1. Field of the Invention
The present invention relates to apparatus and methods for estimating and compensating sampling clock offset (SCO) for orthogonal frequency division multiplexing (OFDM) communications, and more particularly to the apparatus and the SCO estimation and compensation methods for multi-band OFDM-based ultra-wideband (UWB) systems.
2. Description of Related Art
Multi-band orthogonal frequency division multiplexing (OFDM) based ultra-wideband (UWB) communication has attracted considerable attention in the recent years, as described in the following two references: [1] “A. Batra, J. Balakrishnan, G R. Aiello, J. R. Foerster, and A. Dabak, “Design of a multiband OFDM system for realistic UWB channel environments,” IEEE Trans. Microwave Theory and Techniques, vol. 52, no. 9, pp. 2123-2138, September 2004.”; [2] “WiMedia MBOA, MultiBand OFDM Physical Layer Specification, ver. 1.1.5, Jul. 14, 2006.”. The large bandwidth occupancy of UWB (from 3.1 GHz to 10.6 GHz) and the high efficiency in spectrum utilization provided by OFDM make it possible for the OFDM-UWB technology to achieve very high channel capacity. The OFDM-UWB system can provide low-cost and high-speed wireless connectivity among devices within a short range. The wireless universal serial bus (USB), for example, has adopted the OFDM-UWB radio layer with the data rate up to 480 Mbps.
The extremely wide-band processing has brought a lot of challenges to the OFDM-UWB system design, especially to the design of some crucial receiving modules such as the symbol timing, the carrier frequency offset (CFO) and sampling clock offset (SCO) compensation, as well as the channel frequency response (CFR) estimation. The SCO issue is caused by the sampling clock frequency mismatch between the transmitter and the receiver. Since the UWB device operates at a very high sampling rate (at least 528 Mbps), a small SCO shall cause the phase-shift among the received frequency-domain complex data at all subcarriers, which, after accumulating over a certain period, becomes significant and will seriously degrade the system performance if not well tracked and compensated. Due to its high complexity, the maximum likelihood (ML) phase tracking approach is prohibitive in this case, as described in references [3] “P.-Y. Tsai, H.-Y. Kang, and T.-D. Chiueh, “Joint weighted least-squares estimation of carrier-frequency offset and timing offset for OFDM systems over multipath fading channels,” IEEE Trans. Veh. Technol., vol. 54, no. 1, pp. 211-223, January 2005.” and [4] “J. Liu and J. Li, “Parameter estimation and error reduction for OFDM-based WLANs,” IEEE Trans. Mobile. Computing, vol. 3, no. 2, pp. 152-163, April-June 2004”. Moreover, a time-domain interpolator is used to compensate the SCO in reference [3]. However, the time-domain interpolator is implementation expensive in case of high-speed processing.
Therefore, efficient SCO estimation and compensation technologies are critically desirable for improving the performance of the multi-band OFDM-based UWB system.
One object of the present invention is to provide a method for estimating sampling clock offset (SCO) in a multi-band orthogonal frequency division multiplexing (OFDM)-based ultra-wideband (UWB) system. The SCO estimation method of the present invention is of low complexity and high interference-resistant capability which make it robust even under low signal-to-noise ratio (SNR) conditions.
Another object of the present invention is to provide a method for compensating SCO estimation which is low cost and ease of implementation even under high-speed processing.
According to both objects, an apparatus for sampling clock recovery is provided. The apparatus comprises: a symbol timing adjustment module for receiving transmitted OFDM symbols and shifting forward or backward symbol timing of the transmitted OFDM symbols; a discrete Fourier transform (DFT) processor for performing DFT to an output from the symbol timing adjustment module; a channel estimator for undertaking a channel frequency response (CFR) estimation based on the transmitted OFDM symbols of a channel estimation sequence from an output of the DFT processor; a sampling clock offset (SCO) phase rotator for receiving and performing phase shift on the transmitted OFDM symbols of a frame header and a frame payload from the output of the DFT processor; an SCO estimation stage for undertaking an SCO estimation based a pilot-subcarrier-related output of the SCO phase rotator and the CFR estimation from the channel estimator; and an SCO compensation distributor for dividing the SCO estimation into the integer and fractional portions and then distributing them into the symbol timing adjustment module and the SCO phase rotator, respectively.
According to the first object, a method for estimating SCO for a multi-band OFDM-based UWB system on a plurality of transmitted OFDM symbols is provided. The transmitted OFDM symbols are divided into OFDM symbol groups, indexed with m, each group has K OFDM symbols, indexed with i, i=0, 1, . . . , K−1; each OFDM symbol has R pilot subcarriers, ascendingly indexed with {p(0), p(1), . . . , p(R−1)}; the method for obtaining an accumulated normalized SCO (ANSCO) estimation, {circumflex over (η)}m−1(i), on the ith OFDM symbol in the (m+1)th group, using an ANSCO estimation {circumflex over (η)}m(i), on the ith OFDM symbol in the mth group, comprises: grouping R pilot subcarriers into Q pilot pairs; each pilot pair, {p(l1), p(l2)}, having a separation factor, β(l1,l2); obtaining a channel frequency response (CFR) estimation, hr, on an rth sub-band; obtaining a pilot-subcarrier related input of an N-point inverse discrete Fourier transform (IDFT) processor and a pilot-subcarrier related output of an N-point discrete Fourier transform (DFT) processor; obtaining a residual SCO estimation related value,
According to the second object, a method for compensating SCO for a multi-band OFDM-based UWB system is provided. The method comprises: obtaining an accumulated normalized SCO (ANSCO) estimation for a transmitted OFDM symbol; distributing the ANSCO estimation into integer and fractional portions; shifting sample timing at an interval of sampling period in time-domain by an amount of the modulus of the integer portion of the ANSCO estimation; and correcting phase shift in frequency-domain with a rotating factor corresponding to the fractional portion of the ANSCO estimation.
The preferred embodiments of the present invention will be described in detail by way of examples and with reference to the above-mentioned figures.
As shown in
The K OFDM symbols in a group may be transmitted in multibands indexed with r. The center frequency for the transmission of each OFDM symbol is prescribed by a time-frequency code (TFC).
Each OFDM symbol employs N=128 subcarriers, which include Q1=112 actual tones (carry useful information), Q2=10 guard tones, and Q3=6 virtual (null) tones. Of the Q1 actual tones, R=12 subcarriers are assigned as pilot tones (pilot subcarriers). The subcarrier frequency spacing is Δfsp=4.125 MHz. We consider the generation of the nth OFDM symbol (n=Km+i, i ∈, m ∈), and let
sm(i)=[sm(i)(0), sm(i)(1), . . . , sm(i)(N−1)]T (1)
be a vector of N complex data symbols, where (.)T denotes transpose and sm(i)(k), k ∈, is the data symbol used for modulating the kth subcarrier. Define an R×1 vector, p=[p(0), p(1), . . . , p(R−1)]T=[5, 15, 25, 35, 45, 55, 73, 83, 93, 103, 113, 123]T. Let Q0=(Q1+Q2)/2, and sm(i)(k) is drawn from the quadrature phase-shift keying (QPSK) constellation - denoted as ±c±jc with j=√{square root over (−1)} and c=√{square root over (2)}/2, if k ∈∪, and, in particular, s,m(i)(k) is known at the receiver end (for the pilot tones) if k ∈ {p(l)}l=0R−1. Also, sm(i)(k)=0, if (k=0)∪k ∈. The symbol vector, sm(i), is fed to an N-point inverse discrete Fourier transform (IDFT) processor that yields an N×1 time-domain vector (IDFT output), denoted by xm(i) (see xm(0), xm(1), xm(2), xm(3), xm(4), and, xm(5) in
It should be pointed out that the UWB channel of the multi-band OFDM-based UWB system is modeled as an Nh-tap finite impulse response filter whose impulse response on the rth sub-band is denoted as
hr(t)=[hr(t)(0), hr(t)(1), . . . , hr(t)(Nh−1)]T, r ∈ (2)
where the superscript (t) indicates time-domain. The corresponding channel frequency response (CFR) on the rth sub-band, hr=[hr(0), hr(1), . . . , hr(N−1)]T, is given by hr=FN
In the present invention, we assume that the UWB channel is invariant over the transmission period of one OFDM frame. The estimation of CFR is thus performed once in a frame by the channel estimator 25 using the received channel estimation sequence included in the frame preamble. We define the obtained estimate of hr as ĥr=[ĥr(0), ĥr(1), . . . , ĥr(N−1)]T, r ∈.
We consider that εΔfsp CFO and δTs SCO are present, where Ts is the sampling interval. With the assumption that Nh≦Ng, the output of the DFT processor corresponding to the nth received OFDM symbol (that is, the ith OFDM symbol in the mth group) is given by
ym(i)(k)=sm(i)(k)hr(k)ej(θ
i ∈, r=|i|3+1, and k ∈, where |.|3 stands for the modulo-3 operation, and vr(k) is the channel noise on the rth sub-band, which is modeled in frequency-domain as a zero mean Gaussian process with variance σr2. Let χm(i)=(Km+i)(N+Ng), and denote by ηm(i)=χm(i) δ the accumulated SCO (normalized by Ts, and if not compensated) when receiving the (Km+i)th OFDM symbol. According to reference [3], we have
θm(i)≈2π/N·ε(1+δ)χm(i) (4)
and
Obviously, the phase-shift, θm(i), termed as the common phase error (CPE), is mainly CFO related and is independent of the subcarrier index, k, whereas the phase-shift, φm(i)(k), caused by the SCO, is proportional to k. It should be pointed out that, in the derivation of (3), (4), and (5), ε and δ are assumed to be small. In particular, in our discussion, we assume that the CFO has been first estimated using the frame preamble and then compensated in all the subsequent OFDM symbols. In other words, ε actually represents the residual CFO (normalized by the subcarrier spacing) after the initial compensation and thus we can safely assume |ε⊕<0.02. Observe from (3), (4) and (5), the CPE and the SCO can be decoupled easily.
In order to decouple the CFO and SCO as mentioned above, the apparatus 2 further comprises a CPE mitigation module and an SCO mitigation module. The CPE mitigation module includes a CPE estimation stage 30 and a CPE correction stage 31. The CPE estimation stage 30 undertakes CPE estimation based on the CFR estimation and the pilot vectors (that is, the vectors on pilot subcarriers) extracted from the output of the SCO phase rotator 26. The CPE correction stage 31 compensates the output of the N-point DFT processor 24 based on the CPE estimation from the CPE estimation stage 30. The transmitted OFDM symbols from the CPE correction stage 31 are applied, in turn, to an equalizer 32 and a decoder 33 for further processing.
The SCO mitigation module comprises an SCO estimation stage 28 and an SCO compensation distributor 29. The SCO estimation stage 28 estimates the SCO involved in the (m+1)th group of OFDM symbols based on the pilot vectors (after SCO compensation) which belong to the mth group of OFDM symbols. Thus, the SCO estimation stage 28 performs SCO estimation in a predictive mode as manifested by a delay operation in a delay stage 27. The SCO compensation distributor 29 divides the obtained SCO estimation into integer and fractional portions, and then, distributes them to the symbol timing adjustment module 21 and the SCO phase rotator 26, respectively. The SCO compensation is implemented in the symbol timing adjustment module 21 by shifting forward or backward the sample timing at an interval of sampling period based on the integer portion, and in SCO phase rotator 26 by correcting the phase shift based on the fractional portion.
ej(θ
where
Referring to the definition of R pilot tones as described above, we group them into a certain number of pairs, denoted by {p(l1), p(l2)}, where l1 ∈ and l2 ∈. Obviously, in this case, the grouping yields
(Q=21, when R=12) pilot pairs in total, each of them is associated with a separation factor, denoted by β(l1,l2):=p(l2)−N−p(l1)=10(l2−R−l1), l1 ∈ and l2 ∈. Thus, from (6), (7), and (4), we can derive
where am(i)(l1,l2)=(Am*(i)(l1,l2)Bm(i)(l1,l2)Cm(i)(l1,l2)), bm(i)(l1,l2)=ℑ(Am*(i)(l1,l2)Bm(i)(l1,l2)Cm(i)(l1,l2)) and dm(i)(l1,l2)=|Am(i)(l1,l2)|2 with
Am(i)(l1,l2)=ŷm(i)(p(l1))ĥr(p(l2))
Bm(m)(l1,l2)=ŷm(i)(p(l2))ĥr(p(l1))
and
Cm(i)(l1,l2)=sm(i)(p(l1))(sm(i)(p(l2)))*.
Here, Δηm(i)(l1,l2), instead of Δηm(i), is used to relate itself to the pilot pair {p(l1), p(l2)}. (x) and ℑ(x) denote the real and imaginary parts of x, respectively, and (.)* denotes conjugation. It should be noted that |sm(i)(p(l2))|2=1 has been used in the derivation of (8).
Being aware of |2πβ(l1,l2)Δηmi(l1,l2)/N|<<1 and applying Euler's formula, ejφ=cos φ+j sin φ, and sin(φ)≈φ (when |φ|<<1) to (8), we have
By this approximation, no actual trigonometric operation for angle calculation is required. Using the full set of pilot tones, by averaging, the estimation of the residual SCO, Δ{circumflex over (η)}m(i), is obtained as
where
if
In this way, the division operations can be avoided in obtaining the estimation as shall be clear in the following. In fact, the use of the proportion property here has an important implication in the presence of noise. Observe from (6) that we have |ŷm(i(p(l1))|=ĥr(p(l1))| due to |sm(i)(p(l1))|=1. Thus, we can obtain dm(i)(l1,l2)=|ĥr(p(l1))|2|ĥr(p(l2)2|. The last equality in (10) can be rewritten as
where
It can be seen that the use of the proportion property in (10) is actually equivalent to weighting the residual SCO estimation obtained with the pilot pair {p(l1), p(l2)} by a weighting factor, g(l1,l2) , which is the normalized product of CFR magnitudes (squared) on that pilot pair, i.e., {p(l1), p(l2)}. A larger g(l1,l2) means a higher carrier to noise ratio (CNR), which translates to a more reliable estimation of the residual SCO on the respective pilot pair {p(l1), p(l2)}, and vice versa. Therefore, the last equality in (10) has performed a CFR-assisted combination of the estimations of the residual SCO using all Q pilot pairs which can reduce the estimation error caused by the channel noise.
Albeit effective in compensation of the noise-impairment effects on the estimation of the residual SCO, in the presence of heavy noise, i.e., under considerably low SNR conditions, the estimation in (10) (last equality) is prone to causing errors which, in turn, may make the SCO tracking unstable due to the limited number of pilot pairs available for use in (10). Being aware of this, a very simple yet effective error suppression technique is devised as described below.
We define from (10)
and
Note that, ρm(i)>0. Then, we can find two values, Nmp, the number of γm(i)'s (among K with i ∈ and γm(i) being called as a symbol-level residual SCO estimation related value) which satisfy γm(i)>0, and Nmn, the number of γm(i)'s which satisfy γm(i)<0. Let μ>0 be a system design parameter defined as the micro-shift of SCO which can be fixed at a small value, and θ=[θ(0),θ(1), . . . , θ(K)] be a predefined non-negative integer vector which satisfies θ(l+1)≧θ(l) and θ(l) ∈. Then, the estimation of the residual SCO, Δ{circumflex over (η)}m(i), in (10) is replaced with
Δ{circumflex over (η)}m=sgn(Nmp−Nmn)θ(|Nmp−Nmn|) (14)
where sgn(x) equals to 1, if x>0, and, −1, if x<0, otherwise, 0. In this embodiment, Equation (14) combines the K SCO estimations which are obtained independently by applying the last equality in (10) into each individual OFDM symbol of the mth group. The combined estimation is robust and noise resistant in the sense that it does not require using the exact value of Δ{circumflex over (η)}m(i) given by (10), but involves a unique approximation and average process for combining a group of estimations. The combination requires two parameters, μ and θ, whose settings relate to the maximum permissible SCO, maximum duration of an OFDM UWB frame, and, in particular, the system's tolerance to the residual SCO, i.e., the amount of SCO which has negligible impairment effect on system performance. The first two factors (the maximum permissible SCO and maximum duration) are available from the OFDM-UWB specification in reference [2] while the last factor (the system's tolerance) can be evaluated based on the trial and error method via simulations. As an example, we have used μ= 1/32 and θ=[0, 1, 2, 2, 2, 3, 3] with K=6 in the present invention which yields good SCO tracking performance under all system conditions as shall be demonstrated through our numerical simulations. It should be emphasized that the actual setting of μ and θ may not necessarily follow this example exactly as the setting itself is actually not very sensitive to the system performance and thus can be easily adjusted, if necessary, for meeting the requirements of different practice designs.
Finally, we obtain the ANSCO estimation, {circumflex over (η)}m+1(i), in the (m+1)th group by using the known (i.e., previously estimated) ANSCO estimation, {circumflex over (η)}m(i), in the mth group and the residual SCO estimation, Δ{circumflex over (η)}m, as
{circumflex over (η)}m+1(i)={circumflex over (η)}m(K−1)+(i+1)Δ{circumflex over (η)}m+{circumflex over (η)}m(i)/m (15)
which shall be used to compensate the ith OFDM symbol in the (m+1)th group. The last term on the right-hand side of (15) is used to bridge the time gap between the estimation and compensation due to the processing delay for one group of OFDM symbols.
To avoid using a time-domain interpolator, which is computational and implementation expensive in a high speed processing environment, the present invention also provides a simple SCO compensation method. In this SCO compensation method, the compensation is jointly performed in the time-domain and the frequency-domain. Referring to
We shall now use a numerical example to demonstrate the effectiveness of the proposed sampling clock recovery apparatus and methods.
The effectiveness of the sampling clock recovery method of the present invention has been verified via numerical results. In the simulations, we consider the OFDM-UWB system with the data rate of 80 Mbps. The selection of a relatively low data rate as example here is for demonstrating the effectiveness of the proposed techniques under low SNR conditions. The UWB channel model CM1, which is a line of sight (LOS) S-V multipath channel has been used. Reference [1] describes the formation of the S-V multipath channel models. Also, TFC=1, and the frame payload is 1024 bytes long. The channel estimation is performed using the maximum-likelihood (ML) algorithm proposed in reference [5]: “L. Deneire, P. Vandenameele, L. V. d. Perre, B. Gyselinckx, and M. Engels, “A low complexity ML channel estimator for OFDM,” IEEE Trans. Commun., vol. 51, no. 2, pp. 135-140, February 2003.” with the assumption that Nh=32. For comparison convenience, perfect symbol timing is assumed whereas the CFO estimation and correction as well as the CPE tracking and compensation are included.
We assume that 40 ppm SCO is present. This corresponds to the worst case SCO as defined by the OFDM-UWB specification of reference [2].
Various modifications to the embodiments of the present invention described above may be made. For example, other method steps and modules can be added or substituted for those above. Thus, although the invention has been described above using particular embodiments, many variations are possible within the scope of the claims, as will be clear to the skilled in the art, without departing from the scope of the invention.
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Number | Date | Country | |
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20090279421 A1 | Nov 2009 | US |