Adaptive denoising at Infrared wireless receivers Xavier N. Fernando, Sridar Krishnan, Hongbo Sun and Kamyar Kazemi-Moud Department of Electrical and Computer Engineering, Ryerson University Toronto,ON, M5B 2K3, Canada (
[email protected]) ABSTRACT This paper proposes an innovative approach for noise cancellation at infrared (IR) wireless receivers. Ambient noise due to artificial lighting and the sun has been a major concern in infrared systems. The background induced shot noise typically has a power from 20 to 40 dB more than the signal induced shot noise and varies with time. Due to these changing conditions, infrared wireless receivers experience high level of non-stationary noise. The objective of the work mentioned in this paper is to develop digital signal processing algorithms at the infrared wireless system to combat high power non-stationary noise. The noisy signal is decomposed using a joint time and frequency representation such as wavelets and wavelet packets, into transform domain coefficients and the lower order coefficients are removed by applying a threshold. Denoised version is obtained by reconstructing the signal with the remaining coefficients. In this paper, we evaluate different wavelet methods for denoising at an infrared wireless receiver. Simulation results indicate that if the noise is uncorrelated with the signal and the channel model is unavailable the wavelet denoising method with different wavelet analyzing functions improves the signal to noise ratio (SNR) from 4 dB to 7.8 d B. Keywords : optical wireless, infrared, receiver, noise, wavelet transform, denoising
1. INTRODUCTION The emerging technologies like mobile portable computing and multimedia terminals at living and work environments are the main forces driving companies ,scientists and researchers to progress in the challenging field of wireless local area networks(WLAN). The need for higher speed and wider bandwidth in data communication networks is gradually replacing electrical transmission medium to optical. Wireless infrared LA Ns are important part of indoor transmission systems and enable high bit-rate data transferring over short distances [1]. Infrared systems occupy no radio frequency (RF) spectrum and they can be used where electromagnetic interference is critical. The infrared spectral region offers a large, virtually unlimited, bandwidth that is unregulated worldwide. Since infrared communications are confined to rooms, there is no interference between communication systems operating in different rooms, which result in secure communications. In contrary to RF transmission systems, the light is reflected diffusely on the wall surface of the rooms and the channel estimation will be a non-trivial subject for infrared systems. A non-directed wireless optical communication system can be either line-of-sight (LOS) or diffuse. A LOS system is designed under the assumption that the LOS path between transmitter and receiver is unobstructed. A diffuse system is defined as one which does not rely upon the LOS path, but instead relies on reflections from a large diffusive reflector such as the ceiling. In both cases, an optical signal in transit from transmitter to receiver undergoes temporal dispersion due to reflections from walls and other reflectors; the intersymbol interference (ISI) that results is an impediment to communication at high speeds. Single diffuse infrared links can operate with bit rates as high as 100 Mb/s [2]. Since it is possible to operate at least one infrared link in every room of a building without interference, the potential capacity of an infrared-based network is extremely high. The propagation characteristics of diffuse infrared signals resemble those of radio signals. The measured received power at different positions using a photodetector much smaller than the light wavelength will result in multipath fading like fluctuations in received power. In the real diffuse infrared systems, however, the detector size is much larger than the wavelength, so that the multipath fading like power fluctuations are averaged out effectively. While multipath propagation does not lead to fading, it causes temporal dispersion. The tail caused by higher order taps of the indoor channel impulse response induces ISI in high bit -rate communications.
Indoor infrared transmission suffers from a number of impairments the most important ones being shot noise from the ambient light and restricted symbol rate due to multipath dispersion. Noise plays a severe role in the performance of wireless infrared networks. Background illumination has two distinct effects in the performance of optical receivers; one is noise due to the steady and invariant irradiance from undesired light sources which results to shot noise at the photodetector, the other one is interference generated by high frequency components of some light sources. Typically, natural and artificial ambient light contribute to high levels of shot noise in a photodetector which degrades the performance of the transmission system. For data-rates up to 10 Mbps, the major degrading factor of the infrared communication systems is the shot noise induced in the receiver due to ambient light. Unfortunately, ambient light sources (sunlight and artificial light) also radiate in the same spectral wavelengths used by infrared transducers. Thus shot noise presents a strong spatial and temporal dependence. Several advanced techniques for the design of nondirected wireless infrared communication systems have been already proposed in order to minimize these signals to noise ratio (SNR) fluctuation effects. These ambient light levels to a significant degree determine the optical power required for reliable transmission. The shot noise induced by ambient light may vary over several decades during a day in a typical indoor environment. The interfering signal from the fluorescent light is periodic and deterministic. The spectrum of fluorescent lights driven by electronic ballasts may extend up to frequencies around 1MHz interference of which will cause serious degradation at infrared receivers even after high-pass electrical filtering [3-5]. The objective of the work mentioned in this paper is to develop a digital signal processing algorithm at the infrared wireless system to combat uncorrelated noise without a reference channel model. In Section 2, we introduce and classify different noise sources at the infrared receivers [3]. Section 3 will focus on the definition of wavelet transform and analyzing functions which will be used in Section 4 to introduce a new methodology for noise cancellation. The new wavelet–based denoising technique and the results of wavelet denoising are discussed Section 4. The conclusions are provided in Section 5.
2. NOISE AT THE RECEIVERS Noise in the infrared optical receivers is a critical parameter of performance analysis . There are different sources of noise that contribute to overall performance of the wireless network link. Thermal noise of the photodetector is dominant for weak steady background illumination. Thermal noise is critically dependent to the front-end design of the receiver (e.g. preamplifier). Shot noise is induced by the quantum nature of photons randomly arriving at the photodetector. It is proportional to the average received optical power. Natural and artificial background light may come from different light sources. Different background noise source contributions are from sun, incandescent lamps, fluorescent lamps with conventional ballasts and electronic ballasts. The slow variations in intensity of the light coming from the Sun make it a strong source of shot noise. The spectrum of natural light coming from the Sun in a shiny day is spread over entire responsivity curve of the PIN photodetector resulting to a steady background noise current of an order of a mA stronger than a well artificially illuminated room. Shot noise is larger under directional lamps and near windows exposed to sunlight. Furthermore, it can vary drastically during a normal day with the position of the sun and with the indoor lighting conditions. Due to the temporal variation and directional nature of both signal and noise, the SNR at the receiver can vary significantly. Artificial light sources also contribute to shot noise as well as interference at the infrared receiver. Incandescent lamps interference is periodic with a frequency of 100 Hz. Its spectrum has frequency components up to 2 KHz. Harmonics at the frequencies of higher than 800 Hz do not carry a significant amount of energy and they are 60 dB below the fundamental harmonic. In case of the incandescent lamps the amplitude of the interference is one tenth of the current generated by the slow variations of intensity. Researchers have already extracted an experimental interference model for typical incandescent lamp s [3].
Fluorescent lamps equipped with conventional ballasts driven at power-line of 50 or 60 Hz, they induce interference at harmonics up to 20 KHz. This interference is periodic with a frequency of 50 Hz and its harmonics are 50 dB below the 100 Hz component for frequencies higher than 5 KHz. Interference amplitude in this case is 2 to 6 times lower than the shot noise current Interference model for the fluorescent lamps driven by conventional ballasts has also been extracted experimentally [3]. The fluorescent lamps with electronics ballasts have higher power efficiencies and use the same concept of switching power supplies. Interference generated by fluorescent lamps with electronics ballasts has lower amplitude compared to other types of ambient lights but its spectrum is very broad and has frequency harmonics up to 1MHz. The spectrum produced by an electronics-ballast-driven lamp consists of low and high frequency regions. The low frequency region resembles the spectrum of a conventional fluorescent lamp while the high frequency region is attributable to the electronic ballast. These two components of the spectrum have been modeled using the same experimental approaches as the other noise sources [3]. In these model equations the relative amplitude and phase of the harmonics can be easily identified. For diffe rent class of lamps all the average parameters for interference models can be easily identified [3]. Several schemes have been proposed in order to reduce the power penalty induced by ambient artificial light sources in an indoor infrared wireless system [5-7].
3. WAVELET TRANSFORM Wavelets are functions that satisfy certain mathematical requirements and are used in representing data or other functions. The wavelet analysis procedure is to adopt a wavelet prototype function, called an "analyzing wavelet". The wavelet transform has become a powerful tool for signal analysis and is widely used in many applications, including signal detection and denoising. The complexity of structures presented at infrared wireless receivers requires the development of an adaptive, low level representation in order to provide a meaningful analysis of the system. In Fourier, the basis functions are sine and cosine which are not suitable in capturing the subtle changes of received signals at the infrared receivers because of their inability to localize the temporal information. The wavelet transformation is a time-frequency decomposition technique and with the choice of smooth multiresolution wavelet analyzing functions that use long time intervals for capturing low frequency information of the desired signal and short time intervals for high frequency information, one can have a joint temporal and spectral representation of that signal. Temporal analysis is performed with a contracted, high-frequency version of the prototype wavelet, while frequency analysis is performed with a dilated, low-frequency version of the prototype wavelet. Because the original signal or function can be represented in terms of a wavelet expansion (using linear combination of the coefficients and the wavelet basis functions), data operations can be performed using just the corresponding wavelet coefficients. In wavelet transformation, any signal can be decomposed into components with good time and scale properties. Wavelets have the advantages to express any signal with fewer coefficients [9]. The basis functions are obtained by shifting and modulated the amplitude of the “analyzing wavelet”. The design of basis functions must be optimized, so that the number of non-zero coeffic ients will be minimal and the input signal is approximated by projecting it over the basis functions selected adaptively. In wavelet-based denoising, the noisy signal is decomposed into transform domain coefficients, and the lower order coefficients are removed by applying a threshold. If we assume that ? (t) is the analyzing wavelet function then the continuous multi-resolution wavelet frame transform, F[m,n], of a signal f(t) is defined:
F[ m , n] =< Ψm, n (t ), f ( t ) >=
+∞
∫Ψ
m, n
−∞
( t ) ⋅ f (t ) ⋅dt
The inverse wavelet transform is defined as
f (t ) =
∑∑ F[m, n] ⋅ Ψ
m, n
(t )
m∈ ℑ n ∈ℑ
here m and n belong to the set ℑ , the set of integer numbers defining each wavelet basis function, ?(t) , in the two dimensional wavelet space. The main difference between wavelet and wavelet packet analysis is that the latter allows an adjustable resolution of frequencies through filter bank decomposition. Filter banks split the whole spectrum into two equal bands at different frequency levels, obtaining a general tree structure that is called the wavelet packet expansion. Wavelet packet allows searching the optimum decomposition of the tree looking for the branch with the best entropy criterion of the input signal [7]. Researchers in related engineering and applied mathematics areas have developed many different wavelet transform systems each with specific properties. The difference between these wavelet transforms is mainly their analyzing functions and the way that they are developed. There are two major classes of wavelet transform systems. One class consists of orthogonal wavelets and the other one consists of biorthogonal wavelets. Other wavelet transform systems, not included in the two main categories, have generally limited applications [8].
4. NOISE CANCELATION METHOD In order to cancel the effect of uncorrelated Gaussian noise in the indoor infrared wireless channel we introduce the wavelet transform applied to the signal in electrical domain. Figure 1 shows the schematic diagram of the wireless infrared link and the receiver with the wavelet transform denoising block.
Figure 1 – Schematic of the wavelet based denoising wireless infrared link
In this system, the high pass electrical filter will reduce the interference induced by incandescent light and fluorescent light by conventional ballasts . The comb filter block will cancel the high frequency interference from the fluorescent lamps driven by electronics ballasts [11]. In the wavelet denoising block, the received signal is being transformed using pre-defined analyzing function. Once the wavelet decomposition of the signal is achieved the next step is thresholding. Thresholder block will remove the coefficients of the signal which have smaller absolute value than a predefined threshold. Different methods can be used to determine the threshold level that results in performance improvement in addition to rescaling the coefficients to the noise level. If wm denotes the wavelet coefficients of the decomposed signal and A the threshold level then the hard thresholding can be described mathematically as:
wm wˆ m = 0
wm ≥ A wm < A
In order to avoid the denoising effect of certain filters that remove the sharp features of the signals, soft thresholding will discard the coefficients with small and insignificant contribution to the information and can be performed as:
Sgn( wm )( wm − A) wˆ m = 0
wm ≥ A wm < A
where the Sgn(.) is the signum function. The remaining wavelet coefficients produce the denoised signal which will be demodulated and decoded. The aim is to alleviate the shot noise generated by incandescent light, the thermal noise from the receiver electronics by this denoising block. For simulation the denoising algorithm is applied to a pulse train with frequency of 10 KHz that passes through an infrared channel that contributes additive Gaussian noise with a SNR of 4 dB. Data signal with additive white Gaussian noise and its spectrum is shown in Figure 2-a and 2-b respectively.
(a)
(b)
Figure 2: The received signal passed over an additive white Gaussian noise channel (a) the spectrum of the received signal (b).
The simulations has been done using seven different wavelet analyzing functions and the results of SNR improvements are summarized in Table 1. The “SNR improvement” is defined as the value that SNR after denois ing subtracted by SNR before denoising. Orthogonal wavelet transforms used in the simulation were Haar, Daubechies, Coiflets, Symlets and discrete Meyers’s wavelet transform. Figure 3 shows the original received noisy signal (above) and denoised version of the same signal after applying discrete Meyer’s wavelet transform (below). SNR improvement of the denoised signal in this case is 3.8 dB. In the thresholding block the wavelet coefficients obtained from signal decomposition that are lower than the threshold level are discarded. Figure 4 shows the original Gaussian noise of the channel (above) and the temporal representation of the discarded coefficients (below).
Waveform ‘Haar’ ‘db’ ‘sym’ ‘coif’ ‘bior’ ‘dmey’
SNR improvement 2.3279 3.4801 3.4522 3.5583 3.7485 3.8281
Table 1: SNR improvement of wavelet denoising method using different analyzing functions
Figure 3: The original noisy 10 KHz pulse train (above) and the denoised version using the discrete Meyer’s transform (below)
Figure 4: The original Gaussian noise (above) and the reconstruction of wavelet coefficients discarded by thresholder (below)
Figure 5: The original noisy 10 KHz pulse train (above) and the denoised version using the Haar transform (below)
Figure 6: The original Gaussian noise (above) and the reconstruction of wavelet coefficients discarded by thresholder (below)
In Figure 5 shows the denoised version of the received signal using the Haar wavelet transform has been shown (below). Reconstructed signal from the discarded coefficients in the thresholder is shown in Figure 6 (below). By using Haar wavelet transform a SNR improvement of 2.3 dB has been achieved. Haar wavelet analyzing has sharp edges compared to the Meyer’s wavelet mother function which is smoother and this results to the loss of signal information over those sharp edges therefore a lower SNR improvement. Overall the use of the wavelet deoinsing method with any of the analyzing functions results to a SNR improvement of approximately 3 to 4 dB which means a signal twice more powerful than the noisy one. This improvement can be achieved for a noise which is uncorrelated with the information signal, and where a reference channel for noise is not available .
5. CONCLUSIONS Different noise contributions at the infrared wireless receivers have been mentioned. A new denoising method for uncorrelated noise in wireless infrared receivers was introduced using the wavelet transform. In this new method denoised version is obtained by reconstructing the signal with the remaining coefficients after passing through a thresholder. We evaluated Coiflet, Daubechies, Haar, Symmlets, Biorthogonal and Meyer wavelet analyzing functions for denoising at an infrared wireless receiver. Overall using the wavelet with any of the analyzing functions in the simulation has resulted to a SNR improvement of approximately 3 to 4 dB with the input SNR of 4 dB. If the power density function of the noise which is uncorrelated to the information signal is known and the reference channel model is unknown, the use of self-defined adaptive wavelet analyzing functions can improve the SNR of received signal whose spectrum overlaps with that of the noise. A comparison of SNR improvement for different wavelet analyzing functions has been done. Results also indicate that the smoother wavelet analyzing functions can preserve more signal information hence they will result to a higher SNR improvement. But one should consider that overall SNR improvement using the wavelet decomposition method for denoising is between 3 and 4 dB for different wavelets therefore we suggest the use of wavelets that can be implemented easier on digital signal processors (DSP) chips and have efficient calculation time in order to satisfy speed constraints of the electronics used in the lightwave system.
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