Patent Application
20110090975
1. Field of the Invention
The present invention relates to Orthogonal Frequency Division Multiplexing (OFDM) modulation methods, and more specifically to an OFDM channel estimation and inter-carrier interference cancellation method.
2. Description of the Related Art
The OFDM signal includes a number of independently modulated, mutually orthogonal subcarriers over which large constellation signals can be transmitted, allowing very effective use of the spectrum with high bandwidth efficiency. High data rate broadband transmissions suffer inescapably from frequency selectivity, which causes Inter Symbol Interference (ISI). A Cyclic Prefix (CP) of length greater than or equal to the channel length is appended to the OFDM symbol to absorb the ISI, but at the expense of a rate loss. The CP thus serves to decouple the OFDM symbols, resulting in a simplified, single-tap equalizer structure at the receiver. The ability of OFDM to allow high-speed data transmission over frequency selective channels with simple equalizers has led to its adoption for many conventional broadband standards, including Digital Audio and Video Broadcasting (DAB, DVB), wireless local area network (WLAN) standards (e.g., IEEE 802.11a/b/g and HIPERLAN/2) and high-speed transmission over digital subscriber line (DSL). A number of emerging broadband wireless communication standards are using or planning to use OFDM modulation, including 802.16 (WiMAX), 802.20 Mobile Wireless Broadband Access (MWBA) and other emerging cellular wireless communication systems, such as 3GPP evolution and 4G.
The orthogonality of the subcarriers of the OFDM system is of critical importance. If this orthogonality is lost, the information on one subcarrier is leaked to other adjacent subcarriers, i.e., the subcarriers are no longer decoupled. This leakage is termed as inter-carrier interference (ICI). There are three main contributing factors to ICI, namely, phase noise, frequency error, and Doppler shift. In practice, the effect of phase noise and frequency error can be minimized by proper receiver design, and thus these two factors do not amount for a large ICI component. Doppler shift appears due to the relative motion of the transmitter and receiver and is the main cause of ICI, especially in mobile wireless environments where the channel is continuously changing with time. Under such conditions, maintaining the orthogonality of OFDM subcarriers is a challenge, particularly if the time variation is large.
The interaction of the subcarriers due to ICI complicates the data detection process at the receiver, as detection can no longer be performed on a carrier-by-carrier basis. Rather, some form of equalization must be employed. The degree of time variation of the channel is directly related to the magnitude of ICI. For example, Doppler shift is an issue for the DVB-H system, which targets highly mobile users. The problem is more severe for DVB-H systems in the United States, as compared to those planned for the rest of the world. This is because, in the United States, the carrier frequency for DVB-H is between 1.67-1.675 GHz, which is roughly twice the highest frequency being considered elsewhere, meaning that the Doppler shift will be higher for the U.S. system. Also, the bandwidth of the U.S. system is 5 MHz, as opposed to the 8 MHz bandwidth of the rest of the world, so that the frequency spacing for the U.S. system will be reduced by a factor of ⅝.
In the absence of ICI (as long as the channel remains constant within one OFDM symbol), to obtain the estimate of the channel matrix H, one needs to estimate N parameters (i.e., only the diagonal of the N×N channel matrix H). On the other hand, for severe time variation, one needs to estimate all the N2 parameters (i.e., every element of H). For mild time variation, it would be sufficient to assume H to have M diagonals and estimate only MN parameters. Faster time variation requires frequent updates of channel estimate. This burdens the receiver, as the channel gains have to be periodically estimated before equalization can be performed.
A solution to the high frequency of channel estimation and the large number of parameters that need to be estimated is to send a large amount of training data, but this reduces the useful data throughput of the system. By making proper use of the a priori available information (data and channel constraints) about the system, we can reduce this training overhead. Another solution is to use Iterative methods for ICI cancellation, but these not only suffer from inherent latency, but also prove to be computationally costly.
Thus, an OFDM inter-carrier interference cancellation method solving the aforementioned problems is desired.
The OFDM channel estimation and inter-carrier interference cancellation method uses a few pilots within Orthogonal Frequency Division Multiplexing (OFDM) systems in general, and mobile OFDM systems in particular. The frequency domain channel is estimated using an eigenvalue-based model reduction technique with high accuracy. A Minimum Mean Square Error-based (MMSE) Finite Impulse Response (FIR) equalizer is then used to obtain an ICI free estimate of the transmitted signal.
A method is provided for ICI cancellation in OFDM systems in a high-Doppler environment, the received signal comprising a plurality of subcarriers. Furthermore, the ICI cancellation method, in the frequency domain, at least partially removes the overlap between M adjacent interfering subcarriers. The ICI cancellation method is fast and computationally efficient.
The method includes a receiver structure for efficiently canceling ICI using an MMSE-based FIR equalization filter. The taps of the filter are updated based on the estimate of the channel taps by the channel estimation logic.
An ICI cancellation method is provided for use in an OFDM communication system experiencing high Doppler, in which the receiver estimates the channel from the pilots inserted in the OFDM symbol at the transmitter. The method at the transmitter includes processing and precoding the data, arranging the data and pilots on the respective subcarriers, modulating it to an OFDM symbol, inserting the CP, and transmitting the OFDM symbol over the channel. The method steps at the receiver include receiving the transmitted OFDM symbol, removing the CP, demodulating the OFDM symbol, detecting the pilots, using the pilots to estimate the channel, and detecting the transmitted data from the received signal using the channel estimate.
The ICI cancellation method calculates the estimate of the ICI term from the estimate of the Doppler frequency shift of the received signal and uses it to mitigate the effect of ICI on the received signal.
Moreover, the ICI cancellation method is based on an arrangement of pilot subcarriers of the OFDM symbol such that the receiver is able to detect the pilot subcarriers independent of data subcarriers.
The channel is estimated based on pilot subcarriers, which at least minimizes the effect of ICI. Furthermore, the method makes a collective use of the various constraints on the communication system, providing the ICI free signal in a single iteration and, thus, performs faster than iterative ICI cancellation methods.
These and other features of the present invention will become readily apparent upon further review of the following specification and drawings.
Similar reference characters denote corresponding features consistently throughout the attached drawings.
The OFDM channel estimation and Inter-Carrier Interference (ICI) cancellation method uses a few pilots within Orthogonal Frequency Division Multiplexing (OFDM) systems in general, and mobile OFDM systems in particular. The frequency domain channel is estimated using an eigenvalue based model reduction technique with high accuracy. A Minimum Mean Square Error (MMSE) based Finite Impulse Response (FIR) equalizer is then used to obtain an ICI free estimate of the transmitted signal.
At the outset, it should be understood that the various actions could be performed by program instruction running on one or more processors, by specialized circuitry or by a combination of both. Moreover, the method can additionally be considered to be embodied, entirely or partially, within any form of computer readable carrier containing instructions that will cause the executing device to carry out the technique disclosed herein.
The method presented implements a novel algorithm that reduces or mitigates the effects of ICI on signals transmitted in an OFDM system, the frequency domain channel matrix G is estimated in terms of a parameter vector using an Eigenvalue Decomposition (EVD) based approach.
At the receiver 50b, the transmitted symbol is received by the receiving antenna 200 and passed to the CP removal module 210, the FFT module 220 and passes it to the ICI estimation unit 230. The received signal is also fed to the Doppler frequency estimation unit 300, which sends the estimate of the Doppler frequency to a lookup table 310. There are several methods available for the estimation of Doppler frequency any of which maybe employed here. The lookup table then sends the relevant information to the ICI estimation unit 230, which then passes on the signal to the equalizer 240 to remove the ICI. After mitigating the effect of ICI on the received signal, it is passed to the pilot removal module 250, demodulator 260, de-interleaver 270, de-puncturer 280 and decoder 290 so as to obtain the original data.
The encoder 100, puncture 110, interleaver 120 and modulator 130 modules herein refer to any general encoder, puncture, interleaver, modulator and any available implementation can be used for these modules along with their corresponding decoder 290, de-puncturer 280, de-interleaver 270 and demodulator 260.
The CP added to the OFDM symbol by CP insertion module 160 is assumed to be of length equal to or larger than the Channel Impulse Response (CIR) memory length denoted by L. The CP serves to absorb the ISI introduced by the channel. At the receiver 50b, the CP is stripped and the ISI free time domain signal is obtained, mathematically defined by the relation,
y=Hx+v (1)
where y is the received symbol, H is channel matrix given in
y=GX+v (2)
where y=[y(0), . . . y(N−1)]T and x=[x(0), . . . x(N−1)]T are the receive and transmit signals, GQHQH is the channel matrix (QH is the N—point Inverse Fast Fourier Transform (IFFT) matrix) and v is the noise vector, all in the frequency domain. If the channel remains constant for the duration of an OFDM symbol (a block fading channel model), hn(I) is independent of time n making H circulant and hence G becomes a diagonal matrix, i.e. no ICI occurs. Thus in absence of ICI the various subcarriers of the OFDM symbol are decoupled and hence one tap FEQ is optimal.
For time variant channels, as in the case of mobile users, H is no longer circulant and thus G is no longer a diagonal matrix and some of the signal energy is leaked to the neighboring subcarriers. The input/output relationship of the kth subcarrier is given as
The first term on the right side is the desired signal while the second term is the ICI. In a fast varying channel (high Doppler environment), this ICI term becomes significant and produces an irreducible error floor. An extreme worst case of ICI will result in non-zero values for all N2 elements of G. A moderate case of ICI will result in G having M diagonals, i.e. G is banded. For a banded G, all the elements not contributing to the diagonals can be set to zero.
Let RG denote the autocorrelation matrix of vec(G), where vec(G) refers to the mathematical operation of vectorization of matrix G into a column matrix, and RH denote the autocorrelation matrix of vec(H). The relation between them is
R
G=(Q*Q)RH(Q*
Q)H (4)
The time domain channel matrix H, shown as item 20 in
and B is the N×N permutation matrix given as
With BI having I left columns cyclically shifted to the right then RH can be represented as
where CI is the autocorrelation matrix of vec(AI). From Jake's model of time variation, we have
E[h
m(I)hn(I)*]=J0(2πfd(m−n)T)J(m−n) (8)
where J0(.) is the Bessel function of zeroth-order, fd is the Doppler frequency and T is the sampling time period. Based on equation (8), we can represent the elements of matrix C0 as
The rest of the CI's can be obtained in a similar fashion. It is evident from equation (7) that the rank of CI is N and that the matrices CI are never non-zero at the same position (if CI(m, n)≠0 then CI′(m, n)=0 for I≠II). The rank of RH then comes out to be NL. Also, it is evident that the elements of CI belong to the matrix J defined as
The advantage of this decomposition of matrix H is that we can easily obtain the EVD of RH, and hence that of RG, from J, thus this decomposition method is preferable in the present invention.
Let λn be the eigenvalues and vn be the eigenvectors obtained by the EVD of RG, the autocorrelation matrix of vec(G). The EVD of RG can be obtained from the EVD of RH the autocorrelation matrix of vec(H). The matrix H can be expressed as a sum of L matrices (A0, . . . , AL-1) and the EVD of RH can in turn be obtained from the EVD of the autocorrelation matrices of vec(AI), namely CI, which can in turn be obtained from the EVD of the matrix J. The method holds for channels with any arbitrary Power Delay Profile (PDP), in which case the eigenvalues of RH will be scaled by the individual power of each tap.
The matrix J is a positive definite Toeplitz Hermitian matrix, and for large N can be assumed approximately circulant. From the properties of circulant matrices,
J=QQH (11)
where is a diagonal matrix whose mth diagonal element λ(m,m) is given by
Thus the EVD of J, and hence that of RG has very low computational complexity. Using the EVD of RG, the input/output equation of the OFDM system can be written in terms of the NdL dominant parameters αp as
where αp's are independent Gaussian random variables that need to be estimated each with mean zero and variance equal to the eigenvalue λp, Gp=Qdiag(vn)BIQH and εpGpx. The advantage gained by this approach, is that the elements of the N×N matrix G can be estimated using only NdL parameters αp with NdL<<N2 and is an embodiment of the present invention. The λp's and Gp's can be pre-computed and stored in the lookup table 310 and selected on the basis of the estimate provided by the Doppler frequency estimation unit 300. For
In order to determine αp from the kth equation εp(k) has to be known implying εp(k) to be independent of data subcarriers, so the subcarriers x(k−M/2), . . . , x(k+M/2) must be pilots.
In terms of pilot overhead, it is more efficient to place pilots in large groups. For example, assuming G has M=3 main diagonals, placing pilots in a consecutive group {1, 2, 3, 4, 5, 6} produces four ICI free equations y(2), y(3), y(4), y(5) while splitting the pilots in two groups {1, 2, 3} and {11, 12, 13} produces only two ICI free equations namely y(2) and y(12). Let {kt1, kt2, . . . , ktT} be the set of ICI free output carriers that can be used from training. Pruning equation (16) of all carriers that do not belong to the training set, we are left with T equations in NdL unknowns
where the underline denotes the matrices are pruned. In matrix form, it is written as
Thus the problem reduces to a Bayesian estimation problem. The covariance matrix of α is given as Ra=diag([λ1, . . . , λNd]). The estimate {circumflex over (α)} can be estimated using an LMMSE estimator
{circumflex over (α)}=RaEH[Rv+ERaEH]−1y (21)
{circumflex over (α)}=[Rα−1+EHRv−1E]−1EHRv−1y (22)
For the case of white noise, the form of equation (22) reduces the matrix inversion from T to NdL with T≧NdL. The performance of the estimator is measured in terms of the error ε=α−{circumflex over (α)} with mean zero and covariance
C
ε
=[R
α
−1
+E
H
R
v
−1
E]
−1. (23)
Specifically the estimation algorithm detailed here include the following steps: (1) determine the Nd dominant eigenvalues and eigenvectors off offline; (2) determine the NdL dominant eigenvalues and eigen vectors of RH offline from those of J; (3) determine the NdL dominant eigenvalues and eigen vectors of RG offline from those of RH; and (4) compute {circumflex over (α)} using (22) and approximate G using α's and eigenvectors as in (13).
Steps 1-3 of the algorithm can be calculated offline and need to be calculated only once. For a given N and fd, these matrices can be pre-computed and stored in lookup tables. Hence, the complexity comparison is done for step 4 and 5 only. Step 4 consists of 6 operations. For known N, fd and signal-to-noise ratio (SNR), the first five of these can be computed offline to reduce processing complexity and delay. The computational complexity of each operation required to perform steps 4 and 5 of the OFDM Inter-Carrier Interference (ICI) cancellation method is listed in Table 1.
The equalization step is achieved by a Q-tap (Q<<N) MMSE based FIR filter 240 and is an embodiment of the present invention. The equalizer 240 detects each subcarrier individually, taking into account the ICI from neighboring subcarriers.
{circumflex over (X)}m=wmym (24)
where wm is equalization filter taps given by
w
m
=g
m
H(GmGmH+σ2IQ)−1 (25)
where gm is the middle column of Gm.
The simulations are carried out for an OFDM system with FFT size of N=256 and N=1024. A half rate convolutional encoder with bit interleaving is implemented. A Doppler frequency of 10% is applied normalized to the subcarrier spacing. The channel is assumed to be 3-tap (L=3) with an exponential power delay profile. Each channel tap is generated by an independent complex Gaussian random variable with time correlation based on Jakes model.
A larger normalized Doppler results in a larger number of dominant eigenvalues of J. For a Doppler of 10% with the aforementioned FFT sizes, it was found that the first 3 eigenvalues of f are dominant (Nd=3) and the rest of the eigenvalues are approximately zero. Of the available N subcarriers, 15% are used as pilots. The pilots are placed in equispaced clusters of 3 or 5 pilots each. The results are compared with two cases of the perfect channel, also known as the ‘Genie’ channel; when the matrix G is a full matrix and when G is banded. Graph 500 of
Graph 700 of
Advantageously, the present invention allows high-speed data transmission over rapidly changing mobile channels for mitigating the ICI. Moreover, the present invention has a better BER performance for the same number of pilots as compared to previous approaches. Additionally, the present invention makes use of a priori information i.e. frequency and time correlation, and is able to deal with higher Doppler shift than previously available methods, and at a lower computational complexity.
Although the description and discussion were in reference to certain exemplary embodiments of the present invention, numerous additions, modifications and variations will be readily apparent to those skilled in the art. The scope of the invention is given by the following claims, rather then the preceding description, and all additions, modifications, variations and equivalents that fall within the range of the stated claims are intended to be embraced therein.
The method may be implement in modulation or multiplexer circuits in a discrete transmitter, a discrete receiver, or a transceiver. The circuits may utilize a microprocessor, digital signal processor, application specific integrated circuit (ASIC), or other components programmed or configured to implement the steps of the method according to conventional construction techniques.
It is to be understood that the present invention is not limited to the embodiment described above, but encompasses any and all embodiments within the scope of the following claims.
