The present invention is related to wireless communication systems. More particularly, the present invention is related to a method and apparatus for channel estimation in an orthogonal frequency division multiplexing (OFDM) system.
OFDM technology has been adopted in several wireless communication standards, such as IEEE 802.11 a/g/n and HIPERLAN. OFDM techniques have a merit of high spectral efficiency since adjacent OFDM sub-carriers may share the same spectrum while still remain orthogonal to each other.
A receiver requires a signal-to-noise ratio (SNR) and channel information prior to decoding data, (e.g., for minimum mean square error (MMSE) decoding). Therefore, channel estimation directly affects the performance of the receiver in terms of a packet error rate (PER), a bit error rate (BER), or the like.
Multiple-input multiple-output (MIMO) techniques have a merit of high throughput, since MIMO provides multiple orthogonal eigen-channels which facilitate the transmission of multiple spatial streams for each pair of transceivers. In MIMO systems, the information of the channel matrix is essential for decoding transmitted data correctly. If the channel matrix is not estimated accurately, the eigen-channels cannot be fully decoupled at the receiver and the spatial streams may be coupled, which results in inter-spatial stream interference (ISSI). As a channel estimation error increases, the ISSI, and consequently the PER and BER, increases.
In a conventional wireless communication system, the channel is usually estimated in a frequency domain. However, when the coherent bandwidth of the channel is larger than the signal bandwidth, (e.g., in an indoor wireless local area network (WLAN) environment), it is more advantageous to estimate the channel in a time domain than in a frequency domain.
For example, 64 sub-carriers are used in the 20 MHz mode of an IEEE 802.11n standard. Using a preamble, the receiver estimates the channel transfer functions for 56 out of 64 sub-carriers. For small indoor environments, the delay spreads are very small. For example, the delay spread is only 90 nsec for the TGn B channel. Each channel would require only 2 to 3 taps in the time domain channel model because the sampling interval is fixed at 50 nsec. Thus, a time-domain channel estimation will be far more efficient than a frequency domain channel estimation in terms of mitigating the noise effects on channel estimation.
A time domain truncation (TDT) method has been proposed for improving the channel estimation. In a conventional TDT method, channel transfer functions are obtained for all sub-carriers using a conventional channel estimation method such as a maximum likelihood (ML) technique. A channel impulse response in the time domain is then derived by applying an inverse Fourier transform on the channel transfer functions in the frequency domain. Subsequently, the impulse response is truncated to remove noisy elements of the channel impulse response in the time domain. Finally, a Fourier transform is performed on the truncated channel impulse response to yield an improved channel transfer function in the frequency domain.
The conventional TDT method works well for channels with short delay spreads. However, it requires initial channel estimation for all sub-carriers. If there are null sub-carriers, the TDT approach will induce channel estimation errors. The null subcarrier-induced errors may be small compared to the noise-induced errors when the SNR of the channel is low. However, the null subcarrier-induced errors become more significant than the noise-induced errors when the SNR is high. Therefore, the conventional TDT approach is not applicable to high SNR conditions.
In addition, the conventional channel estimation is performed based on pilot symbols, (i.e., known preambles or training sequences). Since the pilot symbols are assigned to the small number of subcarriers, some type of interpolation is performed to generate channel estimates for the whole subcarriers based on the channel estimates of the pilot subcarriers. However, the channel estimation using interpolation produces large errors for the frequency selective channels.
The present invention is related to a method and apparatus for channel estimation in an OFDM system. A frequency domain channel estimate Ĥ is computed for non-nullified subcarriers. An inverse Fourier transform on the frequency domain channel estimate Ĥ is performed to obtain a time domain channel estimate ĥ. The number of taps L of a channel model is determined based on the time domain channel estimate ĥ. An improved time domain channel estimate {tilde over (h)} is obtained by computing L tap coefficients of the channel model from the frequency domain channel estimate Ĥ. An improved frequency domain channel estimate {tilde over (H)} is obtained by performing a Fourier transform on the improved time domain channel estimate {tilde over (h)}. Alternatively, a time domain truncation may be performed selectively only if the SNR is below a threshold. Alternatively, a frequency domain channel estimate Ĥp for all pilot subcarriers are converted to a time domain channel estimate ĥ, and an improved frequency domain channel estimate may be obtained based on the number of pilot subcarriers and a delay spread.
The channel estimation method of the present invention may be implemented in a wireless transmit/receive unit (WTRU) or a base station. The terminology “WTRU” includes but is not limited to a user equipment (UE), a mobile station, a fixed or mobile subscriber unit, a pager, a cellular telephone, a personal digital assistant (PDA), a computer, or any other type of user device capable of operating in a wireless environment. The terminology “base station” includes but is not limited to a Node-B, a site controller, an access point (AP), or any other type of interfacing device capable of operating in a wireless environment.
Hereinafter, the present invention will be explained with reference to an IEEE 802.11n system as an example. However, it should be noted the reference to IEEE 802.11n system is only for illustration, not as a limitation, and the present invention is applicable to any OFDM-based wireless communication systems.
The present invention provides a model-based channel estimation method to circumvent the null subcarriers-induced errors. In the model-based method, the channel is modeled as a tapped delay line. The tap coefficients of the tapped delay line are obtained using a least square approach in the time domain. As long as there are more non-null subcarriers than the number of taps, the model-based approach of the present invention works well for all SNRs.
After the number of taps (L) is determined, the tap coefficients of the channel impulse response may be expressed in terms of the estimated channel transfer functions and an improved time domain channel estimate {tilde over (h)} is obtained by computing L tap coefficients of the channel model from the frequency domain channel estimate Ĥ, which will be explained in detail hereinafter (step 108). After computing the improved time domain channel estimate {tilde over (h)}, an improved frequency domain channel estimate {tilde over (H)} is computed by performing a Fourier transform on the improved time domain channel estimate {tilde over (h)} (step 110).
The process 100 is explained in detail with exemplary reference to the mathematical equations hereinafter. For the kth sub-carrier, let Hij(k) denote frequency domain channel estimate, (i.e., channel transfer function), for the ith receive antenna and the jth transmit antenna. For a 20 MHz bandwidth in the IEEE 802.11n standard, 64 sub-carriers (k=0, 1, 2, . . . , 63) are used. A time domain channel estimate hij (l), (i.e., channel impulse response), is an inverse Fourier transform of a frequency domain channel estimate Hij(k) as follows:
In an IEEE 802.11n 20 MHz mode, l=0, 1, 2, . . . , 63 and the sampling interval is 50 nsec.
In one example for an IEEE 802.11n system, a high throughput long training field (HT-LTF) is used to estimate a channel matrix where the transmit antennas are excited one at a time for each sub-carrier. After OFDM demodulation, the estimation of Hij(k) can be formulated as follows:
ri(k)=Hij(k)sj(k)+ni(k); Equation (2)
where sj(k) is the jth transmit training signal, ri(k) is the ith received signal, and ni(k) is the ith received noise. If the noise is Gaussian, the frequency domain channel estimate may be given as follows:
Ĥij(k)=ri(k)/sj(k) Equation (3)
Since sj(k) is non-zero for only 56 sub-carriers, (k=1˜28 and 36˜63), and eight (8) subcarriers, (k=0 and 29˜35), are nullified in an IEEE 802.11n 20 MHz mode, the frequency domain channel estimate in Equation (3) can be derived for only 56 sub-carriers at step 102.
At step 104, a time domain channel estimate ĥij(l) is derived by performing an inverse Fourier transform on the frequency domain channel estimate Ĥij(k) in Equation (3) over the 56 sub-carriers as follows:
To improve the time domain channel estimate in Equation (4), a frequency domain interpolation and/or extrapolation may optionally be performed to provide approximately the frequency domain channel estimate Ĥij(k) at the null sub-carriers (k=0 and 29˜35).
At step 106, the number of taps (L) of the tapped delay line of the channel model is determined. The number of taps may be derived from an estimated maximum delay spread (TT), (i.e., TT=L×50 nsec). If the SNR on the channel is known, a threshold for time domain channel estimate element hij may be chosen based on the SNR and the maximum delay spread may be determined by comparing the threshold with the elements of the time domain channel estimate. The number of taps may be determined by many different ways.
When the number of taps (L) is determined, the tap coefficients of the channel model can be expressed in terms of the frequency domain channel estimate as follows:
If the number of taps (L) is less than the frequency domain channel estimates, (e.g., 56 in an IEEE 802.11n 20 MHz mode), an improved time domain channel estimate may be obtained by solving the tap coefficients directly from Equation (5) at step 108. Equation (5) may be rewritten as follows:
Ĥij≈Fhij, Equation (6)
wherein hij is an L×1 vector for L unknown tap coefficients, Ĥij is a 56×1 vector of the 56 estimated channel transfer functions, and F is a 56×L Fourier transform matrix. F does not depend on the antenna indexes ij. The least square solution of Equation (6) is as follows:
{tilde over (h)}ij=(FHF)−1FHĤij; Equation (7)
and the lth element of the improved time domain channel estimate is approximated by the lth element of {tilde over (h)}ij in Equation (7).
At step 110, an improved frequency domain channel estimate is obtained by performing Fourier transform on the improved time domain channel estimate as follows:
where Ĥij(k) represents the estimated channel transfer function. The mean in Equation (9) is made over 2,000 channel realizations.
In the simulations, two values of maximum delay spread are chosen for each channel model. The maximum delay spread is 400 nsec or 800 nsec for channel B, and 700 nsec or 800 nsec for channel D. In other words, the maximum number of taps (L) is 8 or 16 for channel B, and 14 or 16 for channel D. Since the two L values for channel D are close to each other, the MSE results derived by these two values are also close to each other for both TDT and model-based methods. However, the MSE results are very different for channel B.
For the model-based method of the present invention, using a smaller L removes more noises and the optimum L is when the maximum delay spread is equal to the effective channel delay spread. It is not the case for the TDT approach. Although a smaller L still removes more noises, it also magnifies the effects due to null carrier frequencies. Thus, a small L is not necessary better for the TDT method. An optimum L will be usually greater than the effective channel length.
Comparing to the model-based result with L=8, the ML result is 4 dB worse (i.e., higher) for all SNRs for channel B. Comparing to the TDT result with L=16, the ML result is 2 dB worse at SNR=10 dB but is 5 to 6 dB better at SNR=25 dB for channel B. For channel D, the ML result is 3 dB worse than the model-based result for all SNRs. It is 2 dB worse at SNR=10 dB but is 5 dB better at SNR=25 dB than the TDT result. Thus, the model-based approach provides the best results (smallest MSE) for all situations. TDT is a simplified version of ML. It provides smaller MSE than ML at low SNRs.
An SNR is measured (step 502). A channel estimation is then performed using a conventional method, (such as ML or MMSE estimation), to obtain a frequency domain channel estimate Ĥ (step 504). The SNR is compared to a threshold (step 506). If the SNR is not below the threshold, the process 500 stops.
If the SNR is below the threshold, interpolation and/or extrapolation is performed on the frequency domain channel estimate Ĥ for the nullified subcarriers to generate an interpolated/extrapolated frequency domain channel estimate {circumflex over (Ĥ)} (step 508). For simplicity, the frequency domain channel estimate of the adjacent subcarrier may be copied to the nullified subcarrier. The interpolated/extrapolated frequency domain channel estimate {circumflex over (Ĥ)} is then converted to a time domain channel estimate, {circumflex over (ĥ)}=IFFT({circumflex over (Ĥ)}) (step 510). A delay spread L is then estimated from the time domain channel estimate {circumflex over (ĥ)} for a time domain filtering window WL=[11 . . . 100 . . . 0]T (step 512). The number of is in the time domain filtering window equals to L. The time domain filtering window is applied to the time domain channel estimate {circumflex over (ĥ)} such that {tilde over (h)}={circumflex over (ĥ)}·WL, (i.e. zeroing the components of {tilde over (h)} on the outside of the delay spread window) (step 514). An enhanced frequency domain channel estimate {tilde over (H)} is computed from the filtered time domain channel estimate {tilde over (h)} by performing Fourier transform such that {tilde over (H)}=FFT({tilde over (H)}) (step 516).
Np and L are compared at step 708 and an improved time domain channel estimate {tilde over (h)} is estimated depending on the number of pilot subcarriers Np and the delay spread L as follows. If Np=L, the following equation is solved: {tilde over (h)}=A−1Ĥp, (i.e., Ĥp=A{tilde over (h)}), where A is (Np×L), Ĥp is (Np×1), and {tilde over (h)} is (L×1) (step 710). The row of A is the Fourier transform coefficients corresponding to the pilot subcarrier. If Np>L, the following equation is solved: {tilde over (h)}=(AtA)−1AtĤp (step 712). If Np<L, the channel estimation is performed for the (L-Np) decision-directed data which have a high SNR (step 714) and the process 700 proceeds to step 710. An enhanced frequency domain channel estimation {tilde over (H)} is then computed by performing Fourier transform on the improved time domain channel estimate {tilde over (h)}, {tilde over (H)}=FFT({tilde over (h)}) (step 716).
Although the features and elements of the present invention are described in the preferred embodiments in particular combinations, each feature or element can be used alone without the other features and elements of the preferred embodiments or in various combinations with or without other features and elements of the present invention. The methods or flow charts provided in the present invention may be implemented in a computer program, software, or firmware tangibly embodied in a computer-readable storage medium for execution by a general purpose computer or a processor. Examples of computer-readable storage mediums include a read only memory (ROM), a random access memory (RAM), a register, cache memory, semiconductor memory devices, magnetic media such as internal hard disks and removable disks, magneto-optical media, and optical media such as CD-ROM disks, and digital versatile disks (DVDs).
Suitable processors include, by way of example, a general purpose processor, a special purpose processor, a conventional processor, a digital signal processor (DSP), a plurality of microprocessors, one or more microprocessors in association with a DSP core, a controller, a microcontroller, Application Specific Integrated Circuits (ASICs), Field Programmable Gate Arrays (FPGAs) circuits, any other type of integrated circuit (IC), and/or a state machine.
A processor in association with software may be used to implement a radio frequency transceiver for use in a wireless transmit receive unit (WTRU), user equipment (UE), terminal, base station, radio network controller (RNC), or any host computer. The WTRU may be used in conjunction with modules, implemented in hardware and/or software, such as a camera, a video camera module, a videophone, a speakerphone, a vibration device, a speaker, a microphone, a television transceiver, a hands free headset, a keyboard, a Bluetooth® module, a frequency modulated (FM) radio unit, a liquid crystal display (LCD) display unit, an organic light-emitting diode (OLED) display unit, a digital music player, a media player, a video game player module, an Internet browser, and/or any wireless local area network (WLAN) module.
This application claims the benefit of U.S. provisional application No. 60/777,879 filed Mar. 1, 2006, which is incorporated by reference as if fully set forth.
Number | Date | Country | |
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60777879 | Mar 2006 | US |