The present invention generally relates to channel estimation, and more particularly relates to channel estimation for OFDM systems.
The response of a wireless communication channel is estimated by a wireless receiver so that the receiver can coherently demodulate received data symbols. Channel estimation is typically performed using known symbols referred to as pilot symbols. Pilot symbols are transmitted in the time-frequency domain in OFDM (Orthogonal Frequency-Division Multiplexing) systems. The pilot symbols sample the time-frequency response of the OFDM channel which is a slow-varying, two-dimensional process. The response of an OFDM channel is conventionally estimated based on pilot symbols using minimum mean-square error estimation (MMSE), maximum-likelihood (ML) estimation or other approaches that are suboptimal such as interpolation.
MMSE channel estimation typically requires prior knowledge of channel statistics and tends to be highly complex because of the matrix inversion performed during the channel estimation process. The size of the matrix inversion performed by an MMSE estimator depends on the number of pilot symbol observations. In OFDM systems, pilot symbol density must be sufficiently large so that receiving devices can properly reconstruct an accurate representation of the time-frequency channel response. This in turn can dramatically increase the size of the matrix inversion performed by an MMSE channel estimator, significantly increasing MMSE estimation complexity. ML channel estimation also tends to be relatively complex, but not as complex as MMSE estimation. When pilot symbols are regularly spaced, ML estimation can be implemented using a two-dimensional FFT (fast-Fourier transform) process that yields the channel response in the delay-Doppler domain.
The complexity of both MMSE and ML estimators tends to increase significantly when pilot symbol spacing is irregular. Many types of OFDM systems have high pilot symbol density and irregular pilot symbol spacing. For example, the downlink specified in IEEE (the Institute of Electrical and Electronics Engineers) standard 802 16e (WiMAX) has 120 pilots for each OFDM symbol. Pilot spacing is also irregular, meaning that pilot symbols are transmitted at different time and frequency intervals. The Long Term Evolution (LTE) standard specified in Release 8 of 3GPP (3rd Generation Partnership Project) also calls for irregular pilot symbol spacing. The matrix inversion performed by a conventional MMSE estimator increases significantly when pilot symbol spacing is irregular. The complexity of a conventional ML estimator also increases when the estimator processes irregularly-spaced pilot symbols. An interpolation-based technique can be used to perform channel estimation when pilot symbol density is relatively high, but is sub-optimal and sacrifices accuracy for less complexity.
SUMMARY
Smaller patterns of regularly-spaced pilot symbols can be discerned from a larger pattern of irregularly-spaced pilot symbols transmitted in the time-frequency domain. Accordingly, the irregularly-spaced pilot symbols can be partitioned into at least two different groups of regularly-spaced pilot symbols in the time-frequency domain. Each group of regularly-spaced pilot symbols is individually processed with lower complexity and the results combined to generate an accurate time-frequency channel response estimate.
According to an embodiment, a set of irregularly-spaced pilot symbols is transmitted over a time-frequency window. Channel response is estimated based on the pilot symbols by grouping the pilot symbols into subsets of regularly-spaced pilot symbols. An intermediate quantity is generated for each subset of regularly-spaced pilot symbols as a function of the pilot symbols included in the subset. The channel response is estimated over the time-frequency window as a function of the intermediate quantities.
Of course, the present invention is not limited to the above features and advantages. Those skilled in the art will recognize additional features and advantages upon reading the following detailed description, and upon viewing the accompanying drawings.
In yet another embodiment, irregularly-spaced OFDM pilot symbols can be grouped into subsets of regularly-spaced pilot symbols by blindly detecting the communication mode used to transmit the pilot symbols. The baseband processor 130 and/or the pilot symbol partition unit 134 can determine if a pilot symbol pattern is irregular based on the communication mode, and if so, whether the irregular pattern can be partitioned into smaller, regularly-spaced patters. The communication mode may correspond to the transmission technology (e.g., WiMAX, LTE, etc.) or can be any other type of information relating to the communication of information over a wireless channel that can be used to determine pilot spacing. The pilot symbols are then grouped into subsets of regularly-spaced pilot symbols based on the communication mode. In each pilot grouping embodiment, the channel estimator 132 generates a composite channel estimate based on the smaller subsets of regularly-spaced pilot symbols instead of a single larger set of irregularly-spaced pilot symbols.
X[t,f]=H[t,f]A[t,f]+Z[t,f] (1)
where the index [t,f] corresponds to the fth frequency sub-carrier in the tth OFDM symbol, H[t,f] is the time-frequency response of the channel at a particular point, Λ[t,f] is the transmitted symbol and Z[t,f] represents Additive White Gaussian Noise (AWGN). The baseband processor 130 estimates the channel response H[t,f] based on known pilot symbols and uses the channel response H[t,f] to coherently demodulate received data symbols. The pilot observations X[t,f] can be concisely expressed in matrix form by arranging the observations into a column vector as given by:
X
1=Λ1H1+Z1 (2)
where Λ1 is a diagonal matrix containing the pilot symbols as diagonal elements and X1, H1 and Z1 are column vectors of the same size corresponding to the pilot observation, channel and noise, respectively.
The observations from all regular pilots can be stacked into a column vector as given by:
The column-vector form of equation (3) can be converted to matrix-form by introducing the subscript t as given by:
X
t=ΛtHt+Zt (4)
In one embodiment, the channel H[t, f] can be modeled as a two-dimensional, zero-mean White Sense Stationary (WSS) Gaussian random process having the following correlation:
Γ[t1−t2]≡E{H[t1,f1]H*[t2f2]} (5)
The channel correlation represented by equation (5) is typically known or can be estimated from past observation. The MMSE channel estimation can be formulated based on the channel statistics and the matrix representation of equation (4) as explained next.
In more detail, let H denote the column vector containing the channel response at the locations to be estimated in the time-frequency domain. For example, this can be any part of the 16 OFDM symbols by 56 frequency sub-carriers shown in the window area of
where ΠHt=E{HtHtH} denotes the auto covariance matrix of Ht, ΠHHt=E{HHtH} is the covariance matrix between H and Ht and HHXt is the similarly defined covariance matrix between H and Xt. The elements in the different covariance matrices can be derived using the channel correlation function of equation (5). Accordingly, the MMSE channel estimation process becomes a linear operation that transforms the pilot observation vector Xt into a vector containing the channel estimates at the desired locations.
The pilot symbol observations 500 corresponding to the ith regular pilot symbol pattern over the time-frequency window limited by the symbol range 0≦t<NSYM and the frequency sub-carrier range 0≦f<NSUB are given by:
where φi represents frequency offset, ψi represents time offset, 0≦n<Q, 0≦m<K, NSYM=NQ and NSUB=MK . A more concise matrix expression of equation (4) when considering i subsets of regularly-spaced pilot symbols is given by:
X
i;n,m=ΛiHi;n,m+Zi;n,m (8)
According to the MMSE estimation embodiment, the intermediate quantity derived for each subset of regularly-spaced pilot symbols is an intermediate channel response estimate Ĥi[t, f] 510 computed using equations (6) and (8) where the index i corresponds to the ith regularly-spaced pilot pattern 500 under consideration. Thus, each subset of regularly-spaced pilot symbols determined by the pilot symbol partition unit 134 is used to generate an intermediate MMSE channel estimate Ĥi[t, f] 510. A signal combiner 520 included in or associated with the channel estimator 132 combines the different intermediate MMSE channel estimates Ĥi[t, f] to form a composite MMSE estimate of the channel as given by:
Each intermediate delay-Doppler image Ii[τ, v] 610 represents the two-dimensional DFT (discrete Fourier transform) of the observation 600 of size (Q,K) corresponding to the ithregular pilot symbol pattern. Patterns of different offsets (φi,ψi)are phase modulated by the leading term in equation (10). A signal combiner 620 included in or associated with the channel estimator 132 combines the different intermediate delay-Doppler images Ii[τ,v] 610 to obtain a composite delay-Doppler image as given by:
The baseband processor 130 and/or the channel estimator 132 convert the composite delay-Doppler image ICOMP[τ, v] from the delay-Doppler domain to the time-frequency domain to obtain a composite estimate ĤCOMP of the channel. In one embodiment, the composite delay-Doppler image is converted to the time-frequency domain by a two-dimensional inverse DFT (IDFT) function 630 of size(NSYM,NSUB). In one embodiment, the composite delay-Doppler image ICOMP[τ,v] is filtered before conversion to the time-frequency domain. According to this embodiment, the two-dimensional IDFT function 630 is performed over the entire time-frequency window to yield the composite channel estimate ĤCOMP as given by:
where W[τ,v] is a windowing function for removing sampling artifacts. In one embodiment, the windowing function W[τ,v] is a two-dimensional brick-wall filter that eliminates non-zero elements of the composite delay-Doppler image outside the maximum delay-Doppler spread as given by:
With the above range of variations and applications in mind, it should be understood that the present invention is not limited by the foregoing description, nor is it limited by the accompanying drawings. Instead, the present invention is limited only by the following claims, and their legal equivalents.
This application is a continuation of U.S. application Ser. No. 12/265,220, filed Nov. 5, 2008, now pending, the disclosure of which is incorporated herein by reference.
Number | Date | Country | |
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Parent | 12265220 | Nov 2008 | US |
Child | 13277754 | US |