PERFORMANCE OF DIFFERENT BIT LOADING ALGORITHMS FOR OFDM AT

PLC CHANNEL 1Isha 2 Pankaj Rana 3 Ravikant saini

1Student of M.Tech(EC) in Shobhit University, Meerut(UP), India 2 Student of M.Tech(CSE) in NITTTR,Chandigarh, India

3Ph.D. Research Scholar in IIT Delhi, India 1isha0129@gmail.com

2 pankaj.rana2004@gmail.com 3 sravikantk2@rediffmail.com

ABSTRACT: In OFDM-based systems, bit allocation techniques are used according to channel response, as noisy sub-channels should carry little or no data. In this paper, we compare four different types of bit loading algorithms and analyze bit allotment per sub channel and energy consumed at a fixed bit error rate and fixed target total number of bits. Index Terms—adaptive bit allocation, Orthogonal Frequency Division Multiplexing (OFDM), multicarrier modulation, multipath channel, power line channel.

I. INTRODUCTION

Orthogonal frequency division multiplexing (OFDM) has developed into a popular scheme for wideband digital communication, whether wireless or over copper wires, used in applications such as digital video and audio broadcasting, wireless networking, broadband Internet access and Power line communication. Several broadband Power line communication standards [8],[9] employ OFDM. These systems are also used for high-bit-rate wireless applications. The OFDM systems can establish the coexistence with the existing shortwave wireless systems by masking appropriate subcarriers and the cyclic prefix of OFDM could sufficiently mitigate the frequency selective channels caused by multipath effect[4].

OFDM is a frequency-division multiplexing (FDM) scheme used as a digital multi-carrier modulation method. The primary advantage of OFDM over single-carrier schemes is its ability to cope with severe channel conditions without complex equalization filters. A large number of closely-spaced orthogonal sub-carriers are used to carry data. The data is divided into several parallel data streams or channels, one for each sub-carrier. The orthogonal sub-channels are spaced 1/T Hz apart and overlap in frequency. The use of a guard interval between

OFDM symbols make it possible to eliminate intersymbol interference (ISI), so it can support efficient spectrum utilization. It is conveniently implemented using IFFT and FFT operations.[2] Initially, OFDM-based systems employ conventional multi-carrier modulation that uses the same modulation scheme (such as quadrature amplitude modulation or phase-shift keying).Then, the overall bit-error rate (BER) performance of these systems is dominated by the sub-channels with the worst performance. Hence, in order to improve the system-wide BER performance, adaptive bit allocation is done to each sub-channel according to their channels states. More bits should be concentrated on the sub channels with a higher channel frequency response, and noisy sub-channels should carry little or no data[5].

In this paper, a comparison is made among different bit-loading algorithms for OFDM based on minimizing the bit error rate(BER) and total energy used with fixed target bits constraint. The first section explains channel model used for simulation, second section explains bit loading technique with different algorithms, then in third section numerical results are shown and in the last conclusion is given.

II. MULTIPATH CHANNEL MODEL

We evaluate the bit loading algorithms on diverse multipath channels which are randomly generated according to Zimmermann’s multipath power line channel model [3]. The frequency responses of multipath power line channels can be approximated as, . . . . /

where the parameters are listed in Table 1.

2012 Second International Conference on Advanced Computing & Communication Technologies

978-0-7695-4640-7/12 $26.00 © 2012 IEEE

DOI 10.1109/ACCT.2012.88

490

2012 Second International Conference on Advanced Computing & Communication Technologies

978-0-7695-4640-7/12 $26.00 © 2012 IEEE

DOI 10.1109/ACCT.2012.88

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TABLE I

PARAMETERS OF THE MODEL OF THE TRANSFER FUNCTION

i Number of path, where the path with the shortest delay has the index i=1

a0,a1 Attenuation parameters k Exponent of the attenuation factor (typical

values are between 0.5 and 1)

gi Weighting factor for path i di Length of path i

Delay of path i OFDM-based systems divide the available bandwidth into a set of N orthogonal sub-channels. With a sufficiently long cyclic prefix playing the role of a guard interval, these N sub-channels can be treated as independent parallel locally flat channels corrupted by additive white gaussian noise (AWGN)[5]. We assume that the bandwidth of all sub-channels is narrower than the coherence bandwidth. III. BIT LOADING

The bit loading uses the channel estimates to determine an appropriate bit allocation across all the subcarriers. As a result, each subcarrier is allocated a different number of bits. Furthermore, constraints are applied to the algorithm to ensure that the allocation stays within a desired range of values. The objective of bit loading algorithms is to minimize the total energy used, while the constraint is a limit on the mean bit error rate (BER) and total number of bits allocated. Then, energy of each sub-channel is described in[1] as, e 2 1 . ΓCNR

Where, bi is number of bits allocated on ith sub-channel, CNRi is carrier to noise ratio on i-th sub-channel and Γ is the SNR gap that is obtained by the gap-approximation analysis based on the target bit error rate (BER), the applied coding scheme, and the system performance margin [5]. Γ =-ln (5* BER)/1.5[7] IV. DIFFERENT TYPES OF

ALGORITHMS In this paper, the comparison is done among different types of algorithms, used for bit loading in OFDM systems, on the basis of bit allocation and energy consumed on each sub-channel. Different algorithms are compared with No Bit Loading technique (where

number of bits allocated evenly to each sub-channel) used as a reference for comparison. The compared algorithms are,

• No Bit Loading • Bit loading algorithm • Chow Bit Loading algorithm • Fast Bit Loading algorithm • Simple Bit Loading algorithm

A. BIT LOADING ALGORITHM

This algorithm assigns the in-phase and quadrature (IQ) mapping on each subcarrier for the given whole code rate and carrier to noise ratio (CNR) on each subcarrier, to maximize the throughput subject to a constraint that average BER is less than Pe, where Pe is bit error rate[4]. It optimizes the bits quantity on each subcarrier subject to constraints on the total BER and transmission power on each subcarrier. The incremental bit errors at every additional one bit on each subcarrier is used to maximize the bit rate and to make indicator matrix which tells about the number of bits allocated to each sub-carrier.

B. CHOW BIT LOADING ALGORITHM

This algorithm consists of three main sections. It first finds the (approximately) optimal system performance margin, 10 log 2

Then, it guarantees convergence with a suboptimal loop and number of bits allocated is defined by, log 1 Γ

And lastly, it adjusts the energy distribution accordingly on a sub channel-by-sub channel basis[6].

C. FAST BIT LOADING ALGORITHM This algorithm uses water filling solution to obtain the optimal solution of energy minimization problem with target bit rate and fixed energy constraints using the Lagrange multiplier method [5]. At the initial bit allocation step, most bits of the target rate are assigned to sub-channels according to channel states. The optimal solution is achieved by allocating bi into sub-channel i:

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b_ log K. CNRt

Where, K 2B ∑ CNRN At the final bit allocation step, multiple bits are assigned to sub-channels in order to guarantee the target rate. In order to converge to target bit, bits are allocated or removed accordingly.

D. SIMPLE BIT LOADING ALGORITHM

This algorithm converges to an optimal bit allocation without using a complex computation procedure to calculate k as in fast bit loading algorithm above. Most bits of the target rate are assigned to sub-channels at the initial bit allocation step, according to channel response and the computational steps are reduced efficiently. Multiple bits are added to or removed from all sub-channels simultaneously in order to approach the optimum bit allocation with no more than 1 bit difference from the optimum bit allocation per sub-channel at the intermediate bit allocation step. At the final bit allocation step, algorithm uses a bit-filling or bit removal procedure in order to guarantee the target rate[5]. Energy required to add one more bit at sub-channel i that is carrying bi, Δe b 2 . CNR for 1 ≤ i ≤ N And the power saved by removing 1 bit at sub-channel i that is carrying bi is given by, Δe b 2 . CNR for 1 ≤ i ≤ N

V. SIMULATION & RESULTS In this section, numerical results are shown which indicates the comparison among different algorithms explained above with the help of graphs and tables. All the algorithms works on a particular channel having CNR values shown in figure 1 with noise spectral density is 10^-7. Assume M-QAM modulation is applied. For 110 total target bits, there is 12 maximum bits allocated to each sub channel and Ber =10^-4 and for 120 total target bits, there is 12 maximum bits allocated to each sub channel and Ber =10^-3. Figure 2 and 4 shows the comparison of number of bits allocated per sub channel, for different algorithms for target bits is 110 and 120 respectively.

Figure 3 and 5 shows comparison of energy used per sub channel, for different algorithms for target bits is 110 and 120 respectively. Total energy consumed for different algorithms is shown in table 2 and 3 for target bits is 110 and 120 respectively.

Figure 1: CNR for different sub channel

Figure 2: Bit Allotment for target bits= 110

Table II

Total energy consumed for bit target=110

No Bit Loading

Bit Loading

Chow Bit Loading

Fast Bit Loading

Simple Bit Loading

31.3382 10.7893 7.3742 3.7303 7.2385

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Figure 3: Energy Consumed for target bit=110

Figure 4: Bit Allotment for target bits=120

Figure 5: Energy Consumed for target bit=120

Table III Total energy consumed for bit target=120

No Bit Loading

Bit Loading

Chow Bit Loading

Fast Bit Loading

Simple Bit Loading

26.948 10.855 6.5781 4.7542 6.4589

VI. CONCLUSION

In this paper, we compare four different algorithms with no loading technique for OFDM and analyze these techniques with bit allotment per sub carrier, energy consumed per sub carrier and total energy used with constraint on BER and total number of bits to be allocated. Finally, we conclude that fast and chow algorithm has minimum energy consumed and simple algorithm has lowest complexity for the same optimal bit allotment.

REFERENCES [1] J. G. Proakis, Communication Systems Engineering, 2nd ed. Prentice-Hall, 2002. [2] RF signal processing, By Louis Litwin and Michael Pugel, ’The principle of OFDM’. [3] M. Zimmermann and K. Dostert, “A multipath model for the power line channel,” IEEE Trans.commun., vol. 50, no. 4, pp. 553–559, Apr. 2002. [4] Taro Hayasaki, Daisuke Umehara, Satoshi Denno, and Masahiro Morikura ’A Bit-Loaded OFDMA for In- home Power Line Communications’, IEEE International Symposium on Power Line Communications and Its Applications, 2009. ISPLC 2009,pp-171-176. [5] Hyeonmok Ko, Kiseok Lee, Seungyoul Oh, Cheeha Kim, ’ Fast Optimal Discrete Bit-Loading Algorithms for OFDM-based systems’, Proceedings of 18th Internatonal Conference on Computer Communications and Networks, 2009. ICCCN 2009. [6] P. S. Chow, J. M. Cioffi and J. A. C. Bingham, “A Practical Discrete Multitone transceiver Loading Algorithm for Data Transmission over Spectrally Shaped channels”, IEEE Transactions on Communications, Vol. 43, No. 234, 2002. [7] Jihang Jang and Kwang Bok Lee, ”Transmit Power Adaptation for Multiuser OFDM Systems” IEEE J. Select. Areas Commun. vol. 21, no. 2, pp. 171-178, Feb. 2003. [8] HomePlug AV White Paper. HomePlug Powerline Alliance (HPA). [Online]. Available: http://www.homeplug.org/ [9] Digital Home Specification White-paper. Universal Powerline Association (UPA). [Online]. Available: http://www.upaplc.org/ [10] Nikolaos Papandreou,Theodore Antona kopoulos, “A New Computationally Efficient Discrete Bit-Loading Algorithm for DMT Applications”, IEEE trans communications, VOL. 53, NO. 5, MAY 2005.

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