Cyclic Prefix Assisted Sparse Channel Estimation for OFDM Systems

P.Sudheesh Ashwin Jayakumar R.Siddharth M.S.Srikanth N.H.Bhaskar V.Sivakumar C.K.Sudhakar

Department of ECE, AmritaVishwaVidyapeetham, Coimbatore, TamilNadu, India. p_sudheesh@cb.amrita.edu srikanthsudhakar.m@gmail.com siddhr@gmail.com

ashwinjk1990@gmail.com

Abstract – In this paper an efficient algorithm is presented for the estimation of a channel modelled as sparse for an OFDM system. Conventional Pilot-Based techniques and blind estimation techniques require a large number of pilot tones and complex mathematical computations respectively to estimate the channel vector. This drawback is particularly pronounced in sparse systems where the effective channel vector has a very few number of taps. The proposed method uses a modification made to the Cyclic Prefix to detect the position of the most significant taps (MST) for a sparse channel. Least Square estimation method is then used to effectively estimate the channel vector. Prior knowledge of the most significant tap positions obtained from the cyclic prefix ensures spectral and computational efficiencies.

Index Terms—MIMO-OFDM, sparse channel estimation, most significant taps, cyclic prefix, PAPR.

I. INTRODUCTION

Orthogonal frequency-division multiplexing (OFDM) is a

method of encoding digital data on multiple carrier

frequencies. OFDM has developed into a popular scheme

for widebanddigital communication, whether wireless or

over copper wires, used in applications such as digital

television and audio broadcasting, DSLbroadband internet

access, wireless networks, and 4G mobile

communications.[1]Multiple Input Multiple Output

(MIMO) systems has revolutionised the field of high

speed communication. It has resulted in increased data

rates and enhanced performance in challenging

environments.

A wireless channel is modelled as sparse when the delay

spread is larger than the symbol duration and the number

of most significant paths is usually small[2]. Based on this

assumption of an equivalent discrete time channel where

usually only a few taps are considered to be significant, in

the channel vector, this sparse structure can be employed

to improve channel estimation for OFDM systems by

reducing the computational complexity. In a high data rate

communication system, the signal bandwidth exceeds the

coherence bandwidth; hence the channel is frequency

selective in nature.

Channel Estimation is of prime importance to OFDM and

Multiple Input Multiple Output (MIMO)-OFDM systems.

Broadly speaking, channel estimation techniques can be

classified into three types-Blind, Trainer-Based and Semi-

blind approaches. Blind estimation techniques require the

use of second order statistics which makes it a spectrally

efficient method [3]-[5]. Trainer-Based method employs

known pilot signals to render an accurate estimation of

channel vector. However, the main drawback of this

approach is its spectral inefficiency [6]-[7]. Semi-Blind

approach is a hybrid method that makes use of both a

known pilot signal and second order statistics to

accurately estimate the channel while being spectrally

efficient[8]-[9].

In the existing literature that deals with blind estimation

approach, a large number of OFDM symbols are used to

accurately estimate the channel. However, the

disadvantage of this method is that it is difficult to receive a

lot of OFDM symbols within the coherent time for an

accurate estimation of the channel [3]-[5]. Similarly, in

existing literature dealing with pilot based methods, a

large number of pilot symbols are utilized in order to

estimate the channel accurately [6]-[7]. This drastically

reduces the spectral efficiency and also is a major

hindrance to the data rate.

(1)

is the delay associated with the lthMST

is the co-efficient of the lth MST

Our proposed estimation method uses a distinct symbol to

estimate the position of MSTs in the channel and a few

pilot tones to estimate the channel vector. This method is

spectrally more efficient than conventional pilot-based

channel estimation methods as it uses lesser number of

pilot tones and is more superior to blind estimation

technique as it provides greater accuracy and reduced

computational complexity. Conventional Pilot-based

methods ensure that length of cyclic prefix is greater than

the channel length[5]. Usually, the cyclic prefix is

discarded at the receiver end. By superimposing a user

database signal, all cyclic prefix ensures that all the Most

Significant Taps (MST) positions are detected using

cyclic prefix without affecting the orthogonality of actual

OFDM symbol. This method is employed in stationary

communication systems.

II. DATA MODEL

The transmitted mth OFDM symbol in an OFDM system

can be explained as a vector of the sub carrier frequencies,

Here the number of subcarriers is denoted by K. The time-

domain OFDM signal is found using the inverse discrete

Fourier transform (IDFT) processing,

A cyclic prefix is then added after which each OFDM

symbol is sent out by the transmit antenna. This cyclic

prefix is removed at the receiver after which this

frequency-domain signal is DFT processed. The received

signal is expressed as,

The DFT processed signal is expressed as

In broadband wireless communications for which the

OFDM systems are designed, it follows that the signal

bandwidth is larger than the coherence bandwidth. This

implies that the channel is frequency selective. Almost all

the channel estimation techniques work on discrete time

channel which can be modelled by an L-tap FIR filter.

The channel is assumed to be constant for number of

OFDM symbols. It is described by

Let the channel length be L. If the length of the cyclic

prefix is not less than L, the time domain signal model for

the frequency selective fading channel is

(6)

Here g denotes the number of OFDM symbols within the

coherence time i.e. channel vector h, has to be estimated

for every g symbols and K is the number of samples in an

OFDM symbol.

III. PROPOSED CHANNEL ESTIMATION

ALGORITHM

The first step in estimating the channel vector is to detect

the positions of the MSTs. This is done by using a

dedicated symbol (P) similar to a comb type pilot tone

(i.e. u(f) ) but this means that the entire spectrum is

wasted in that symbol duration. This loss of spectral

efficiency is rectified by appending the time domain

equivalent of the signal to a conventional cyclic prefixed

OFDM symbol [4]-[5].

(7)

where is a scaling constant.

This symbol P is then added to a conventional data

carrying cyclic prefixed OFDM symbol. The resulting

OFDM symbol has a very large value as its first sample.

The combined symbol is then sent to the transmitting

antenna.

(8)

isthe mth cyclic prefixed OFDM signal.

This means that peaks in the received signal correspond to

most significant delays in the channel vector (since each

significant peak is a delayed version of the first sample)

that is the MST positions are obtained by a direct analysis

of the CP of the received signal. Since the effect of the

appended symbol is restricted to within the cyclic prefix

the orthogonality of the original data carrying OFDM

symbol remains unaffected.

The MST positions are obtained by applying a threshold

condition on the received signal defined as the average

signal power within the cyclic prefix.

(9)

wherek is the length of the cyclic prefix.

The accuracy of the MST position determined is

proportional to the value of the constant . Higher the

value of , greater is the accuracy of the detection

algorithm. However, a large value of causessudden

surges in the received signal (PAPR). Hence, based on

the system design and the nature of the channel, an

optimum value for should be determined to achieve

maximum accuracy within permissible levels of PAPR.

IV. MST ESTIMATION

When the MST positions are known the received signal

(10)

For a known value of X(n) and received Y(n) and known MST positions, a linear equation of the channel coefficients can be obtained

(11) whereC contains the channel coefficients,

Acontains

andX contains the known transmitted symbol X(m).

The coefficient matrix C is estimated as the least

squaresolution

(12)

The accuracy of the solution depends on the order of A

(i.e. the number of pilot tones used ) . The system

accuracy can thus be improved by estimating the C matrix

through an analysis of the combined pilot tones from

adjacent symbols.

V. SIMULATION RESULTS

The algorithm is simulated in a SISO OFDM system. We

consider an OFDM symbol to contain 1024 sub-carriers.

The channel vector h(t) is a 13-tap FIR filter modelled as

a Sparse Rayleigh channel with the value of the

coefficients lying between 0.4 to 1. The OFDM symbol is

designed to contain pilot tones at prime sub-carrier

frequencies i.e.:2 , 3 , 5 . These positions

are selected to ensure that the order of the estimator

matrix is greater than or equal to the number of channel

coefficients.

In the simulation, the value of is chosen in the range

of 0.6-0.8. This results in a peak to average power ratio

(PAPR) of around 16dB. This PAPR is of limited

significance as the surges occur within the cyclic prefix

(CP), an unprocessed portion of the received signal.

The MST positions are estimated and the positions are

then given to the estimator block which generates the

estimator matrix (A) of order m × n where n is the

number of significant taps in the channel vector(MST’s).

The coefficient matrix C is estimated as

(13)

Where, contains the known pilot tones and B is

the received symbol.

In a noise free environment the mean square error

between the actual vector and the estimated channel

vector is of the orderof - 200dB, which is negligible.

Therefore our estimation method provides very reliable

results at extremely low spectral wastage and minimal

computational complexity.

The modulation scheme is simulated in 1024 subcarrier

OFDM symbol with 30 subcarriers dedicated for training

purpose. The error between the actual and the estimated

channel vector is illustrated in Fig. 3 as a plot of the

variations of average mean square error with respect to

SNR of the signal, for different number trainer signals

used. The scheme is iteratively repeated and the results

are averaged. It is seen that the proposed method produces

results better than that of a conventional LS channel

estimation technique at a reduced spectral cost. Also the

computational complexity associated with this method is

greatly reduced compared to the conventional blind

estimation method. Hence the proposed technique is

found to provide better results than the existing

techniques available [4]-[8].

For the simulation, a 13-tap sparse channel vector having

3 MST’s is generated in Fig. 1. Using the proposed

method in a noise-free environment, the channel vector is

obtained from the received signal in Fig. 2 with an MSE

margin of -461dB.

Fig. 1 Actual Channel Vector

Fig. 2Estimated Channel Vector

VI. CONCLUSION

A sparse channel estimation algorithm has been proposed

for OFDM systems. It is seen that the proposed method

produces results better than that of a conventional LS

channel estimation techniques at a reduced spectral cost.

Also the computational complexity associated with this

method is greatly reduced compared to the conventional

blind estimation method. Hence the proposed estimation

algorithm is found to provide better results than the

existing techniques available.

REFERENCES

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[2] M.R.Raghavendra and K.Giridhar, “Improving channel estimation in OFDM systems in sparse multipath channels”, IEEE Signal Processing Letters, vol.12, no.1, pp.52-55, 2005.

[3]C.Shin, R.W. Heath and E.J.Powers,” Blind Channel Estimation for MIMO-OFDM systems”, IEEE Trans. On Vehicular Technology,vol.56, no.2, pp. 670-685, 2007

[4]F.Gao, Y.Zeng,A. Nallanathan and T.Ng, ”Robust subspace blind channel estimation for cyclic prefixed MIMO – OFDM systems : algorithm, identifiability and performance analysis”, IEEE Journal on Selected Areas in Communications, Vol.26, no.2, pp.378-388, February 2008.

[5]C.Shin, R.W.Heath and E.J.Powers,”Non Redundant precoding-based blind and semi-blind channel estimation for MIMO Block Transmission with a cyclic prefix”, IEEE Trans. On Signal Processing, Vol.56, no.6, pp. 2509-2523, June 2008.

[6]M.Shin, H.Lee, C.Lee, ”Enhanced Channel Estimation Technique for MIMO-OFDM systems”, IEEE Trans. On Vehicular Technology,Vol.53, no.1,pp.261-265,Jan 2004.

[7]H.LI, C.K.Ho, J.W.M. Bergmans and F.M.J. Willems,”Pilot-aided angle domain channel estimation techniques for MIMO-OFDM systems”, IEEE Trans. On Vehicular Technology,Vol.57, no.2, pp. 906-920, March 2008

[8]Feng Wan, W.-P. Zhu, and M.N.S. Swamy, “Semi-Blind Sparse Channel Estimation for MIMO-OFDM Systems”, IEEE transactions on vehicular technology, vol. 60, no. 6, july 2011

[9] F. Wan, W.-P. Zhu, and M. N. S. Swamy, “Semi-blind most significant tap detection for sparse channel estimation of OFDM systems”, IEEE Trans. on Circuits and Systems I: Regular Papers, vol. 57, no. 3, pp. 703–713, 2010.

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Fig. 3MSE Vs SNR plot for varying number of pilot

sub-carriers. It is seen that there is a significant decrease

in the mean square error values for increasing number of

pilots.