DOWN-SAMPLED IMPULSE RESPONSE CHANNEL ESTIMATION
A method for deriving a channel transfer function from an Orthogonal Frequency-Division Multiplex (OFDM) signal received over a channel and having unmodulated sub-carriers and sub-carriers modulated with symbols, includes the steps of sampling the received OFDM signal at a sampling rate greater than the bandwidth of the OFDM signal, deriving from the sampled OFDM signal a set of time domain coefficients representative of the channel impulse response, and deriving from a subset of the set of time domain coefficients a channel transfer function in the frequency domain.
1 . A method of deriving a channel transfer function from an OFDM signal received over a channel, the OFDM signal having unmodulated sub-carriers and sub-carriers modulated with symbols, the method comprising:
a) sampling the received OFDM signal at a sampling rate greater than or equal to the bandwidth of the OFDM signal;
b) deriving from the sampled OFDM signal a set of time domain coefficients representative of the channel impulse response; and
c) deriving from a subset of the set of time domain coefficients a channel transfer function in the frequency domain.
2 . A method as claimed in claim 1 , wherein the modulated sub-carriers comprise pilot symbols which are predetermined and data symbols which are arbitrary, comprising deriving the set of time domain coefficients from the pilot symbols.
3 . A method as claimed in claim 1 , wherein the subset as a proportion of the set is greater than the proportion of modulated sub-carriers among the sub-carriers.
4 . A method as claimed in claim 3 , wherein the subset as a proportion of the set is two thirds.
5 . A method as claimed in claim 1 , wherein the time domain coefficients of the subset are selected at equal time intervals from the set of coefficients.
6 . A method as claimed in claim 1 , wherein the time domain coefficients of the subset are selected at non-equal time intervals from the set of coefficients.
7 . A method as claimed in claim 2 , comprising in step b) deriving the set of time domain coefficients representative of the channel impulse response as
h =( F L H A p H A p F L ) −1 F L H A p H Fr , where
h is a vector of dimension L×1 comprising the set of time domain coefficients, and L is the number of samples of the received OFDM signal,
r is a vector of dimension L×1 comprising the L samples of the received OFDM signal,
F is a Fourier transform matrix of dimension N×N, where N is the number sub-carriers in the plurality of sub-carriers,
F L is a Fourier transform matrix of dimension an N×L for transforming L samples in the time domain into N frequency coefficients in the frequency domain,
F L H is an inverse Fourier matrix of dimension L×N for transforming N frequency coefficients in the frequency domain into L coefficients in the time domain,
A p is a diagonal matrix of dimension N×N containing diagonal elements representative of the transmitted pilot symbols, and
A p H is the hermitian of a diagonal matrix containing the pilot symbols in the pilot positions and zero elsewhere.
8 . A method as claimed in claim 2 , comprising in step b) deriving the set of coefficients representative of the channel impulse response as
h =(σ w 2 I L +R h F L H A p H A p F L ) −1 R h F L H A p H Fr , where
h is a vector of dimension L×1 comprising the set of time domain coefficients, and L is the number of samples of the received OFDM signal,
r is a vector of dimension L×1 comprising the L samples of the received OFDM signal,
F is a Fourier transform matrix of dimension N×N, where N is the number sub-carriers in the plurality of sub-carriers,
F L is a Fourier transform matrix of dimension N×L for transforming L samples in the time domain into N frequency coefficients in the frequency domain,
F L H is an inverse Fourier matrix of dimension L×N for transforming N frequency coefficients in the frequency domain into L coefficients in the time domain,
A p is a diagonal matrix of dimension N×N containing diagonal elements representative of the transmitted pilot symbols,
A p H is the hermitian of a diagonal matrix containing the pilot symbols in the pilot positions and zero elsewhere,
R h is the covariance matrix of h,
σ w 2 I L is the covariance matrix of the estimated noise power.
9 . A method as claimed in claim 7 , comprising deriving the channel transfer function in step c) as F L DS ×h DS , where h DS is a vector of dimension L DS ×1 comprising the subset of time domain coefficients of h, L DS is the number of samples of the subset, and F L DS is a matrix of dimension N×L DS comprising only the columns of F L which correspond to the subset of the time domain coefficients of h.
10 . Apparatus adapted to perform the method of claim 1 .
11 . Computer program code adapted to perform the method of claim 1 .
12 . A computer readable medium comprising computer program code adapted to perform the method of claim 1 .
13 . A method as claimed in claim 2 , wherein the subset as a proportion of the set is greater than the proportion of modulated sub-carriers among the sub-carriers.
14 . A method as claimed in claim 13 , wherein the subset as a proportion of the set is two thirds.
15 . A method as claimed in claim 2 , wherein the time domain coefficients of the subset are selected at non-equal time intervals from the set of coefficients.
16 . A method as claimed in claim 3 , wherein the time domain coefficients of the subset are selected at non-equal time intervals from the set of coefficients.
17 . A method as claimed in claim 13 , wherein the time domain coefficients of the subset are selected at non-equal time intervals from the set of coefficients.
18 . A method as claimed in claim 14 , wherein the time domain coefficients of the subset are selected at non-equal time intervals from the set of coefficients.
19 . A method as claimed in claim 8 , comprising deriving the channel transfer function in step c) as F L DS ×h DS , where h DS is a vector of dimension L DS ×1 comprising the subset of time domain coefficients of h, L DS is the number of samples of the subset, and F L DS is a matrix of dimension N×L DS comprising only the columns of F L which correspond to the subset of the time domain coefficients of h.