A novel transform domain processing based channel estimation method for OFDM radio-over-fiber systems

Li Tao; Jianjun Yu; Qi Yang; Yufeng Shao; Junwen Zhang; Nan Chi

doi:10.1364/OE.21.007478

1. Introduction

Optical orthogonal frequency division multiplexing (OFDM) becomes a very attractive modulation scheme, because it exhibits high spectrum efficiency, flexible coding and strong tolerance towards channel impairments. In recent years, it has been widely utilized in 60 GHz Radio-over-fiber (RoF) systems, which have been considered as a promising candidate to provide multi-Gbps data rate [1-5]. OFDM modulation scheme could employ training symbols (TSs) as the overhead to perform channel estimation, which can provide the key information of the transmission channel, so the optical channel impairments caused by chromatic dispersion (CD) and polarization-mode dispersion (PMD) could be estimated easily. In order to increase the accuracy of channel estimation, which is mainly affected by optical noise in transmission link, time domain averaging based (TDA) [6] and frequency domain averaging (FDA) [7] based method are proposed. The former one averages the channel transfer function estimated by multiple TSs, but the disadvantage is that the required number of TSs is large and the estimation could hardly work when the transmission channel is poor. The latter one averages the estimated transfer function over multiple adjacent frequency domain subcarriers in the same TS. This method could improve the accuracy of channel estimation in the presence of large optical noise and reduce the requirement of the overhead, but inaccurate channel estimation occurs on the edge subcarriers because of the averaging windows are not symmetric, thus the system performance would be deteriorated when the considering number of OFDM neighboring subcarriers is decreased. In the wireless communication field, transform domain processing (TDP) based channel estimation method is proposed to overcome this problem, which benefits from the overhead reduction and identical channel estimation accuracy over the whole subcarriers [8].

In this paper, the TDP-based channel estimation method for OFDM RoF system is investigated theoretically. The system performances of three different kinds of channel estimation methods are compared. Then an 8 x 4.65 Gb/s multiple-user OFDM RoF system based on TDP-based channel estimation is demonstrated experimentally. The transmission performance of the TDP and TDA based channel estimation method is measured and the BER performance for all 8 wireless users is tested. Obviously TDP scheme can outperform TDA scheme with a sensitivity enhancement about 1.8 dB.

2. Principle

2.1 Theoretical analysis of TDP-based channel estimation

Figure 1 shows the schematic diagram of an OFDM RoF system over 60 GHz wireless link by utilizing photonic heterodyning up-conversion. The expression of the signal after intensity modulator can be given as

e (t) = e^{j ω_{c} t} \cdot (1 + γ s (t))

Where

s (t)

represents the generated OFDM signal,

ω_{c}

is the angular frequency of the chosen signal carriers from the generated multi-tone.

γ

is the modulation index of intensity modulator.

Fig. 1 The schematic diagram of OFDM RoF system. ECL: external cavity laser, TOF: tunable optical filter.

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After multiplexing with the beat carrier of a specified frequency spacing and fiber link, the signal at the output of optical band-pass filter can be expressed as

e_{o u t} (t) = (e (t) + e^{j (ω_{c} + ω_{r}) t}) \otimes h_{f} (t)

Here

ω_{r}

is the frequency spacing between the signal carrier and beat carrier.

h_{f} (t)

and

H_{f} (ω)

are the fiber channel response in time-domain and frequency-domain respectively, i.e.

h_{f} (t) = \frac{1}{2 π} \int_{- \infty}^{\infty} H_{f} (ω) \exp (j ω t) d ω

. “

\otimes

” is the symbol of convolution.

The PD at the receiver side works as an envelope detector for photonic up-conversion. The output photon current can be expressed as

\begin{array}{l} I_{P D} (t) = R \cdot e_{o u t} (t) \cdot e_{o u t}^{*} (t) \\ = R {| (1 + γ s (t)) \otimes h_{f} (t) + e^{j ω_{r} t} |}^{2} \\ = R [1 + {((1 + γ s (t)) \otimes h_{f} (t))}^{2} + 2 ((1 + γ s (t)) \otimes h_{f} (t)) \cos (ω_{r} t)] \end{array}

Here R denotes the responsivity of PD. The wireless signal with carrier frequency of

ω_{r}

at the Tx antenna is expressed as

I_{T} (t) = 2 R (((1 + γ s (t)) \otimes h_{f} (t)) \cdot \cos (ω_{r} t)) \otimes h_{w} (t)

It should be noted that the direct current and low frequency component are removed in above equation because of the band-pass filter at the wireless signal transmitter. $h_{w} (t)$ and $H_{w} (ω)$ is the channel response in time-domain and frequency-domain at wireless signal transmitter respectively, i.e. $h_{w} (t) = \frac{1}{2 π} \int_{- \infty}^{\infty} H_{w} (ω) \exp (j ω t) d ω$ . After wireless transmission link, down-conversion and low-pass filter is employed to extract the payload signal, which can be expressed as

I_{R} (t) = R A + R A γ s (t) \otimes h_{f} (t) \otimes h_{w} (t)

where A represents the power attenuation during the wireless transmission. From Eq. (5), the channel transfer function of the RoF system consists of the fiber channel response and wireless channel response. The channel transfer function of the sampled value can be expressed in frequency domain as follows

H (k) = H_{f} (k) \cdot H_{w} (k)

Generally, the conventional TDA-based channel estimation method is employed for optical OFDM systems. $H (k)$ is calculated by averaging over multiple training symbols (TSs). More training symbols would increase the accuracy of channel estimation, but the increasing overhead would reduce the effective bitrate of the OFDM system. In order to improve the accuracy of channel estimation and reduce the length of overhead, transform-domain processing based method is proposed for channel estimation. Figure 2 shows the OFDM signal process at the receiver, and only the channel estimation method is different from the conventional OFDM signal process at the receiver. First, the transfer function $H (k)$ is obtained through initial channel estimation. Usually, only one TS is needed for this. Then, $H (k)$ is transformed to $H_{T} (m)$ by employing another discrete Fourier transform (DFT). $H_{T} (m)$ is in transform domain and expressed as

Fig. 2 The schematic diagram of the proposed OFDM signal process at the receiver.

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H_{T} (m) = \sum_{k = 0}^{N - 1} (H (k)) \cdot \exp (- j 2 π m k / N)

It’s defined that the sequence in transform domain is the DFT of its counterpart in frequency domain. In fact, $H_{T} (m)$ is the “spectral sequence” of $H (k)$ , which would reflect the variation of the transfer function in frequency domain. Assuming that $H_{f} (k)$ is mainly affected by chromatic dispersion in fiber link and $H_{w} (k)$ is similar to the frequency response of an equivalent band-pass filter, $H (k)$ and $H_{T} (m)$ of OFDM RoF system are shown in Fig. 3 . Figures 3(a) and 3(b) indicate $H (k)$ of OFDM systems with different CD (the number of subcarriers in one OFDM symbol is 256). Because the channel parameters keep invariant during each OFDM block, which contains a large number of OFDM symbols, most of the power is located in the low “frequency component” of $H_{T} (m)$ and the noise is spread over the whole spectrum in transform domain (as shown in Figs. 3(c) and 3(d)).

Fig. 3 (a) (b) the transfer function $H (k)$ in frequency domain, (c) (d) the “spectral sequence” $H_{T} (m)$ in transform domain, (e) (f) the improved transfer function $\tilde{H} (k)$ in frequency domain in coherent OFDM systems with different chromatic dispersion.

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Because the transfer function is distorted by the high “frequency component” in transform domain, a feasible way to improve the channel estimation is to employ a well-designed filter in transform domain. So an improved transfer function $\tilde{H} (k)$ is given by

\tilde{H} (k) = \frac{1}{N} \sum_{m = 0}^{N - 1} H_{T} (m) \cdot F (m) \cdot \exp (j 2 π m k / N), F (m) = {\begin{cases} 1, \frac{N}{2} - m_{c} < m < \frac{N}{2} + m_{c} \\ 0, others \end{cases}

Here

F (m)

represents the transfer function of a designed filter and

m_{c}

is the cutoff coefficient which changes along with the channel parameters. The cutoff coefficient

m_{c}

of the designed filter affects the accuracy of the channel estimation. Owing to most of the energy distribution in the transform domain locates around the “low frequency” component,

m_{c}

is defined by the following equation.

R_{T} = \sum_{m = N / 2 - m_{c}}^{N / 2 + m_{c}} {| H_{T} (m) |}^{2} / \sum_{m = 0}^{N - 1} {| H_{T} (m) |}^{2}

So

m_{c}

represents the level of energy convergence in transform domain under a specified

R_{T}

and it will be chosen properly according to different channel parameters. Figures 3(e) and 3(f) shows the transfer function after filtering in transform domain.

Figure 4(a) shows the required $m_{c}$ according to the criterion introduced in Eq. (9) for a 10 Gbaud system. It’s observed that $m_{c}$ is increasing with the CD, i.e. the length of fiber link. When the transmission distance is of short region, $m_{c}$ keeps invariant. Furthermore, when the system symbol rate is 40 Gbaud, it is found that $m_{c}$ is more sensitive to CD and higher $m_{c}$ is required at the same CD. Because the impact from CD is considerable and the width of pulse in the transform domain become larger under a high symbol rate system. In order to investigate the relationship between mc and the bandwidth of equivalent band-pass filter in wireless Tx and Rx, we define a parameter BR, which is the ratio between the 3 dB bandwidth of band-pass filter and OFDM signal. It can be observed that BR has an influence on the level of energy convergence in transform domain. Compared with the case without wireless transmission (indicated by the black line in Fig. 4), the case with wireless transmission needs larger $m_{c}$ . Moreover, $m_{c}$ changes along with BR. Therefore, $m_{c}$ is affected by the channel response in the fiber link and wireless link, and an appropriate $m_{c}$ should be chosen according to Eq. (9). It should be noted that an empirical value of R_T is often set before searching $m_{c}$ . If R_T is small, it would lose some useful “low frequency” components in the transform domain and obtain an estimated channel function with distortion. If R_T is very large, more noise would be added into the estimated channel function. Usually, it can be set to 0.9~0.98.

Fig. 4 The relationship between required cutoff coefficient $m_{c}$ and channel parameters for systems with symbol rate of (a) 10 Gbaud, (b) 40 Gbaud, BR: the ratio between the bandwidth of band-pass filter and OFDM signal.

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The initial channel estimation could be operated by employing only one or several TSs, thus the overhead of OFDM signal can be reduced largely. On the other hand, the proposed method could reduce the noise out of the band in transform domain with appropriate filter, so the new transfer function $\tilde{H} (k)$ will be more accurate.

2.2 Comparison of three channel estimation methods

Table 1 shows the comparison of the three channel estimation methods. The TDA-based method averages the estimated transfer function over multiple TSs, so the required number of TSs is large and the improvement is limited with poor transmission channel. The FDA-based method averages the estimated transfer function over multiple adjacent frequency domain subcarriers in the same TS. It could improve the accuracy of channel estimation in the presence of large optical noise and reduce the overhead. When the number of OFDM subcarriers is decreasing (this probably occurs to reduce the computational complexity of Fast Fourier Transfer in inline digital processing in practical system [9,10]), the edge subcarriers will experience large channel distortion, which leads to the degradation of system performance. The proposed TDP-based method can reduce the required number of TSs and improve the performance of the edge subcarriers compensation.

Table 1. Comparison of the three channel estimation methods

View Table

The computational complexity of TDA-based and FDA-based method is $Ο (n)$ , while the TDP-based method is $Ο (2 n \log (n))$ because of the extra DFT. Here, n represents the number of subcarriers in one OFDM symbols. For a practical OFDM system presented in [9,10], n is not large for the sake of the computational complexity reduction. So the cost of TDP-based method is not high. In addition, for the extra DFT process, only $2 m_{c} + 1$ points are needed to be computed, so the computational complexity of the proposed TDP-based method can be reduced further.

3. Experimental setup and results

In order to investigate the TDP-based channel estimation method, an 8 x 4.65 Gb/s multiple-user discrete Fourier Transform spread (DFT-S) OFDM RoF system is demonstrated. A localized carrier distribution scheme is employed, as shown in Fig. 5(a) , which is different from the interleaved carrier distribution scheme in [11,12], as shown in Fig. 5(b). The middle 4 carriers are beat carriers and another 4 carriers that prepared for signal modulation are located at beat carriers’ left side and right side respectively. Here, 8 signal carriers and 4 beat carriers are demonstrated. Because each beat carrier and the signal carrier at its left or right side can generate mm-wave. Assuming that the total number of carriers is L, the number of carriers that could be used as signal carriers is 2L/3 for the localized schemes, while the number is L/2 for the interleaved scheme. Therefore, the localized scheme cannot only improve the carrier utilization efficiency by 33.3% but also reduce the frequency spacing. The DFT-S OFDM modulation format is utilized because of its good peak-to-average-power-ratio PAPR reduction [13-15]. Note that this localized scheme would increase the spectral efficiency at the cost of hardware complexity [16].

Fig. 5 (a) interleaved carrier distribution scheme [11], (b) localized carrier distribution scheme with 15 GHz carrier frequency spacing.

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The experimental setup is shown in Fig. 6 . A lightwave at 1551.31 nm from external cavity laser (ECL) with a linewidth less than 100 kHz is utilized as a signal source of the multi-tone generator. The phase modulator (PM, Vπ = 2.9 V) is driven by 15 GHz RF signal. The signal carriers and beat carriers are separated through the first waveshaper (WSS1, Finisar WS4000S). The DFT-S OFDM wireless data is generated off-line and mapped to 4QAM constellation, as shown in Inset B of Fig. 6. The DFT-S OFDM baseband signal is constructed with 256 subcarriers and divided into 4 sub-bands, 4 subcarriers of each sub-band are used for phase estimation. After IDFT and cycle prefix insertion, the RF signal is produced through an arbitrary waveform generator at 5 GSample/s. In order to reduce the complexity of transmitter, the discrete multi-tone (DMT) method is employed [17]. The optical up-conversion is based on intensity modulator, because its output is of real value. The fiber launch power is set to 2.3 dBm. Figure 7(a) shows the generated optical spectrum of multi-tone after phase modulator. The separated signal carriers modulated by wireless data is shown in Fig. 7(b). Figure 7(c) denotes the spectrum after multiplexing 8 signal carriers and 4 beat carriers.

Fig. 6 Experimental setup of the DFT-S OFDM multiple-user RoF system, ECL: external cavity laser, PM: phase modulator, EA: electronic amplifier, IM: intensity modulator, AWG: arbitrary waveform generator, WSS: waveshaper.

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Fig. 7 Optical spectrum (a) after phase modulator, (b) after wss1, (c) after 2:1 coupler, (d) after wss2.

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After 40 km fiber link, the second waveshaper (WSS2) is employed as a multi-band pass filter and the specified signal carrier and its corresponding beat carrier are filtered and beating at the PD to generate 60 GHz mm-wave for one wireless user. Figure 7(d) shows the optical spectrum after WSS2. Then the 60 GHz mm-wave is amplified by a power amplifier (PA) with 7 GHz bandwidth centered at 60 GHz and broadcasted through a double-ridge guide rectangular horn antenna with a gain of 25 dBi, frequency range of 50-75 GHz. At the end user terminal, the broadcasted wireless signal is received by another 60 GHz horn antenna with 25 dBi gain at frequency range of 50-75 GHz. The broadcast distance between two antennas is 4cm. The received signal is amplified before mixing with 60 GHz RF clock using a V-band balanced mixer for direct signal down-converted, then amplified with an electronic amplifier again after a lowpass filter (LPF) [1]. The down-converted 4QAM DFT-S OFDM signal is then sampled by a high-speed oscilloscope and processed off-line. For the certain wireless user, one of 8 signal carriers and its corresponding beat carrier could be chosen, so the total rate of this multiple-user system is 8 x 4.65 Gb/s (4.65 Gb/s for each one of 8 wireless users with considering the cost of overhead and inserted pilot). For the offline processing, the cyclic prefix is removed after signal synchronization and digital bandpass filter firstly. Then 256 x 2 points DFT is used to convert the signal in time domain into frequency domain and the baseband signal is divided into 4 sub-band signals and each sub-band signal is processed individually. The TDP-based channel estimation that introduced in Section 2 is employed. A 64-point IDFT is used to recover the signal and the inserted pilot subcarriers in each sub-band are used for phase noise estimation. At last, the errors were counted over 10⁵ bits.

Figure 8 shows BER curve of one chosen channel with different channel estimation schemes. TDP-based method outperforms the other schemes. Compared with TDA-based scheme with 8 and 16 TSs, 0.8 dB and 1.6 dB improvements at BER of 3.8 x 10⁻³ (7% FEC threshold) are observed respectively (the constellations are shown as the insets in Fig. 8). It can be also found that TDA-based scheme with only one TS performs worst. Therefore, TDP-based scheme only needs one TS for the initial channel estimation and revises the transfer function with the help of the lowpass filter in the transform domain. Furthermore, it is observed that the improvement is almost the same when changing the received optical power level. Because noise in the transmission system is the main factor that impacts the accuracy of channel estimation. The improvement would be similar when received power is changing in a low level range. If received optical power level is very high, the improvement would not be considerable, because TDA processing can also obtain accurate channel estimation with less training symbol. We have tested all 8 channels and the calculated BER of DFT-S OFDM signal for each wireless user after 40 km fiber link and 60 GHz wireless link is shown in Fig. 9 , and find that the BER for all channels are all below 3.8 x 10⁻³. This clearly shows that TDP-based scheme is feasible and it could reduce the overhead of DFT-S OFDM signal and improve transmission performance. It should be noted that there are some leakage in Fig. 7(d) when choosing signal and beat carrier for the nonperfect filter effect of WSS. The BER performance can be improved further when this leakage is suppressed by using the well designed bandpass filters.

Fig. 8 BER vs received optical power of one chosen channel after 40 km fiber link and 60 GHz wireless link.

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Fig. 9 BER of DFT-S OFDM signal for all 8 wireless users after 40 km fiber link and 60 GHz wireless link.

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4. Conclusion

We propose a novel channel estimation method based on transform domain processing, which could reduce the overhead of OFDM signal and shows identical channel estimation accuracy over the whole subcarriers. An 8 x 4.65 Gb/s multi-user OFDM RoF system based on this method is demonstrated. Compared with the TDA-based scheme with 8 and 16 TSs, 1.8 dB and 0.8 dB improvements at BER of 3.8 x 10⁻³ are observed respectively. The calculated BER of all 8 channels are below 3.8 x 10⁻³ and this clearly shows the feasibility of TDP-based channel estimation.

Acknowledgments

This work was partially supported by the NHTRDP (973) of China (Grant No. 2010CB328300), and NNSF of China (No. 61107064, No. 61177071, No. 600837004), Doctoral Fund of Ministry of Education, NHTRDP (863 Program) of China (2011AA010302, 2012AA011302), The National Key Technology R&D Program (2012BAH18B00).

References and links

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Method	Required number of TSs	Low compensation performance of edge subcarriers	Computational complexity
Transform Domain Processing	1 or Several	No	$Ο (2 n \log (n))$
Time Domain Averaging	Large	No	$Ο (n)$
Frequency Domain Averaging	Several	Yes	$Ο (n)$

A novel transform domain processing based channel estimation method for OFDM radio-over-fiber systems

Abstract

1. Introduction

2. Principle

2.1 Theoretical analysis of TDP-based channel estimation

2.2 Comparison of three channel estimation methods

3. Experimental setup and results

4. Conclusion

Acknowledgments

References and links

Cited By

Figures (9)

Tables (1)

Equations (9)

Optics Express