proposes an estimation and subsequent equalization algorithm for the Fi-Wi CDMA uplink. The estimation employs the properties of pseudo noise (PN) sequences and the equalization uses a novel Hammerstein type decision feedback equalizer (HDFE). The estimation and equalization are performed in the presence of multiple access interference (MAI) and wireless and optical channel noise. The cumulative effects of multiuser interference, multipath dispersion, nonlinear distortion, and noise are all considered in our analysis. Correlation properties of white-noise like PN sequences enable decoupling of the linear (wireless) and nonlinear (optical) channel portions. Furthermore, we propose a unique algorithm to mitigate MAI. Numerical evaluations show a good estimation and equalization of both the linear and nonlinear channels. Bit error rate (BER) simulations show that this algorithm leaves only small residual MAI. Index Terms—Fiber-wireless systems, radio over fiber, code division multiple access, parameter estimation, identification, pseudo noise process, multiple access interference, channel estimation and equalization.

I. I NTRODUCTION

F

OURTH generation (4G) wireless systems promise data rates of up to 1 Gb/s over the air interface for a truly interactive wireless multimedia experience [1]. However, many technical issues need to be resolved before providing these high data rates. One fundamental concern is the RF power required for transmitting these extremely high bit rates. A simple investigation shows that since the energy per bit is inversely proportional to the bit rate, the received signal to noise ratio will proportionally decrease with bit rate even with the same transmitted power and path loss. The increment of free space path loss with carrier frequency makes the situation worse at high carrier frequencies which some 4G operators may want to use. Furthermore, the number of symbols that will experience inter symbol interference (ISI) under the same multipath conditions will also significantly increase at these high bit rates. Power consumption of hand held devices will be much higher in this scenario due to the increased transmit

Paper approved by J. A. Salehi, the Editor for Optical CDMA of the IEEE Communications Society. Manuscript received February 24, 2009; revised November 9, 2009. The authors are with Ryerson University, Department of Electrical and Computer Engineering, 350 Victoria Street, Toronto, Ontario, Canada M5B 2K3 (e-mail: {spinter, xavier}@ieee.org). Digital Object Identifier 10.1109/TCOMM.2010.06.090114

power and additional signal processing requirements. All these issues suggest that the cell size should be significantly smaller in 4G networks. Some authors suggest multi-hop architecture to address this cell size limit [2]. However, multi-hop architecture severely limits the throughput in high-speed communication links. Traditional micro cell solutions will be costly due to the cost of base station equipment [3]. Fiber radio systems, on the other hand, can provide short range wide band air interfaces by bringing the radio access point closer to the user at relatively low cost [4]. These fiber-wireless (Fi-Wi) networks can be rapidly deployed and support immense traffic. For example, BriteCell𝑇 𝑀 , a Fi-Wi network installed for the Sydney 2000 Olympics made hundreds of thousands of mobile phone calls possible. It was estimated that over 500,000 wireless calls were made from Olympic Park venues using more than 500 remote antenna units on the opening day. Over 175,000 calls were made in the minutes leading up to the opening ceremony [5]. Another advantage of Fi-Wi networks is that radio resources can be allocated when and where it is most needed. The possibility of using existing fiber for Fi-Wi networks makes it even more attractive. In this paper, we investigate and suggest performance improvements for a radio-over-fiber (ROF) based Fi-Wi solution that will support broadband access envisioned in 4G networks. Direct sequence code division multiple access (DS-CDMA) with proper equalization has been investigated for 4G uplink for a number of good reasons [6], [7]. Direct sequence CDMA does not require synchronization among users and enables low power transmission. Therefore, in this paper we assume a pseudo noise (PN) sequence based DS-CDMA uplink. A. Radio-over-Fiber for 4G The basic Fi-Wi access architecture for 4G cellular networks is shown in Fig. 1. Radio-over-fiber, where an optical signal is modulated at radio frequencies and transmitted over an optical fiber ([8], [9]), provides the broadband link needed to bring the radio-access-point (RAP) closer to the user. In this scenario, the RAP provides wireless access to the user instead of conventional base stations. The RAP is connected to the central base station via the ROF link. Typically, the complexity, cost, and power consumption of the RAP is kept at a minimum in order to allow large scale deployment. This architecture significantly shortens the air interface and supports broadband services. The RAP performs RF-to-optical (uplink) and optical-toRF (downlink) conversions only. The baseband to RF modulation/demodultion is done at the central base station or at

c 2010 IEEE 0090-6778/10$25.00 ⃝

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TABLE I S YMBOL DESCRIPTIONS FOR F I -W I UPLINK .

Symbol 𝑥𝑗 (𝑛) ℎ𝑗 (𝑛) 𝑛𝑤(𝑗) (𝑛) 𝑞(𝑛) 𝐹 (⋅) 𝑛𝑜𝑝 (𝑛) 𝑟(𝑛)

Fig. 1.

Fiber-wireless cellular architecture.

the user handsets only. The optical fiber and the RAP handle RF/optical signals and not baseband. Hence, the baseband analysis and signal processing has to be done for the concatenated fiber-wireless system together. This is done at the central base station for the uplink. This concatenation makes the Fi-Wi CDMA link special and different than regular CDMA links. There are many studies around multiuser and iterative detection algorithms in CDMA systems [10]. The main difference in this paper is that here we estimate and equalize a multiuser CDMA system in a combined linear-nonlinear channel environment where multipath dispersion is coupled with nonlinear distortion. The noise is also added twice to the signal (at the optical receiver and the RF receiver). The important issues with Fi-Wi uplink transmission are: strong ISI, multiple access interference (MAI), nonlinear distortion, and noise. The ISI effect is severe because it is coupled with the nonlinear distortion of the optical link. The multipath wireless channel has been very well studied and will not be repeated here. We will briefly review the ROF link. In the ROF uplink, the RF signal from the air interface is converted to optical (E/O) typically in either a directly modulated laser diode or in an external modulator such as Mach-Zehnder modulator1. Unfortunately, both laser and external modulators are inherently nonlinear devices. Their mild and memoryless nonlinearity can be modeled with polynomials [11]. The light modulated at radio frequencies then travels over the fiber; the fiber dispersion and distortion can be ignored up to several tens of kilometers when the radio frequency is only a few GHz [12], [13]. The received optical signal at the central base station is then converted to RF with a photo detector2 . Therefore, major issues of the ROF link are 1 There 2 More

will be electrical noise added at the antenna front end. optical noise will be added at the photo detector.

Description input PN spreading sequence, 1 ≤ 𝑗 ≤ 𝑁 wireless channel impulse response, 1 ≤ 𝑗 ≤ 𝑁 wireless channel Gaussian noise, 1 ≤ 𝑗 ≤ 𝑁 signal sent to optical channel optical channel nonlinear function optical receiver Gaussian noise signal sent to central base station

mild nonlinear distortion, loss, and noise [14]. The loss and noise will determine the power budget and radio cell size. That is not our focus here. Developing an algorithm to handle the nonlinear distortion coupled with multipath dispersion is the focus of this paper. In the case of the Fi-Wi uplink, the system of interest consists of a linear part (wireless channel) followed by a mildly nonlinear part (ROF optical link)3 . This arrangement is considered a Wiener system. Some work has been done with similar classes of systems. In [16] (and the references therein) the Wiener model is analyzed in a single control signal (or single user) continuous-time environment. Correlation analysis was used to decouple the identification of the linear and nonlinear component subsystems. The use of PN sequences for estimation of the 4G Fi-Wi uplink is attractive because these spreading codes are already in place. Other Wiener system identification methods involve using orthogonal wavelet neural networks or frequency domain identification as in [17] and [18], respectively. The concept of Wiener representation and correlation analysis is applied to estimate the multiuser CDMA Fi-Wi uplink in this paper. The Fi-Wi uplink is equalized following the channel estimation using a novel decision feedback equalizer (DFE) enhanced with a unique polynomial nonlinear filter. Other approaches attempted to use a post nonlinearity recovery block by means of solving the laser rate equations [19] or low-cost predistortion circuits [20]. In these approaches, knowledge of the device parameters were needed. The drawback here is that device parameters are device dependent or sometimes not even available. Instead of focusing on compensation at the device level, we focus on compensation at the system level. With our approach, the nonlinearity is looked at in terms of its input-output signal characteristics. Therefore, it is device independent and the entire system can be adaptively modeled and variations can be tracked. Therefore, the goal in this paper is to first estimate the parameters of the Fi-Wi channel and then to devise an appropriate equalization and compensation scheme. This work is significantly different from previous work ([21], [22]) because we perform identification for an asynchronous multiuser CDMA system where each user encounters a different wireless channel. Therefore, we propose an algorithm to alleviate MAI first. The MAI mitigation algorithm uses an iterative technique to estimate channel impulse response (CIR). 3 This is different from [15] because here we consider a multipath wireless channel.

PINTER and FERNANDO: ESTIMATION AND EQUALIZATION OF FIBER-WIRELESS UPLINK FOR MULTIUSER CDMA 4G NETWORKS

Fig. 2.

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Fiber-wireless uplink in a multiuser CDMA environment with a separate wireless channel for each user and a single nonlinear (optical) channel.

The paper is organized as follows. Section II introduces the theoretical background for the multiuser Fi-Wi uplink. Section III describes important correlation relationships and an iterative technique for minimizing the effect of MAI that are required for successfully estimating the CIR of the multiuser Fi-Wi uplink. Section IV describes the theoretical background for estimating the optical channel. Section V presents the simulation results and discussion for the Fi-Wi uplink estimation. Section VI and VII present Fi-Wi uplink equalization techniques and the equalization simulation results and discussion. A summary of the work and general comments about the technique are discussed in Section VIII. II. S YSTEM M ODEL FOR M ULTIUSER F IBER -W IRELESS U PLINK In this section, the nonlinear multiuser Fi-Wi uplink will be analyzed in discrete-time. The multiuser CDMA environment with separate wireless channels for each user is shown in Fig. 2 (all signals used in analyzing the Fi-Wi uplink are shown in Table I). In the reverse link, each user generates an independent PN sequence. This signal is transmitted through a wireless channel (specific to that user) and subjected to independent wireless channel noise4 . At the RAP, the received multiuser RF signals are combined and transmitted through the nonlinear optical link. At the central base station the RF signal is recovered with additional optical receiver noise. This signal is down converted for baseband signal processing. The signal is subjected to a multitude of impairments: ISI from the wireless channels, different path loss (for each user) which affects dynamic range, addition of wireless and optical channel noise, MAI due to CDMA at the RAP, and carrier regrowth, inband distortion, and cross multiplication of terms, all resulting from the nonlinear optical link. 4 Different ‘initial seed’ settings are used during simulation to ensure independence.

First we define the system output. The summation of all wireless channels at the RAP in Fig. 2 can be written as 𝑞(𝑛) =

𝑁 ∑

[𝑥𝑗 (𝑛) ∗ ℎ𝑗 (𝑛) + 𝑛𝑤(𝑗) (𝑛)],

(1)

𝑗=1

where ‘ ∗ ‘ is the convolution operator and 𝑁 is the number of PN sequences, and hence the number of users. According to the theorem of Weierstrass [23], any function which is continuous within an interval may be approximated to any required degree of accuracy by polynomials in this interval. So, after the nonlinear channel, the output of the Fi-Wi uplink is, 𝑟(𝑛) = =

𝑙 ∑ 𝑘=1 𝑙 ∑

𝐴𝑘 𝑞 𝑘 (𝑛) + 𝑛𝑜𝑝 (𝑛) 𝐴𝑘

𝑁 (∑

[𝑥𝑗 (𝑛) ∗ ℎ𝑗 (𝑛) + 𝑛𝑤(𝑗) (𝑛)]

)𝑘

+ 𝑛𝑜𝑝 (𝑛),

𝑗=1

𝑘=1

(2)

giving the final output as 𝑟(𝑛) =

𝑙 ∑ 𝑘=1

𝐴𝑘

𝑁 ( {∑

∞ ∑

𝑗=1

𝑚1 =−∞

...

∞ ∑

𝑘 ∏

𝑚𝑘 =−∞ 𝑖=1

)} ℎ𝑗 (𝑚𝑖 )𝑥𝑗 (𝑛 − 𝑚𝑖 ) + 𝑛𝑘𝑤(𝑗) (𝑛) + CMT + 𝑛𝑜𝑝 (𝑛), (3) where the cross multiplied terms (CMT) can be found using the multinomial theorem [24] with [2×𝑁 ] terms and 𝑙th order. The output can also be written as a summation of the output of the isolated 𝑙𝑡ℎ order kernel as 𝑟(𝑛) = 𝑤1 (𝑛) + 𝑤2 (𝑛) + ... + 𝑤𝑙 (𝑛) + 𝑛𝑜𝑝 (𝑛),

(4)

where CMT is included in the terms 𝑤1 (𝑛), 𝑤2 (𝑛), ..., 𝑤𝑙 (𝑛). Expressing the output in the form of equation (4) is a crucial step in developing the correlation relationships that follow. The linear and nonlinear channels can be estimated by studying the

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correlation between the output 𝑟(𝑛) and the input 𝑥𝑗 (𝑛), as well as the output of the 1st order kernel 𝑤1 (𝑛) and the input 𝑥𝑗 (𝑛). III. C ORRELATION R ELATIONSHIPS The next step in the estimation of the Fi-Wi channel is to further process the above defined input-output relations by using correlation properties of PN sequences. The analysis presented in this section is significantly different from a previous work ([21], [22]) because here the identification is performed for a multiuser CDMA system where each user encounters a different wireless channel. Furthermore, we develop an algorithm to alleviate MAI. A. Generalized input-output correlation

However, if 𝑧𝑟 (𝜎) is evaluated directly as defined above, ∑ℜ 𝑙 the terms 𝑘=2 ℜ𝑧𝑤𝑘 (𝜎) give rise to anomalies associated with multidimensional autocovariances of PN sequences [16]. This problem can be overcome by isolating ℜ𝑧𝑤1 (𝜎) using multilevel input testing. It should be noted that if the channel were linear there would be no need to isolate ℜ𝑧𝑤1 (𝜎) because ℜ𝑧𝑤1 (𝜎) = ℜ𝑧𝑟 (𝜎). Multilevel testing [16] enables the extraction of ℜ𝑧𝑤1 (𝜎) from ℜ𝑧𝑟 (𝜎). This step is crucial for successful estimation of the wireless channel. Multilevel testing is implemented at the RAP by using the signal 𝛼𝑚 𝑞(𝑛), where 𝛼𝑚 ∕= 𝛼𝑙 ∀ 𝑚 ∕= 𝑙, and repeated 𝑙 times. In other words, multilevel input testing requires the transmission of 𝑙 inputs, each with a different input amplitude. For example, with a 3rd order nonlinearity the output of the multiuser system can be written as 𝑟(𝑛) = 𝐴1 𝑞(𝑛) + 𝐴2 𝑞 2 (𝑛) + 𝐴3 𝑞 3 (𝑛) + 𝑛𝑜𝑝 (𝑛)

A commonly defined input 𝑧(𝑛), where 𝑧(𝑛) = 𝑥𝑗 (𝑛), is used in the derivation of the correlation relatioships. The cross covariance between the input 𝑧(𝑛) and the output 𝑟(𝑛) can then be written as5

With the multilevel input 𝛼1 𝑞(𝑛), the above equation becomes

ℜ𝑧𝑟 (𝜎) = (𝑟(𝑛) − 𝑟(𝑛))(𝑧(𝑛 − 𝜎) − 𝑧(𝑛 − 𝜎)).

𝑟𝛼1 (𝑛) = 𝐴1 𝛼1 𝑞(𝑛) + 𝐴2 𝛼21 𝑞 2 (𝑛) + 𝐴3 𝛼31 𝑞 3 (𝑛) + 𝑛𝑜𝑝 (𝑛)

(5)

The cross covariance relationship is used extensively throughout this section. From this point onward 𝑟(𝑛), 𝑞(𝑛), 𝑛𝑜𝑝 (𝑛), 𝑧(𝑛), and 𝑥𝑗 (𝑛), 𝑛𝑤(𝑗) (𝑛) for 1 ≤ 𝑗 ≤ 𝑁 will refer to their respective signals with the mean removed. In some cases [23], a mean level is added to the input to ensure that both odd and even terms in equation (4) contribute to the 1st order inputoutput cross correlation. However, in this case, only the output of the 1st order kernel is of interest (discussed shortly) and hence a mean level is not needed. With means removed, the cross covariance can be written as, ℜ𝑧𝑟 (𝜎) = 𝑟(𝑛)𝑧(𝑛 − 𝜎).

(6)

Substituting equation (4) into the above equation and simplifying gives, ℜ𝑧𝑟 (𝜎) = [𝑤1 (𝑛) + 𝑤2 (𝑛) + ... + 𝑤𝑙 (𝑛) + 𝑛𝑜𝑝 (𝑛)][𝑧(𝑛 − 𝜎)] = 𝑤1 (𝑛)𝑧(𝑛 − 𝜎) + 𝑤2 (𝑛)𝑧(𝑛 − 𝜎) + ... +𝑤𝑙 (𝑛)𝑧(𝑛 − 𝜎) + 𝑛𝑜𝑝 (𝑛)𝑧(𝑛 − 𝜎) = 𝑤1 (𝑛)𝑧(𝑛 − 𝜎) + 𝑤2 (𝑛)𝑧(𝑛 − 𝜎) + ... + 𝑤𝑙 (𝑛)𝑧(𝑛 − 𝜎) + 𝑛𝑜𝑝 (𝑛)𝑧(𝑛 − 𝜎) = ℜ𝑧𝑤1 (𝜎) + ℜ𝑧𝑤2 (𝜎) + ... + ℜ𝑧𝑤𝑙 (𝜎) + ℜ𝑧𝑛𝑜𝑝 (𝜎), (7) which can be written in a more compact form as ℜ𝑧𝑟 (𝜎) =

𝑙 ∑

ℜ𝑧𝑤𝑘 (𝜎) + ℜ𝑧𝑛𝑜𝑝 (𝜎).

(8)

𝑘=1

Assuming the input PN sequence and noise process to be statistically independent, i.e., 𝑛𝑜𝑝 (𝑛)𝑧(𝑛 − 𝜎) = 0 ∀ 𝜎, the term ℜ𝑧𝑛𝑜𝑝 (𝜎) becomes negligible. Equation (8) then becomes, 𝑙 ∑ ℜ𝑧𝑤𝑘 (𝜎). (9) ℜ𝑧𝑟 (𝜎) = 𝑘=1 5 Note that the near-far problem of transmission is not taken into account here, it shall be considered in a separate study.

= 𝑤1 (𝑛) + 𝑤2 (𝑛) + 𝑤3 (𝑛) + 𝑛𝑜𝑝 (𝑛).

(10)

= 𝛼1 𝑤1 (𝑛) + 𝛼21 𝑤2 (𝑛) + 𝛼31 𝑤3 (𝑛) + 𝑛𝑜𝑝 (𝑛), (11)

which when used to find ℜ𝑧𝑟 (𝜎) gives the following modified form of equation (9): ℜ𝑧𝑟𝛼𝑚 (𝜎) =

𝑙 ∑

𝛼𝑘𝑚 ℜ𝑧𝑤𝑘 (𝜎),

𝑚 = 1, 2, ..., 𝑙

(12)

𝑘=1

where 𝑟𝛼𝑚 is the response of the system to multilevel inputs. An important condition for nonlinear system identification using multilevel inputs is that the number of levels shall be equal to or greater than the highest polynomial order (𝑙). Representing equation (12) in matrix form gives, ⎤⎡ ⎤ ⎡ ⎤ ⎡ ℜ𝑧𝑟𝛼1 (𝜎) ℜ𝑧𝑤1 (𝜎) 𝛼1 𝛼21 . . 𝛼𝑙1 ⎢ℜ𝑧𝑟𝛼 (𝜎)⎥ ⎢𝛼2 𝛼22 . . 𝛼𝑙2 ⎥ ⎢ℜ𝑧𝑤2 (𝜎)⎥ 2 ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥=⎢ . ⎥ . (13) ⎢ ⎢ . . . . . . ⎥ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎦ ⎣ . ⎦ ⎣ . . . . . . ⎦⎣ ℜ𝑧𝑟𝛼𝑙 (𝜎) ℜ𝑧𝑤𝑙 (𝜎) 𝛼𝑙 𝛼2𝑙 . . 𝛼𝑙𝑙 To check the above 𝛼 matrix into two matrices as follows ⎤⎡ ⎡ 1 𝛼1 0 . . 0 ⎢ 0 𝛼2 0 . 0 ⎥ ⎢1 ⎥⎢ ⎢ ⎢ ⎢ . 0 . . 0⎥ ⎥ ⎢. ⎢ ⎦ ⎣ . . . . . ⎣. 0 0 . . 𝛼𝑙 1

for singularities, it is divided 𝛼1 𝛼2 . . 𝛼𝑙

𝛼21 𝛼22 . . 𝛼2𝑙

⎤ . 𝛼𝑙−1 1 ⎥ . 𝛼𝑙−1 2 ⎥ . . ⎥ ⎥. . . ⎦ . 𝛼𝑙−1 𝑙

(14)

The matrix on the left side of (14) is nonsingular for 𝛼𝑚 ∕= 0. The matrix on the right side of (14) is the Vandermonde matrix which has a non-zero determinant given by ∏ (𝛼𝑗 − 𝛼𝑖 ), (15) 1≤𝑖 20 dB in order to give an acceptable identification. Therefore, an SNR of 25 dB (i.e., a Gaussian noise variance of 0.003162) was used in all simulations. All user curves were included in Figs. 4 and 5 to show that the algorithm works well for all the users. Fig. 4. Normalized error between the actual channel impulse response (CIR) and the estimated CIR as a function of the number of iterations for 10 users in an ROF microcell.

Figure 3 shows the actual, initial, and iterated CIR estimates for a representative channel of the 1st user given by, ℎ1 (𝑛) = 0.07𝛿(𝑛) − 0.21𝛿(𝑛 − 5) − 0.5𝛿(𝑛 − 9)+ 0.72𝛿(𝑛 − 12) + 0.36𝛿(𝑛 − 16) − 0.21𝛿(𝑛 − 19)+ 0.065𝛿(𝑛 − 23) − 0.065𝛿(𝑛 − 27). (32) In section V-C, it will be shown that the iterated CIR estimate translates into a much more accurate estimate of the polynomial. This is mainly because the iterative algorithm is able to remove small non-zero erroneous peaks and better estimate the actual CIR peaks. Due to the interconnected effect, even a small improvement in the CIR estimate goes a long way in the polynomial estimate. Figure 4 shows 𝜌 versus the number of iterations for ten different users (i.e., 10 various CIRs). From this figure it is clear that after just 2 iterations there is a significant decrease in 𝜌. As an example, the quality of fit for user 10 improves by 94.83% over the initial CIR error, i.e., 𝜌 improves from 2.634 × 10−3 to 0.1361 × 10−3 . Further iterations (> 3)

C. Fiber link identification Investigations presented in [27] showed that the laser diode nonlinearity can be modeled with a saturating third order polynomial. By running curve fitting algorithms on measured ROF link characteristics [28] an expression for the polynomial can be written as, 𝑟(𝑛) = −0.35𝑞 3(𝑛) + 𝑞(𝑛),

0 ≤ 𝑞(𝑛) ≤ 1.

(33)

The algorithm shall identify this polynomial. The fit of the nonlinear identification depends on how much data is available, and so it is desired to have the input cover a large dynamic range. This is achieved by using a long PN sequence and strong multipath conditions. Figure 6 shows the estimated polynomial (with and without using iterations). Iterations significantly increase the accuracy of the polynomial estimate. The SNR is 25 dB while estimating the CIR. This CIR is then used to estimate the polynomial. The estimated polynomial (using iterations) is 𝑟(𝑛) = −0.3559𝑞 3(𝑛) − 0.0095𝑞 2(𝑛) + 0.9716𝑞(𝑛), (34) which is accurate compared to the actual polynomial of equation (33). The mean squared error for the above case was 5.5954 × 10−4 .

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Fig. 6.


Estimated and actual nonlinearity of the ROF link.

Fig. 8.

Estimated and actual nonlinearity of the ROF link with 18 users.

equalization of the wireless channel of the 4G Fi-Wi uplink in this paper. The architecture of a DFE is shown in Fig. 9. Once the CIR is estimated, optimization of the DFE coefficients is a well established technique [29]. Hence, the feed forward filter (FFF) and feedback filter (FBF) taps can be readily determined.

Fig. 7. Normalized error between the actual channel impulse response (CIR) and the estimated CIR as a function of the number of iterations for 18 users in an ROF microcell.

D. Additional users The effect of additional users is shown in Figs. 7 and 8. With additional users it takes more iterations to decrease 𝜌 and the estimated polynomial starts to deviate further away. On average, 𝜌 = 1.212×10−4 with 18 users and 10 iterations, but 𝜌 = 3.012 × 10−5 with 10 users and 5 iterations. The difference between the two 𝜌’s is due to residual MAI. With 18 users the iterative algorithm still improves the CIR estimate, but relies more on the initial CIR estimate. The identification starts to degrade rapidly with more than 18 users. VI. F IBER - WIRELESS U PLINK E QUALIZATION The structure of the Fi-Wi equalizer is shown in Fig. 9. The receiver consists of a polynomial, which inverse models the optical link, followed by a DFE arrangement that compensates for the wireless channel dispersion. A. Wireless channel equalization by DFE Decision feedback equalizers are well known for equalizing wireless channels. Therefore, a DFE is implemented for

B. Linearization by series reversion Nonlinear channel compensation is implemented in this paper by including an inverse polynomial (or additional filter) prior to the aforementioned DFE using series reversion. Series reversion is one of the simplest techniques for nonlinear compensation and therefore has its limitations. A comprehensive treatment on series reversion is given by Tsimbinos in [30]. One main advantage of series reversion is simplicity; once 𝐹 (.) is known, finding the coefficients of 𝐺(.) is straightforward. Some disadvantages of series reversion include: 1) limited amplitude interval for inversion and 2) dependency on nonlinearity strength. In our case, series reversion provides a significant bit error rate (BER) improvement that will be shown in section VII. The polynomial 𝐹 [.] and the inverse polynomial 𝐺[.] are defined as 𝑟(𝑛) = 𝐹 [𝑞(𝑛)] + 𝑛𝑜𝑝 (𝑛) = 𝐴1 𝑞(𝑛) + 𝐴2 𝑞 2 (𝑛) + ... + 𝐴𝑙 𝑞 𝑙 (𝑛) + 𝑛𝑜𝑝 (𝑛)

(35)

and 𝑞˜(𝑛) = 𝐺[𝑟(𝑛)] = 𝑔1 𝑟(𝑛) + 𝑔2 𝑟2 (𝑛) + 𝑔3 𝑟3 (𝑛) + ... + 𝑔𝑙𝑖𝑛𝑣 𝑟𝑙𝑖𝑛𝑣 (𝑛)

(36)

respectively, where 𝑙 is the order of the polynomial and 𝑙𝑖𝑛𝑣 is the order of the inverse polynomial. The series reversion generated coefficients of the inverse polynomial 𝐺[.] are given in terms of 𝐴𝑘 and can be found in [31]. The order of the inverse polynomial 𝑙𝑖𝑛𝑣 must be selected to maximize linearity. The resulting compensation contains higher order nonlinear terms that produce distortion which is negligible at low signal amplitudes but become detrimental at high signal amplitudes [30]. This affects the compensation interval.


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Fig. 9. Block diagram for fiber-wireless uplink equalization scheme. Note that the inverse polynomial filter is common for all users while the DFE is different for each user.

VII. E QUALIZATION : S IMULATION R ESULTS AND D ISCUSSION The simulation parameters were the same as in section V-A. The channel is estimated under a multiuser environment and the equalization is done individually for each user. Additional parameter definitions include the order of the inverse polynomial 𝐺[.] and the number of DFE taps. Various inverse polynomial orders were tested and a 7th order polynomial was selected, which was the lowest order that gave the best linearization. The number of DFE taps were derived based on the memory of the CIR from Fig. 3, which has a memory (𝐿) of 28. In order to completely eliminate postcursor interference, the number of FBF taps must satisfy the condition 𝐾2 ≥ 𝐿 [29]. A common practice is to chose the number of FFF taps to be 2𝐿. Hence, 56 FFF taps and 28 FBF taps were chosen for the simulation. Figure 10 shows the BER performance of the estimation algorithm under two different scenarios: ‘Multiuser (MU) estimation’ (with details specified on the figure) when the equalization parameters are derived under the multiuser condition (the ones from section V) and ‘Single user (SU) estimation’ when the equalization parameters are derived with only a single user. The BER simulations were performed by transmitting a large number of frames in parallel by using the Matlab𝑇 𝑀 CDMA blockset. Therefore, we were able to simulate up to 10−10 BER. The following are some conclusions from Fig. 10. 1) Multiuser estimation without iterations and multiuser estimation without nonlinearity compensation gives unacceptable BER (traces marked by ∗ and △). 2) Multiuser estimation with five iterations (∘) is as good as single user estimation (⋄). This shows that our algorithm is able to almost completely cancel the MAI even in the presence of a nonlinearity with enough iterations (five in this case).

Fig. 10. BER of fiber-wireless uplink; multiuser estimation with 5 iterations comes very close to that of single user estimation.

3) The trace marked by □’s is the performance of the DFE in a linear channel. Better polynomial compensation methods will shift the BER (∘) to the left, i.e., towards the □ trace. However, this will require more complex polynomial compensation techniques than series reversion. A better nonlinearity compensation than series reversion such as orthogonal polynomials and orthogonal inverses can overcome some of the negative effects of residual terms [30]. This is left for future work. In general, BER performance depends on the severity of multipath conditions [29]. An acceptable BER for transmitting data is 10−6 , which our algorithm can achieve at an SNR of about 27 dB. This is comparable to the DFE BER curves obtained in [22] and [29].

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VIII. C ONCLUSION This paper presented an efficient algorithm for the identification and equalization of the uplink in a multiuser CDMA FiWi network. Estimation was performed using the correlation properties of PN sequences and equalization was performed using a unique equalizer that has separate linear and nonlinear modules. The algorithm also mitigates MAI with few iterations. This technique works in an asynchronous CDMA environment, which is ideal for a 4G uplink. A key advantage of this approach is the separate estimation and equalization of the linear and nonlinear portions. Generally, the nonlinearity estimation need not be repeated frequently because the nonlinearity of the ROF link is relatively static. It changes only if the temperature or other physical conditions of the optical transmitter significantly change. On the other hand, estimation and equalization of the linear wireless channel needs to be done frequently (depending on user mobility and channel coherence time). Furthermore, the wireless channel is different for each user while the nonlinear ROF link is common to all users. With the modular architecture of the proposed algorithm, the common polynomial filter weights can be kept constant while updating only the DFE coefficients. This is not the case with most other nonlinear equalization techniques. It was observed that the quality of the CIR estimate depended on the characteristics of the CIR. A major factor was the spread of energy among multipath arrivals. Simply stated, the more severe the multipath, the better the algorithm worked. Under mild multipath (strong line of sight) conditions, the nonlinearity estimation is poor. However, the algorithm always converges because the nonlinearity is always of saturation type. Finally, this approach can be used in any asynchronous CDMA link that experiences multipath dispersion followed by a memoryless mild nonlinearity. This nonlinearity might come from the low noise amplifier at the base station. This may sound strange because most research focuses on the nonlinearity of the transmitter amplifier. Nevertheless, in the CDMA uplink, the transmitter amplifier handles only a single user signal at the handset. The receiver amplifier handles a large multiuser signal and has a high linearity requirement. R EFERENCES [1] W. Tong, E. Sich, P. Zhu, and J. M. Costa, “True broadband multimedia experience," IEEE Microwave Mag., vol. 9, no. 4, pp. 64-71, 2008. [2] E. Kudoh and F. Adachi, “Power and frequency efficient wireless multihop virtual cellular concept," IEICE Trans. Commun., vol. E88-B, no. 4, pp. 1613-1621, 2005. [3] K. Kitao and S. Ichitsubo, “Path loss prediction formula in urban area for the fourth-generation mobile communication systems," IEICE Trans. Commun., vol. E91-B, no. 6, pp. 1999-2009, 2008. [4] A. Alphones, “Double-spread radio-over-fiber system for nextgeneration wireless technologies," J. Optical Netw., vol. 8, no. 2, pp. 225-234, 2009. [5] I. Information Gatekeepers, “Allen telecom’s radio-over-fiber technology powers mobile communications at Sydney 2000 Olympics," Fiber Optics Business, vol. 1, no. 1, pp. 1-2, Nov. 2000. [6] F. Adachi, D. Garg, S. Takaoka, and K. Takeda, “Broadband CDMA techniques," IEEE Wireless Commun., vol. 12, no. 2, pp. 8-18, 2005. [7] F. Khan, “Performance of orthogonal uplink multiple access for beyond 3G/4G systems," in Proc. IEEE Veh. Technol. Conf., Piscataway, NJ, USA, 2006, pp. 699-704.

[8] S. Z. Pinter and X. N. Fernando, “Fiber-wireless solution for broadband multimedia access," IEEE Canadian Rev., no. 50, pp. 6-9, Summer 2005. [9] X. N. Fernando and S. Z. Pinter, “Radio over fiber for broadband wireless access," PHOTONS – Technical Review of the Canadian Institute for Photonic Innovations, vol. 2, no. 1, pp. 24-26, Fall 2004. [10] M. K. Varanasi and B. Aazhang, “Multistage detection in asynchronous code-division multiple-access communications," IEEE Trans. Commun., vol. 38, no. 4, pp. 509-519, 1990. [11] X. N. Fernando and A. B. Sesay, “Higher order adaptive filter based predistortion for nonlinear distortion compensation of radio over fiber links," in Proc. IEEE International Conf. Commun., vol. 1, June 2000, pp. 367-371. [12] X. N. Fernando, “Signal processing for optical fiber based wireless access," Ph.D. dissertation, University of Calgary, 2001. [13] H. Al-Raweshidy and S. Komaki, Radio over Fiber Technologies for Mobile Communications Networks, 1st edition. Norwood, MA: Artech House Publishers, 2002. [14] X. Fernando and A. Anpalagan, “On the design of optical fiber based wireless access systems," in Proc. IEEE International Conf. Commun., vol. 6, June 2004, pp. 3550-3555. [15] X. N. Fernando and A. B. Sesay, “Adaptive asymmetric linearization of radio over fiber links for wireless access," IEEE Trans. Veh. Technol., vol. 51, no. 6, pp. 1576-1586, Nov. 2002. [16] S. A. Billings and S. Y. Fakhouri, “Identification of nonlinear systems using correlation analysis and pseudorandom inputs," International J. Syst. Science, vol. 11, no. 3, pp. 261-279, 1980. [17] Y. Fang and T. W. S. Chow, “Orthogonal wavelet neural networks applying to identification of Wiener model," IEEE Trans. Circuits Syst.I: Fundamental Theory Appl., vol. 47, no. 4, pp. 591-593, Apr. 2000. [18] A. H. Tan and K. Godfrey, “Identification of Wiener-Hammerstein models using linear interpolation in the frequency domain (LIFRED)," IEEE Trans. Instrumentation Measurements, vol. 51, no. 3, pp. 509-521, June 2002. [19] P. Raziq and M. Nakagawa, “Semiconductor laser’s nonlinearity compensation for DS-CDMA optical transmission system by post nonlinearity recovery block," IEICE Trans. Commun., vol. E79-B, no. 3, pp. 424-431, Mar. 1996. [20] L. Roselli, V. Borgioni, F. Zepparelli, F. Ambrosi, M. Comez, P. Faccin, and A. Casini, “Analog laser predistortion for multiservice radio-overfiber systems," J. Lightwave Technol., vol. 21, no. 5, pp. 1211-1223, May 2003. [21] X. N. Fernando and A. B. Sesay, “Fibre-wireless channel estimation using correlation properties of PN sequences," invited paper, Canadian J. Electrical Comput. Eng., vol. 26, no. 2, pp. 43-47, Apr. 2001. [22] ——, “A Hammerstein-type equalizer for concatenated fiber-wireless uplink," IEEE Trans. Veh. Technol., vol. 54, no. 6, pp. 1980-1991, Nov. 2005. [23] S. A. Billings and S. Y. Fakhouri, “Identification of a class of nonlinear systems using correlation analysis," Proc. IEE, vol. 125, no. 7, pp. 691697, July 1978. [24] K. H. Rosen, Discrete Mathematics and its Applications, 4th edition. New York: McGraw-Hill, 1999. [25] P. G. Flikkema, “Spread-spectrum techniques for wireless communication," IEEE Signal Process. Mag., vol. 14, no. 3, pp. 26-36, May 1997. [26] S. Verd´ u, Multiuser Detection. Cambridge, UK: Cambridge University Press, 1998. [27] W. I. Way, “Large signal nonlinear distortion prediction for a singlemode laser diode under microwave intensity modulation," J. Lightwave Technol., vol. LT-5, no. 3, pp. 305-315, Mar. 1987. [28] X. N. Fernando and A. B. Sesay, “Characteristics of directly modulated ROF link for wireless access," in Proc. Canadian Conf. Electrical Comput. Eng., vol. 4, pp. 2167-2170, 2004. [29] J. G. Proakis, Digital Communications, 4th edition. New York: McGrawHill, 2001. [30] J. Tsimbinos, “Identification and compensation of nonlinear distortion," Ph.D. dissertation, University of South Australia, 1995. [31] M. Abramowitz and I. A. Stegun, Eds., Handbook of Mathematical Functions, with Formulas, Graphs, and Mathematical Tables, 10th edition. Washington, DC: U.S. Department of Commerce, 1972.


Stephen Z. Pinter received the B.Eng. (Hons.) and M.A.Sc. degrees in electrical engineering from Ryerson University, Toronto, ON, Canada, in 2003 and 2005, respectively. He received the Ph.D. degree in biomedical engineering from the University of Western Ontario in affiliation with Robarts Research Institute, London, ON, Canada, in 2009. His research interests lie in the area of signal processing and system identification for fiber-wireless access. He is an IEEE student member and can be contacted at [email protected].

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Xavier N. Fernando (www.ee.ryerson.ca/˜fernando) is an Associate Professor and Board Member at Ryerson University, Toronto, Canada. He finished the PhD degree from the University of Calgary and TRLabs, Alberta, in 2001. He is the author of more than seventy research articles and a patent ’An Optical Fiber-Based Wireless Scheme for Wideband Multimedia Access’. He is leading the Ryerson Communications Research Lab with excellent funding. He has delivered invited talks worldwide in the area of Fi-Wi systems. He is on the editorial board of the IEEE COMSOC Wireless Communication Body of Knowledge (WEBOK, http://www.ieee-wcet.org/). He was a visiting scholar at the Institute of Advanced Telecommunications, IAT, Wales, UK in 2008. He has won several awards and prizes including IEEE Toronto Section exemplary service award in 2007 and Canadian best paper award in 2001. His students have won awards including Opto-Canada best poster award in 2003 and second prize in Sarnoff Symposium 2009. He is the Chair of the IEEE Communications Society, Toronto Chapter and won IEEE COMSOC Chapter Achievement Award for 2008. He was the General Chair for IEEE Toronto International Conference on Science and Technology for Humanity 2009.