On Modeling of Spatial Discrete Multi-Tone MIMO Optical Channel

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IPASJ International Journal of Electronics & Communication (IIJEC) Web Site: http://www.ipasj.org/IIJEC/IIJEC.htm

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Volume 4, Issue 1, January 2016 ISSN 2321-5984

Volume 4, Issue 1, January 2016 Page 21

ABSTRACT

The Multiple-input Multiple-Output (MIMO) wireless optical communications are studied in previous work. The spatial

discrete multi-tone (SDMT) modulation technique is investigated in terms of its channel model and its capacity. This paper

focuses on the capability of SDMT spatial modulation to combat the low pass spatial channel, where, a dynamic range

compression technique was applied to exploit unused spatial frequency bins to reduce the peak value of output signals‚ thereby reducing clipping noise.

Keywords – Wireless, MIMO, Optical, Channels, Modeling

I. INTRODUCTION

With the rapid development of solid-state lighting, wireless optical communications are deemed to be an interesting

technology for upcoming indoor wireless communications. To attain high data rate Multiple-input Multiple-Output

(MIMO) wireless optical communications are studied in previous work. This article is primarily a presentation and

review of the literature of signaling and coding of the strategies used for the pixelated wireless MIMO optical channels,

where the prospective of this topology of channel to get high spectral efficiency is validated to be a channel of space-

time able to get high spectral efficiencies by using coding methods available. In this article, the method of spatial

discrete multi-tone modulation (SDMT) is studied, and an assessment of the capacity of a particular channel realization

is afforded as a waterfall spectrum. For systems in which the prediction orthographic assumption holds, it is predicted

that the capacity of the system will be highly reliant on the range between the transmitter and the receiver. The spatial

frequency response of the link descents, as the range rises.

II. CHANNEL MODEL

Fig. 1 depicts a typical MIMO optical wireless channel [1]. We presumed that the transmitter has a square

grid at intervals of , and undistinguishable formed transmit pixels. At time instant t the transmitted amplitude

must satisfy , thanks to the restraints on the channel amplitude. The receiver is located to gather the

transmitted optical intensity image, and produces a signal indicating the spatial distribution of optical power impacting

the device in each symbol interval, where designates the received optical intensity image at time t . The

receiver in this prototype contains pixels of form , separated by intervals of size on a grid of square size

. The receiver output samples , in time and space of the optical intensity distribution.The

corresponding channel's pixel is the modest type of MIMO Optical Wireless channels, which is the one in which each

transmitting component relates to a single pixel received.This channel entails a string of independent and parallel

channels. The channel prototype can be administered as

(1)

On Modeling of Spatial Discrete Multi-Tone

MIMO Optical ChannelAmin Al-Ka’bi

Australian College of Kuwait Kuwait city, Kuwait







Figure 1. Block Diagram of a point-to-point MIMO Wireless Optical Channel.

where is the process of random noise to each received pixel. In this prototype, it is presumed that the optical

MIMO channel is an assembly of sub-channels without cross-channel interference and the noise processes are

identically distributed random variables, with Gaussian probability density distribution functions. It is intended that

these noise sources vary on the array following tolerances of devices and non-identical responses of the optical pixels

[1].

In addition, we assume that each transmitted pixel is modulated with an M-PAM signaling pattern, that is independent

of the other pixels transmitted, and P is the maximum average optical power limit and an optical power limit of

is assigned to each sub-channel. If the array size is set, rising n suggests that the area of each receiving

element declines with n. The channel works in a shot-noise limited mode, if lighting is concentrated, hence, the

variance of the noise generated by each photo in each sub-channel is proportional to the area of the pixel, i.e.

, where is the variance of the sum over all the noises of the component pixels [3].

Unluckily, the capacity of each sub-channel does not have closed form. However, it can be projected by investigating an

electrical channel that has the same variance as the optical constellation intensity. In this case, the signal-to-noise ratio(SNR) in each M-PAM sub-channel is associated to the average optical power as,

(2)

whereW represent the bandwidth support amount required by the pattern, and the signals have a fractional power

bandwidth of , with time-limit of [0, T ). The summation of the individual sub-channel capacities, can approximate

the total capacity of pixel matched system such as,

) [bits/s/Hz] (3)

as ,

= (4)

where OSNR is expressed as . It can be inferred that the capacity is proportional to the quadratic increase of

the OSNR, as the number of pixels approaches infinity. A comparable outcome can be observed in fading-free wireless

channels, where multiplexing spatial gains are achieved by allocating the power restraint over a big number of degrees

of freedom [1], [2].







III. PIXELATED WIRELESS OPTICAL CHANNEL

In digital subscriber lines (DSL), the discrete multi-tone (DMT) modulation is a common signaling pattern of

frequency selective channels [6]. Here, the frequency spectrum is distributed over a number of non-interrelating bins.

Hence, these bins can be regarded as a group of parallel Gaussian channels. The optimum power distribution across the bins is given by a “waterfall” or “water-pouring” spectrum, subject to the total power restraint. Consequently, the

quadratic amplitude modulation (QAM) constellations are determined in each frequency bin according to the rule of

optimum power distribution.

In Discrete Multi-tone (DMT) system, the data is transferred by modulating the spatial frequency domain. The spatial

discrete multi-tone (SDMT) modulation could be regarded as an expansion to DMT. Fig. 2 depicts the SDMT system

block diagram [1].

The proposed channel prototype can be used to estimate the capacity of SDMT spatial modulated point-to-point optical

wireless channel. In order to assess the practicality of attaining a high rate of channel capacity, in this prototype‚ multi-

stage decoding and multi-level codes are employed to the channel simulation to give a feasible system which

accomplishes rates of around 76% of the channel capacity.

Figure 2. Block diagram of SDMT system.

III-1 Dynamic Range Compression

The output signal in DMT systems is the summation of a huge set of independent sinusoidal signals. The distribution of

the amplitudes of these sinusoidal signals can be regarded as Gaussian distribution, and they demonstrate high peak-to-

average ratios, as shown in Fig. 3[8]. As SDMT is a general extension to the traditional DMT, it also demonstrates the

same disadvantageous characteristic.

Nevertheless, in SDMT‚ where the Signal to Noise ratio is too low, there are a significant number of unused spatial

frequency bins where data is not set. These bins provide a significant degree of freedom, and they can be utilized to

decrease the peak amplitude of the resultant output signal. Consequently‚ a repetitive projection procedure is used to

allocate the unused bins [3]. Fig. 4 illustrates the function of the algorithm.







Figure 3. Normalized histograms of received amplitudes given a zero or one are transmitted for

10 × 10 sized macro-pixelsalong with Gaussian density fit.

Figure 4. Block diagram of dynamic range compression algorithm .

The algorithm can be regarded as a repetitive process between the set of signals holding the required data and the set of

signals complying with the peak restraint.Firstly, the data symbols are assigned to the designated spatial frequency

bins, and the other bins are set to zero. The resultant image is converted to spatial domain using the Inverse Fast

Fourier Transform (IFFT) ‚ trimmed to comply with the peak restraint and converted back in spatial frequency domain

using Fast Fourier Transform (FFT). Secondly, the algorithm appoints the data symbols to the allocated frequency bins,

and leaves the other bins intact. This process is repeated for a certain number of iterations. As previously clarified, the

dynamic range compression algorithm can be regarded as a repetitive process between the group of signals complying

with the peak restraint and the group of signals holding the required data. Therefore, as the two sets are convex‚ it can be concluded that the algorithm will find a point in the intersection of the sets‚ if such a point exists [3].

It should be noted that the dynamic range is diminished at the expense of enlarged processing delay, as the number of

iterations rises. The resultant spectrum will have less than 1% of the signal power outside of the Nyquist range after

little iteration. However, by allocating data symbols to unused bins‚ a significant amount of energy is should not be put

above the Nyquist band of the receiver, as it could lead to extra aliasing noise. However, we should take into

consideration that the high spatial frequency bins will be further reduced by the channel response before they are

gathered at the receiver. This aliasing distortion affects the spatial frequency bins near the Nyquist rate and produces a

considerable decline in the dynamic range and the spatial noise.







III-2 Code Design

The SDMT does not provide a feasible procedure to obtain the capacity of the optical pixelated channel, although it

signifies the maximum achievable rate per frame. In this section‚ a close-capacity attaining multi-level coding and

multi-stage decoding scheme for DMT channels is used in the case of SDMT channel [1]. Multi-level codes are a codedmodulation scheme that utilizes binary codes to enhance the consistency of multi-level QAM constellations. For

constellations of size address bits‚ are needed to identify each constellation point. A multi-

level coding scheme allocates a binary code to each based on the “quality” of the corresponding bit channel.

Assuming Y as the received variable‚ the mutual information for channel input to output is equal to I(Y; B) since the

map from B to the constellation points is a one-to-one relation. Consequently, and the chain rule of mutual information

shows that‚

(5)

Assuming are identified‚ therefore the data transfer on the channel can then be regarded as transmission

on M parallel bit channels. A code can be suggested for each channel based on the conditional mutual information of

the sub-channels. Undoubtedly‚ the conditional mutual information in each bit channel is greatly reliant on theidentification of the constellation points. Hence, if Ungerboeck labeling scheme is employed, we get[4],

(6)

Subsequently‚ the rate of codes chosen should rise for higher bits. At the decoder‚ a multi-stage decoding algorithm is

used in which each is decoded based on realizing the decoder output for lower bits . The application of

multi-level codes in DMT can approach the channel capacity over variety types of channels [11]. It can be concluded

that if each code is capacity attaining‚ then the total channel capacity is obtained by utilizing multi-level coding and

multi-stage decoding.

Fig. 5 and Fig. 6 illustrate the multi-level coder and multi-stage decoder block diagrams, used for the SDMT channel.

Bits and in each bin are Gray labeled and treated as a single symbol. These two bits are coded with a close capacity

attaining‚ asymmetrical rate-1/2 low density parity check code (LDPC) with block length [11]. The log-likelihoodratios at the decoder for these bits can be calculated over all constellation points and applied to the LDPC decoder.

Regarding the higher level bits, they are labeled using Ungerboeck’s set labeling. In order to design codes for the upper

bits, a maximum bit-error rate of is assumed. Reed-Solomon codes of block length 255 were applied to correct

enough errors to ensure that the target bit-error rate was met in the upper bit channels which are prototyped as binary

symmetric channels (BSCs).Table 1 depicts the average conditional probability of error for the higher order bits besides

the capacity of the relevant BSCs [1].For and higher label bits‚ the bit channel is good enough to allow for uncoded

transmission while satisfying the bit-error rate target.

Figure 5. Multi-level coder block diagram for SDMT channel.







Figure 6. Multi-stage decoder for the SDMT channel.

CODE DESIG FOR HIGHER LEVEL BIT LABLES

The spectral efficiency of the system‚ depends on the pulse shape employed in the PAM pixel modulation. The system

performance can be achieved from the spectral efficiency which includes the signaling restraints of the system. The

spectral efficiency of this SDMT scheme can be expressed as where T is the frame interval and, is the K%-

fractional power bandwidth of the PAM pulse. When a 99% fractional power definition of bandwidth is assumed and

rectangular PAM modulation is employed for each pixel, the maximum spectral efficiency achieved is around 1.7

Kbits/s/Hz.The resultant rate over all frequency bins was calculated to be =17.1 kbits/frame or approximately 76% of

the estimated channel capacity, after applying multi-level codes.

On the other hand‚ SDMT may also be suitable in channels with moderate spatial variations. Consider the case of two-

dimensional arrays of lasers and photodiodes for chip-to-chip signaling. Repeated deterministic variations of the gain of

these devices over the array exist due to defects or to manufacturing errors [5], [6] which may result in total failure of

certain pixels. In traditional systems‚ where each transmit pixel is sensed by a single receive pixel‚ this alteration can

result in deletions in the received data.However, although the spectral efficiency which is gained is significantly large,

it should be noted that the complexity of carrying out the required signal processing in a real system has not been taken

into consideration. However‚ it is suggested that the available gains from this channel topology merit further study.

IV. CONCLUSIONS

This paper discusses SDMT spatial modulation, where, a dynamic range compression technique was applied to exploit

unused spatial frequency bins to reduce the peak value of output signals‚ and hence reducing trimming noise. A fairly

accurate-capacity attaining coding scheme‚ formerly adopted for DMT systems‚ was applied to the SDMT channel.This code attains rates in simulation of around 17.1 Kbits/frame, which is around 76% of the estimated channel

capacity.

REFERENCES

[1] Wireless Optical Communications Systems, SteveHranilovic, Springer, Science & Business Media, Inc.,

2005.

[2] I. E. Telatar. Capacity of multi-antenna Gaussian channels. European Trans. Telecommun., 10(6):585–595,

Nov.-Dec. 1999.

[3] A. Gatherer and M. Polley. Controlling clipping probability in DMT transmission. In 31st Asilomar

Conference on Signals, Systems & Computers, volume 1, pages 578–584, 1997.[4] G. Ungerboeck. Channel coding with multilevel/phase signals. IEEE Transactions on Information Theory,

IT-28(l):55–67, January 1982.







[5]

M. Châteauneuf, A. G. Kirk, D. V. Plant, T. Yamamoto, and J. D. Ahearn. 512-channel vertical-cavity

surface-emitting laser based free-space optical link. IEEE Journal of Lightwave Technology, 41(26):5552–

5561, September 2002.

[6]

Amin Al-Ka’bi, “On modeling of Wireless MIMO Channel”, Proceedings of IEEE Sixth International

Conference on Intelligent Systems, Modelling and Simulation (ISMS-2015), Kuala Lumpur, Malaysia, on 9 -12 February, 2015.

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On Modeling of Spatial Discrete Multi-Tone MIMO Optical Channel