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Performance Analysis of Analytic Interpolator for Comb-Type Pilot-Aided Channel Estimation in OFDM Systems Without ICI

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Abstract

Pilot-aided channel estimation in orthogonal frequency division multiplexing (OFDM) systems often needs an interpolation technique to construct the channel frequency response on nonpilot subcarriers. Many studies on interpolations have been published; however, the performance of interpolations such as cubic spline interpolation and linear interpolation is limited by either the number or the position of the pilot subcarriers. This paper proposes an analytic interpolator developed using a linear least square criterion to replace conventional interpolation techniques for comb-type pilot-added channel estimation in OFDM systems without inter-carrier interference. The performance evaluation of the analytic interpolator is performed both on the basis of theory and through simulation, and the results from both the analyses are found to be in good agreement. The simulation results show that the proposed method can effectively mitigate the ill-influences of limitations on the number and position of the pilot subcarriers and that it also outperforms the cubic spline interpolation and linear interpolation, especially for short or nonequidistant pilot patterns.

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Abbreviations

N :

number of total subcarriers in an OFDM system

M :

number of pilot subcarriers

Z :

number of data subcarriers

s :

data symbol vector of size Z

p :

pilot symbol vector of size M

X :

symbol vector of size N

G :

diagonal matrix containing channel attenuation factors

x :

IFFT of X

n′:

vector of independent identically distributed (iid) complex Gaussian noise with zero mean and variance \({\sigma_n^2}\)

H :

channel frequency response vector

n :

FFT of n′

\({\odot}\) :

Hadamard product

L :

number of channel paths

h :

channel impulse response

h L :

channel impulse response vector of size L

h :

channel impulse response vector of size N

H :

discrete-time Fourier transform (DFT) of the channel impulse response h

ρ l :

zero-mean complex Gaussian random variable

\({\hat{\bf X}}\) :

symbol vector after one-tap equalization

\({\bar{\bf p}(m)}\) :

received signal at the mth pilot subcarrier

p(m):

prespecified pilot symbol at the mth pilot subcarrier

\({\hat{\bf H}^{\rm d}}\) :

vector of estimated channel frequency response on the data subcarriers

\({\hat{\bf H}^{\rm p}}\) :

vector of channel frequency response on the pilot subcarriers

0 W :

null vector of size W for zero padding

\({\left[ {\bullet}\right]^{t}}\) :

transpose of the matrix \({\left[ {\bullet}\right]}\)

F :

DFT matrix of size N × N

F N × L :

N by L matrix comprising the first L column vectors of F

\({\tilde {\bf F}_{N\times L}}\) :

N by L matrix by moving the pilot rows to the top of the matrix FN × L

\({\tilde {\bf H}}\) :

vector by moving the pilot rows to the top of the vector H

\({{\bf H}_M^{\rm p}}\) :

vector of the first M elements in \({\tilde {\bf H}}\)

\({{\bf H}_Z^{\rm d}}\) :

vector of the last N − M elements in \({\tilde {\bf H}}\)

\({\tilde {\bf E}}\) :

permutation matrix of size N × N

\({\tilde {\bf F}_{M\times L}^+}\) :

Moore-Penrose inverse of \({ \tilde {\bf F}_{M\times L}}\)

E[u]:

expectation of u

tr[Q]:

trace of matrix Q

e :

normalized error of channel estimation

f ne :

noise enhancement factor (NEF)

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Authors and Affiliations

  1. The Institute of Electrical Engineering, National Chung Cheng University, No. 168, University Rd., Min-Hsiung Chia-Yi, Taiwan, ROC

    Chuan-Wang Chang

  2. Department of Electronic Engineering, Chienkuo Technology University, No. 1, Chieh Shou N. Rd., Changhua City, Taiwan, ROC

    Chuan-Wang Chang, Ho-Lung Hung & Shu-Hong Lee

  3. Department of Electrical Engineering, Tunghai University, No. 181, Taichung Harbor Rd., Section 3, Taichung, Taiwan, ROC

    Jyh-Horng Wen

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  1. Chuan-Wang Chang
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  2. Ho-Lung Hung
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Correspondence to Shu-Hong Lee.

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Chang, CW., Hung, HL., Lee, SH. et al. Performance Analysis of Analytic Interpolator for Comb-Type Pilot-Aided Channel Estimation in OFDM Systems Without ICI. Wireless Pers Commun 59, 345–360 (2011). https://doi.org/10.1007/s11277-010-9921-y

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