1. Introduction

Recently, white light emitting diodes (LEDs) has attracted more and more attention for simultaneous illumination and visible light communication (VLC) [1–7]. As the main device for next generation illumination, it provides several advantages over traditional incandescent or fluorescent lamp, such as high efficiency, long lifetime and low power consumption. The feasibility of VLC has been both demonstrated by employing red-green-blue (RGB) LED and phosphor-based LED. But one of the technical limits is the intrinsic small modulation bandwidth of commercially LED. Therefore, spectrally efficient modulation scheme such as discrete multi-tones (DMT) and orthogonal frequency division multiplexing (OFDM) have been widely implemented to mitigate the severe frequency response of VLC system. The highest data rate in the case of bi-directional transmission [2] and the record data rate in uni-directional transmission at a distance of 10-cm [3] are achieved by both adopting OFDM. But the high peak to average power ratio (PAPR), frequency offset and phase noise sensitivity of OFDM is main drawbacks.

In our previous work [8,9], we have suggested an alternative VLC modulation scheme using Nyquist single carrier frequency domain equalization (N-SC-FDE). This scheme has the similarity of spectral efficiency performance to the aforementioned OFDM technology [10], but with a reduced PAPR. In SC system, the adaptive equalization is critical. The equalization method can be performed either in time domain such as cascaded multi-modulus algorithm (CMMA) [11] or in frequency domain such as pre- FDE and post-FDE. Generally speaking, time domain equalization typically requires a number of multiplications per symbol that is proportional to the maximum channel impulse response length. FDE appears to offer a better complexity trade-off than time domain equalization when large taps are needed [10].

In this paper, we propose and experimentally demonstrate a novel hybrid time-frequency adaptive algorithm in an N-SC-VLC system based on a combination of FDE and decision-directed least mean square (DD-LMS). The non-flat frequency response of VLC system can be first mitigated by FDE, and the system performance can be further improved by DD-LMS via symbol decision with an optimum tap number of 33. In this demonstration, the Q-factor performance can be further enhanced at the modulation format of 512-QAM assisted by DD-LMS after FDE. 512-ary quadrature amplitude modulation (512QAM) and wavelength multiplexing division (WDM) are also employed in this system. The aggregate data rate of three wavelength channels are 4.22-Gb/s implementing a commercial commercially available RGB LED and an avalanche photodiode (APD) with 3-dB bandwidth of 100MHz, which are both far below the signals bandwidth of 156.25MHz.The measured Q-factors for all channels are above the Q-limit.

2. Principle of QBD-OFDM

The architecture and principle of the VLC system with the proposed hybrid time-frequency equalizer is shown Fig. 1.In this demonstration, a commercial available RGB LED (Cree, red: 620-nm; green: 520-nm; blue: 470-nm) generating a luminous flux of about 6lm used as the transmitters (TXs) and an avalanche photodiode (Hamamatsu, 0.42-A/W sensitivity at 620-nm and gain = 1, the maximum gain is 30) used as the receiver (RX) are adopted. The concept of Nyquist SC-FDE is very similar to that of OFDM. If no pre-FDE is employed, the only difference is that, in SC-FDE, the inverse fast Fourier transform (IFFT) block is moved from the transmitter to the receiver. The binary data would be firstly mapped into 512-QAM format and then the training sequences (TSs) are inserted into the signals. After making pre-equalization in frequency domain and up-sampling, cyclic prefix (CP) is added. CP is used to mitigate the multipath distortion. Then the real and imaginary components of signals are multiplied with sine function and cosine functions, respectively.

 

Fig. 1 The architecture of the proposed VLC system based on hybrid time-frequency adaptive equalization algorithm (AWG: arbitrary waveform generator, P/S: parallel to serial, EA: electrical amplifier, LPF: low-pass filter, DC: direct current, OSC: real-time oscilloscope).

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Low-pass filters are used to remove out-of-band radiation. Subsequently, amplified by electrical amplifier (EA) ((Minicircuits, 25-dB gain), combined with direct current (DC)-bias via bias tee, and then applied to these three different color chips. Passing through free-space transmission, lens (50-mm diameter) and optical R/G/B filter, the signals are recorded by a commercial high-speed digital oscilloscope (Tektronix MSO5104) and sent for off-line processing.

At the receiver, after synchronization, resampling and removing CP, a two-fold hybrid time-frequency equalization method jointly employing FDE and DD-LMS is carried out. First, the non-flat frequency response is compensated by FDE via zero forcing (ZF) algorithms, then to switch to DD-LMS equalizer once the bit error rate (BER has dropped to a sufficiently low level around 10⁻¹ to 10⁻² [12]. The signals in frequency domain are transformed to time domain and pass through the DD-LMS equalizer. DD-LMS is a stochastic gradient descent algorithm, and does not depend on the statistics of symbols but rely on the symbol decisions. The skeleton structure of DD-LMS equalizer is illustrated in Fig. 2.

 

Fig. 2 The skeleton structure of DD-LMS equalizer.

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The output $y(k)$ of DD-LMS equalizer with L taps is shown as:

where $X(k)$and $w(k)$represent the input signal and weight vectors, respectively of the $k^{th}$DD-LMS section. ${(\cdot )}^H$denotes the Hermitian matrix of $(\cdot )$.

The error signal $e(k)$and weight vector for adaptive updating DD-LMS at the $k^{th}$ iteration are given by

Of which $d(k)$is expected output, $\mu$ is the step size, ${(\cdot )}^{\ast }$denotes the complex conjugate matrix of $(\cdot )$. The DD-LMS error term in Eq. (4) assumes zero values at the symbol points and hence the excess mean-squared error (EMSE) is greatly reduced [12].

3. Experimental results and discussion

The experimental setups are depicted in the insets of Fig. 1(a)-(b). In this demonstration, the N-SC-FDE signals are generated by Tektronix AWG 7122C with the maximum sampling rates of 24-GS/s and bandwidths of 6-GHz, and detected by an APD with 3-dB bandwidth of 100-MHz. The up-sampling factor is 16, and the sample rates of AWG and OSC are set to 2.5-GS/s and 5-GS/s, respectively. The CP length is set to 1/16 symbol length. In order to obtain the same spectral efficiency as OFDM, a square function with roll factor of 0 is used as the filter in the TX and RX. The square filters are employed in the frequency domain.

First of all, we measured the frequency response of the overall system including LED, bias tee, electrical amplifier, and APD. The results are shown in Fig. 3.From Fig. 3 we can find that the gradient of the frequency response is different. However, in order to obtain a relatively flat frequency response, the occupied frequency is starting from 9.76-MHz. Thus, the valid occupied bandwidth of signals is 156.25-MHz ranging from 9.76-MHz to 166.01-MHz. It should be noted that the voltages of bias tee and amplitudes of signals are finely adjusted to render the whole system work at the quasi-linear region of LED. And the mean signal to noise rate (SNR) of red, green and blue LED chips is 30-dB, 25-dB and 25-dB, respectively.

 

Fig. 3 The measured frequency response of three individual VLC links.

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The measured spectra of original SC-FDE signals from the output of AWG, captured signals after red/green/blue LED transmission are depicted in Figs. 4(a)-4(d), respectively. Compared with the original spectrum, the high frequency components of transmitted signals have larger power attenuation. This is mainly caused by the frequency attenuation of indoor channel and bandwidth limitation of APD.

 

Fig. 4 The measured electric spectra of (a) original SC-FDE signal; (b) after red color LED transmission; (c) after green color LED transmission; (d) after blue color LED transmission.

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The optimal number of taps is investigated in red link. In this investigation, two TSs are employed and the modulation format for red LED chip is 512-QAM. The number of taps is ranging from 3 to 53. The results are shown in Fig. 5.The system performance can be improved with the increasing tap number of the equalizer. Considering the system performance and computational complexity, the proper number of taps can be set at 33.

 

Fig. 5 Q-factor performance versus number of taps.

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Then we measured the Q-factor performance versus different modulation orders ranging from 6 to 9 with and without DD-LMS adaptive equalizer. The results are illustrated in Fig. 6.In the case of 512-QAM modulation and 4% TSs in FDE, the Q-factor performance of red, green and blue LED can be further enhanced by 1.4-dB, 1.6-dB, and 1.0-dB, respectively, assisted by DD-LMS. The constellations of 512-QAM before and after DD-LMS equalizer are also depicted in Fig. 6. The aggregate data rate is 156.25x9x3 = 4.22-Gb/s at a distance of about 1-cm, including the CP and TSs. The Q-factor results after DD-LMS are all above the Q-limit of about 8.5-dB, which corresponds to a BER target of 3.8x10⁻³ (7% pre- forward error correction threshold) [13].

 

Fig. 6 Q-factor performance w- and w/o DD-LMS of (a) red color LED; (b) green color LED; (c) blue color LED.

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Next, the joint parameters and performance of FDE and DD-LMS are discussed. The Q-factor versus different numbers of TSs in FDE is depicted in Fig. 7.It can be found that the Q-factor can be about 1dB improved assisted by DD-LMS and with half TSs in the case of high-order modulation format. As mentioned in Section II, FDE is used to make a coarse equalization to open the channel eye, a more reliable and precise decision can be made during the adaptive tap update process of DD-LMS. The EMSE can be reduced and the overall system performance improvement can be achieved.

 

Fig. 7 Q-factor performance with different TSs and w- or w/o DD-LMS of (a) red color LED; (b) green color LED; (c) blue color LED.

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At last, the maximum data rates versus transmission distance are measured and depicted in Fig. 8.The symbol of (A, B, C) in Fig. 8 denotes the highest modulation level of red, green and blue transmission links. For example, (7,6,6) means that at a distance of 35-cm, the maximum modulation orders of red, green and blue links are 7(128QAM), 6(64QAM) and 6(64QAM), respectively. The data rates with DD-LMS equalizer at the distance of 35-cm and 105-cm are 3-Gb/s and 2.5-Gb/s, respectively. And we can find that after adopting DD-LMS, the maximum data rate can also be increased. In this demonstration, only a single RGB-LED is used. The illuminances are about 50-lx and 5-lx at the distance of 35-cm and 105-cm, respectively, which are far below the indoor illuminance standard of about 400-lx. Arrays of LEDs can be implemented to increase the illuminance, whilst maintaining the bandwidth of individual devices. By this way, a longer transmission distance can be realized.

 

Fig. 8 The measured overall data rate as a function of transmission distance.

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4. Conclusion

In conclusion, we have experimentally demonstrated a hybrid time-frequency adaptive equalization algorithm in a RGB-LED-based Nyquist SC VLC system. The system performance can be improved by a combination of FDE and DD-LMS. An aggregate data rate of 4.22-Gb/s enabled by this hybrid equalization, as well with high-order modulation scheme and WDM is successfully investigated. As far as we know, this is the highest data rate ever achieved by using a single commercially available RGB-LED in VLC system. And the capacity of this system can be further improved by a larger bandwidth APD. The data rate is achieved in offline transmission system, and our next goal is to realize high-speed and low cost real time VLC transmission system.