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Abstract- Loading algorithm for Discrete Multitone Modulation calculates number of bits and energy for every sub-channel to maximize rate or maximize performance with constraint of fixed bits/symbol (Rate-adaptive (RA) loading criterion) or fixed energy (Margin-adaptive (MA) loading criterion) respectively. In this paper we investigate performance of optimal and sub-optimal algorithms for MA loading criterion on digital subscriber line (DSL), namely water filling algorithm, chow algorithm and Levin-Campello (LC) algorithm. LC algorithm is observed to perform better as compared to Chow and Water- Filling algorithms.
Data communication is revolutionized by the use of internet. We can share bundles of information with each other on just a click of mouse. So to make internet faster and efficient is a need of time, that why Multicarrier Modulation is area of intensive research now-a-days. Orthogonal frequency division multiplexing (OFDM) is a kind of Multicarrier modulation it assigns equal number of bits to each sub-channel without considering its signal to noise ratio (SNR). Where Discrete Multitone(DMT) is a kind of multicarrier modulation that divides a channel in to many sub-channels and allocates bits to each sub-channel according to the signal to noise ratio (SNR). DMT assigns numbers of bits to each sub-channel with the help of loading algorithms. There are two main type of loading algorithms. Algorithms which maximize data rate subject to fixed energy known as Rate-Adaptive loading criterion. The other type of algorithms minimizes transmitted energy subject to fixed data rate known as Margin-Adaptive loading criterion .
Asymmetric digital subscriber line (ADSL) is a form of DSL which provides high data rate as well as plain telephonic service on same twisted pair. Different standards for ADSL are ITU G.992.1, ITU G.992.1 Annex A, ITU G.992.1 Annex B, ITU G.992.2.
In this paper we will investigate performance comparison of three developed MA loading algorithms on digital subscriber line (DSL), which are Water-Filling MA loading algorithm, Chow MA loading algorithm and Leven-Campello MA loading algorithm
This paper is divided in following sections. Section II will deal with the basic DMT structure, section III discuss MA loading algorithms. Section IV deals with channel modeling and results are presented and discuss in section V. Conclusions are drawn in section VI.
DMT works on the principal of divide and conquer. It is standardized for Digital Subscriber Line (DSL)[1,2].DMT divides DSL transmission line into a large number of small transmission line which are easier to handle. Total data rate of channel is equal to the sum of all the data rates of all sub-channels. Better sub-channels with respect to SNR will get more information while the poor sub-channels will get little or no information .
Basic structure of DMT is as follow and also shown in figure 1. First usable bandwidth is divided in to N number of sub-channels. The number of bits assign to each sub-channel is calculated using loading algorithms. Encoder encode incoming data stream.
QAM assign complex numbers to each encoded symbol so the result is N complex symbols. It is important to understand that QAM is different for different sub-channels as each sub-channel is assigned different number of bits. As we want to transfer a real value signal but after QAM there are N Complex symbols. Serial to parallel conversion is done to break data in to equal number of chunks so a large amount of data can handle at a time. After serial to parallel conversion extension of N-complex numbers to 2N complex conjugate symmetric sequence is done. The result of inverse fast Fourier transform (IFFT) is 2N-real numbers as IFFT is always a real number for complex conjugate symmetric sequence. IFFT is done for sub-channeling formation and modulation. To avoid inter symbol interference (ISI), cyclic prefix (CP) is appended to each DMT symbol. CP consists of last n symbol of each 2N block of data. CP length depends upon channel delay spread.
On receiver side added cyclic prefix is removed first. Fast Fourier Transform (FFT) is performed for de-modulation. De-modulated samples are equalized by zero-force equalizer in order to remove channel effect.2N sample are then reduced to N-samples.QAM demodulation is perform. Decoder finally recovers the data which is compared to the original data in order to find bit error rate (BER) with respect to SNR. The performance of DMT transceiver is observed have improved compared to OFDM and loading algorithms play a significant role in it.
S/P & remove CP
figure 1: DMT STRUCTURE
III. Loading algorithms
For target bit rate transmitted power is allocated to every sub-channel, so to allocate bits according to SNR per sub-channel. There are two kind of loading algorithms. Margin Adaptive loading algorithms in these algorithms we try to minimize energy subject to fixed data rate. While in Rate Adaptive Loading algorithms we try to achieve maximize data rate subject to fixed energy.
Water-Filling MA loading algorihtm
Claud Shannon proposed a solution to the problem of that to optimize transmission bandwidth in 1948 .In this algorithm energy is poured until the number of bits assign to each sub-carrier are calculated using equation (1) and summed up is equal to desired/target data rate .
and are number of bit per symbol ,energy and gain for nth sub-channel respectively . Ò is an SNR gap which presents the difference between channel capacity and target bit rate.
Major drawback of Water-Filling algorithm is that bits per symbol it calculate for every sub-channel can be any real number. Realization of a transmitter with non-integer number is not possible. We may have to round off which result in performance degration compare to other two suboptimal loading algorithms which approximate water-filling results.
Chow MA loading algorithm
Chow algorithm uses the fact that difference in a result of Water-Filling distribution and flat-energy distribution is minimal [4,8]. So equal energy is assigned to each turned on sub-channel, explained mathematically as
is energy for nth sub-channel. E is normalized energy and i is a number of turn on sub-channel. Number of bits allocated to each sub-channel calculated by
is a signal-to-noise ratio on sub-channel n. is a system performance margin. Chow's algorithm is repeated and sub-channel with smallest gain is turned off in each step until optimal margin is achieved and total number of bits becomes equal to target bit rate.
Levin-Campello MA loading algorithm
Levin and Campello worked independently to form an algorithm which is based on greedy approach [5,6]. Each addition bit which has to be sent is place on a sub-channel in which minimum incremental amount of power is required. In other words Levin-Campello algorithm bit distribution is efficient bit distribution. Here efficiency means that there is no other distribution of bits that can reduce the symbol energy.
In this paper we compare the BER performance of above mentioned MA loading algorithms for ADSL channel , with near end crosstalk and far end crosstalk.
IV. modeling of adsl channel
DMT based transceiver used to communicate data through phone line. High frequency electro-magnetic waves which travel on phone line are quickly attenuated and result in loss of their power. On the other hand low frequency travelling waves retain much of their power. ADSL channel is shown in figure 2 and it is look like low pass filter.
Figure 2: ADSL channel frequency response
Crosstalk is a common source of noise in ADSL. The electromagnetic waves which are travelling in twisted pair will induce current in there neighboring twisted pairs. Near-end crosstalk (NEXT) is a type of crosstalk which cause disturbance when signal is travelling in opposite direction on different twisted pairs. Far-end crosstalk (FEXT) occurs when signal is travelling in same direction on different twisted pairs. NEXT modeling and FEXT modeling is done by using equation (4) and equation (5) respectively 
Where and N=number of pair in binder
is power spectral density (PSD) of NEXT and f is frequency PSD of transmitted signal . is a channel in frequency domain and is FEXT PSD.
We have model FEXT and NEXT with 49 number of binder there response is shown below in figure 3 and 4 respectively.
From figure 3 and 4 it can be seen that maximum amplitude for FEXT is -280db very small on the other hand maximum amplitude response for NEXT is -30 db. Even the smallest amplitude of NEXT is far greater than the FEXT maximum amplitude. Additive White Gaussian noise (AWGN) is also included in our channel to represent background noise in ADSL.
Figure 3: FEXT with 49 binders in DSL
Figure 4: NEXT with 49 binders in DSL
V. SIMULATION AND RESULTS
To compare performance of optimal and sub-optimal algorithms for margin adaptive loading we performed simulations on MATLAB.
For our simulation number of sub-channels is 128 so IFFT size is 256 and target bit rate is 500. The AWGN is added to represent background noise while NEXT and FEXT is also added for 49 distributors as mention in section IV.
Figure 5 shows comparison of MA loading algorithms for BER performance in an ADSL channel as well as AWGN background noise too. Figure 6 shows BER performance comparisons when FEXT is also added to ADSL channel and AWGN. Figure 7 shows BER performance comparisons when NEXT added to ADSL channel and AWGN. Figure 8 shows bits distribution for all three algorithms.
Leven-Campello algorithm gives best result as it is optimized with integer number of bits. Water-Filling algorithm is good but as it is optimized with non-integer number its shows a worst BER performance. Chow's algorithm approximates Water-Filling result but keeps number of bits for each sub-channel an integer. Chow algorithm outperforms Water-Filling algorithm. The BER performance is worst in the presence of AWGN and NEXT in an ADSL channel, as shown in fig.6. However, BER performance is best without any crosstalk, whether it is NEXT and FEXT in an ADSL channel.
Figure 5: BER vs Eb/No of various MA loading algorithms in an ADSL channel with AWGN
Figure 6: BER vs Eb/No of various MA loading algorithms in an ADSL channel with AWGN and 49 FEXT disturbers
Figure 7: BER vs Eb/No of various MA loading algorithms in an ADSL channel with AWGN and 49 NEXT disturbers
Figure 8: Bit allocation per sub-channel of various MA loading algorithms in DSL channel
When SNR of a sub-channel is better Levin-Campello algorithm assigns most number of bits to that sub-channel and least number of bits when sub-channel has worst SNR. While Chow's algorithm approximates Water-Filling result, both algorithm shows almost the same from sub-channel whose gain is very low. Because Chow algorithm switches off sub-channels with lowest gain, while water-filling algorithm use all the sub-channels. Figure 8 shows the number of bits per sub-channel allocated by Chow, Water-Filling and LC algorithms. As can be seen in figure 8 most number of bits are assigned by LC algorithm for sub-channel with better SNR as compared to Water-Filling and Chow's algorithms.
In this paper we investigate the performance of three MA loading algorithms for a ADSL channel. We also model FEXT and NEXT to see their effect on BER. Of all three algorithms, Levin-Campello algorithm shows the best result as compared to water-filling algorithm and chow algorithm. Performance of water-filling and chow algorithms are almost same. Moreover, chow algorithm out-performs Water-Fill for higher SNR.
We have evaluate the DMT transreceiver in ADSL channel with FEXT and NEXT as well. The BER deteriorates in the presence of FEXT and NEXT.