The invention relates to communications systems, and more particularly to symbol synchronization for OFDM systems.
In communications systems, the information-bearing signals are transmitted from the source to the destination through a communication channel which causes signal distortion. Depending on the communication channel characteristics, appropriate signal modulation techniques are used.
OFDM (Orthogonal Frequency Division Multiplexing) is gaining popularity in broadband communications. In OFDM systems, the data signal is distributed among many equally-spaced, mutually-orthogonal sub-carriers. OFDM modulation is typically implemented through the IDFT (Inverse Discrete Fourier Transform, typically implemented more efficiently as IFFT—Inverse Fast Fourier Transform) in the transmitter, and the demodulation is typically implemented through the DFT (Discrete Fourier Transform, typically implemented more efficiently as FFT—Fast Fourier Transform).
The transmitted signal is grouped as DFT symbols, each of which consists of all the output samples of one IDFT operation. In order to avoid inter-symbol-interference (ISI), the DFT symbols are usually separated by some guard intervals (GI). One type of commonly used guard interval is called cyclic prefix (CP), which is the duplication of the last Ng samples of the DFT symbol of Nu samples.
Given a search window Ns, an FFT size Nu and guard interval length Ng, the initial symbol start time, n′0, may be obtained by Equation 1:
Note that the operation to compute absolute value may be replaced by alternative operations, such as magnitude square. The search window Ns is set to Nu+Ng. Since n′0 is calculated from only one symbol worth of data, the value is noisy at low signal to noise ratio (SNR). A more accurate estimate of symbol start time, n″0 is then computed by averaging data over a few symbols around n′0 as indicated by Equation 2:
Here, Δ and K′ are the window calculation expansion and the number of symbols for averaging, and r and K′ are integers greater than or equal to 1. For example, r may be set to 16 and K′ may be set to 3 to 5.
The signal samples used in the correlation T(n) are received signals. Although the Ng samples of CP equal exactly the last Ng samples of the DFT symbol in the transmitter, they are not the same at the receiver due to channel distortion. In fact, the first L samples in CP are affected by the previous symbol while the corresponding samples in the DFT symbol are affected by the samples in the same DFT symbol. As a result, this simple peak correlation technique typically works well under relatively good channel conditions, but fails to properly identify the symbol boundaries where the channel conditions are more severe because of the presence of, for example, multi-path and Doppler Effect.
Therefore, there is a need for techniques which can effectively and accurately identify the OFDM symbol boundary even in the presence of severe channel conditions.
In accordance with an embodiment of the invention, symbol synchronization in a communication system is carried out as follows. A plurality of symbols corresponding to a transmitted signal are received, where he plurality of symbols include guard intervals. A peak correlation is obtained using the plurality of received symbols. The second derivative of the peak correlation is obtained to identify one or more peaks each corresponding to a channel impulse response within a guard interval. A symbol start time is estimated for each received symbol based on the second derivative of the peak correlation.
In one embodiment, a position of a window of a predetermined number of samples is located to cover the one or more peaks.
In another embodiment, the predetermined number of samples is equal to or less than guard interval samples.
In another embodiment, the second derivative of the peak correlation is used to identify a window of a corresponding guard interval with a maximum spike energy.
In yet another embodiment, the plurality of symbols are OFDM symbols.
In yet another embodiment, first and second derivatives of the peak correlation are obtained using samples that are apart from one another a predetermined number of samples.
In another embodiment, after estimating the symbol start time, the guard intervals are removed from the plurality of symbols.
In accordance with another embodiment of the invention, symbol synchronization in a communication system is carried out as follows. A plurality of symbols corresponding to a transmitted signal are received, where the plurality of symbols include guard intervals. Peak correlation is obtained using the plurality of received symbols. In each guard interval, a window of samples with the maximum correlation energy based on the peak correlation is obtained. A symbol start time is estimated for each received symbol using the obtained samples.
In one embodiment, the window of samples is equal to or less than guard interval samples.
In another embodiment, after estimating the symbol start time, the guard intervals are removed from the plurality of symbols.
A further understanding of the nature and the advantages of the invention disclosed herein may be realized by reference to the remaining portions of the specification and the attached drawings.
In accordance with an exemplary embodiment of the invention,
As depicted in
Conventional techniques detect the OFDM symbol boundary mainly based on the peak correlation T(n) shown in Equation 2 above. Suppose the transmission channel has an impulse response CIR with length LCIR. At the receiver, the first LCIR samples of a symbol will be affected by the previous symbol. In fact, the last sample of the previous symbol affects the next LCIR samples, which are the first LCIR samples in CP. Therefore, as long as the impact of the last sample in the previous symbol on the current symbol is avoided, ISI is completely removed. Since the first Ng samples of a symbol are in CP that will be discarded before FFT, as long as LCIR≦Ng, ISI is completely avoided if the symbol boundary is identified accurately. The impact of the last sample on the current symbol is in the shape of CIR.
A main objective of the symbol synchronization, in accordance with embodiments of the invention, is to locate the channel impulse response (CIR) within CP, or locate as much energy of CIR within CP as possible. However, the peak correlation T(n) by itself does not easily show the CIR. For example, in
In accordance with a first embodiment of the invention, this problem is addressed as follows. The flow chart in
T′(n)=T(n)−T(n−Δ), n=k·Δ+n″0,−r≦k≦r+1
T″(n)=T′(n+Δ)−T′(n), n=k·Δ+n″0,−r≦k′≦r
where r is the integer part of W/Δ. Eq. (3)
Note that at the start of each group, the change in the slope of T(n) has a noticeable corresponding negative spike. These are marked by dashed arrows in
The minimum of ƒ(n) captures the window of Ng in length around n″0 that contains most negative spikes, which corresponds to the maximum CIR energy, and indicates most likely placement of the channel CIR. Then the start of the channel is the beginning of this window, as shown in the computation of n0 in Equation 4. The factor τ is the adjustment to n0 due to the resolution of Δ, with a maximum value of 16 samples, in accordance with one embodiment.
An alternate embodiment of the invention is depicted by the flow chart in
The two examples respectively depicted by
Because each group in the SFN channel is fading independently with various strengths, the peak of T(n) may not occur in the middle of the SFN groups.
The performance of an exemplary symbol timing estimator measured by the mean channel energy captured (MCEC) within CP is summarized in Table 1. In Table 1, MCEC values are tabulated for SNR=5.4 dB, Doppler=150 Hz, Carrier Offset=1500 Hz, BW=8 MHz, 200 trials using the first embodiment in
Each channel realization is an SFN channel with two or three independent Raleigh fading groups. The separation between the groups is about 50% of LCIR in the three group case and about 95% of LCIR in the two group case. The length of the CIR LCIR is either 90% or 50% of Ng. Ng of length Nu/4 and Nu/8 are simulated as shorter guard intervals are not suitable for such an SFN operating environment. Compared to the performance of the conventional peak correlation method, which at best is 67% for three groups and 75% for two groups under channels that are 90% of Ng in length, the embodiments of the invention provide significant performance improvement.
Another way to gage the performance of the symbol timing estimator is the mean missed distance (MMD) in samples. The missed distance is defined as the difference between the estimated symbol start time and the edges of a “don't care” window. The right edge of the window represents the exact symbol start time, while the left edge of the window represents how much earlier the symbol start estimate can be compared to the exact start time without incurring any ISI. If the symbol start estimate falls outside of this window, then ISI occurs. The length of this window depends on the length of the guard interval length Ng and the length of the channel impulse response LCIR.
Table 2 below summarizes the performance of the symbol timing estimator in terms of MMD under the same simulation conditions as in Table 1, using the first embodiment in
Tables 3 and 4 below respectively tabulate simulated MCEC and MMD values obtained under the same simulation conditions as in Tables 1 and 2, using the alternate embodiment in
Tables 5 and 6 below respectively tabulate simulated MCEC and MMD values obtained under the same simulation conditions as in Tables 1-4, using the conventional method based on the peak of correlation.
The performance of the symbol timing estimator is also evaluated under a static channel condition with only one group, as shown in Tables 7 and 8. In Tables 7 and 8, MCEC and MMD values are tabulated for SNR=5.4 dB, Carrier Offset=1500 Hz, BW=8 MHz, single group, 200 trials using the first embodiment in
Tables 9 and 10 below respectively tabulate simulated MCEC and MMD values obtained under the same simulation conditions as in Tables 7 and 8, using the alternate embodiment in
Tables 11 and 12 below respectively tabulate simulated MCEC and MMD values obtained under the same simulation conditions as in Tables 7-10, using the conventional method based on the peak of correlation.
From these results, it can be seen that the embodiments of the present invention outperform conventional techniques by a large margin, especially in the presence of severe wireless channels.
While the above provides a complete description of the preferred embodiments of the invention, many alternatives, modifications, and equivalents are possible. Further, the features of one or more embodiments of the invention may be combined with one or more features of other embodiments of the invention without departing from the scope of the invention. For these and other reasons, therefore, the above description should not be taken as limiting the scope of the invention, which is defined by the appended claims.
This application claims the benefit of U.S. Provisional Application No. 60/701,000, filed Jul. 19, 2005, which is incorporated by reference in its entirety for all purposes.
Number | Date | Country | |
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60701000 | Jul 2005 | US |