METHOD AND DEVICE FOR FRAME SYNCHRONIZATION IN COMMUNICATION SYSTEMS

Abstract

A device and method for frame synchronizing in a receiver of a communication system. The frame, transmitted in a signal out of a J-PSK constellation, J2, is received including a data sequence, a synchronization marker preceding the data sequence and an acquisition sequence preceding the synchronization marker, and wherein the synchronization marker is searched by using the acquisition sequence. In addition, a sliding observation window with an extended length, being MN can be used. Also, a buffer-based peak detection to find the synchronization marker in a buffered span of received symbols can be used, in addition to list decoding in order to exploit the error detection capability of the channel decoding in the receiver for false alarm detection.

Claims

1. A method for frame synchronizing in communication systems, the method comprising: receiving a frame that comprises a data sequence, a synchronization marker preceding the data sequence, and an acquisition sequence preceding the synchronization marker; and searching for the synchronization marker by using the acquisition sequence.

2. The method according to claim 1, wherein the synchronization marker has a first length, and the searching for the synchronization marker further comprises using a sliding observation window with a second length, where the second length is equal to or greater than the first length.

3. The method according to claim 2, wherein the frame is transmitted in a signal out of a J-PSK constellation, where J2.

4. The method according to claim 2, further comprising: computing a metric of likelihood ratio test the acquisition sequence, LRT-A, which is compared to a pre-defined threshold to determine whether a sequence received in the sliding observation window is the synchronization marker, wherein the metric of likelihood ratio test for the acquisition sequence, denoted by .sub.LRT-A(r), is computed as: ${}_{\mathrm{LRT}-A}\left(r\right)=\ln .Math..Math.\cosh \left({\tilde{r}}_1^{M-N}.Math.a_{M-N}^T\right)+\ln .Math..Math.\cosh \left({\tilde{r}}_{M-N+1}^M.Math.s^T\right)-\ln .Math.\underset{m=1}{\overset{N}{.Math.}}.Math..Math.{}_m.Math.\cosh \left({\tilde{r}}_1^{M-m+1}.Math.a_{M-m+1}^T\right).Math.\cosh \left({\tilde{r}}_{M-m+2}^M.Math.s_{m-1}^T\right)$ where the synchronization marker, s=[s.sub.1, s.sub.2, . . . , s.sub.N], N denoting the length of the synchronization marker, the received sequence in the sliding observation window is denoted by a vector r, r=[r.sub.1, r.sub.2, . . . , r.sub.N], and the acquisition sequence is denoted by a vector a.

5. The method according to claim 1, wherein the synchronization marker has a first length, and the searching for the synchronization marker further comprises: finding a most likely position of the synchronization marker first symbol by detecting at least one peak in a sequence of symbols from the received frame, the sequence being received in a buffer having first buffer length greater than the first length.

6. The method according to claim 5, wherein detecting one peak in the sequence received in the buffer comprises computing a metric .sub.LW(m) as ${}_{\mathrm{LW}}\left(m\right)=\ln .Math..Math.\cosh \left({\tilde{y}}_1^m.Math.a_m^T\right)+\ln .Math..Math.\cosh \left({\tilde{y}}_{m+1}^{m+N}.Math.s^T\right)+\underset{n=m+N+1}{\overset{B}{.Math.}}.Math..Math.\ln .Math..Math.\cosh \left({\tilde{y}}_n\right)$ where the sequence received in the buffer is denoted by y=[y.sub.1, y.sub.2, . . . , y.sub.B], the synchronization marker is denoted by s=[s.sub.1, s.sub.2, . . . , s.sub.N], the acquisition sequence is denoted by a=[a.sub.1, a.sub.2, . . . , a.sub.A], and m denotes a position of the synchronization marker first symbol; and finding the most likely position of the synchronization marker first symbol comprises maximizing the computed metric.

7. The method according to claim 6, further comprising: listing in decreasing order the computed metric .sub.LW(m) for every possible value of m from a set of indices n{1, 2, . . . , B} to obtain a list, .sub.LW(m.sub.1).sub.LW(m.sub.2) . . . .sub.LW(m.sub.B), and performing list decoding over the list.

8. The method according to claim 5, further comprising decoding a set of symbols from the sequence received in the buffer, and applying error detection to the decoded symbols to avoid false dectections of the synchronization marker.

9. The method according to claim 1, wherein the acquisition sequence is selected from a sequence of alternating binary symbols, a sequence of zeros and a constant signal.

10. A frame synchronizer device for a receiver of a communication system, the receiver receiving a frame which comprises a data sequence, a synchronization marker preceding the data sequence and an acquisition sequence preceding the synchronization marker, the device by comprising: a searcher circuit configured to search the synchronization marker by using the acquisition sequence.

11. The device according to claim 10, wherein the searcher circuit is configured to use a sliding observation window with a second length greater than or equal to a length of the synchronization marker.

12. The device according to claim 11, further comprising metric computing instructions configured to compute a metric of likelihood ratio test the acquisition sequence, LRT-A, which is compared to a pre-defined threshold to determine whether a sequence received in the sliding observation window is the synchronization marker, wherein the metric of likelihood ratio test for the acquisition sequence denoted by .sub.LRT-A(r), is computed as: ${}_{\mathrm{LRT}-A}\left(r\right)=\ln .Math..Math.\cosh \left({\tilde{r}}_1^{M-N}.Math.a_{M-N}^T\right)+\ln .Math..Math.\cosh \left({\tilde{r}}_{M-N+1}^M.Math.s^T\right)-\ln .Math.\underset{m=1}{\overset{N}{.Math.}}.Math..Math.{}_m.Math.\cosh \left({\tilde{r}}_1^{M-m+1}.Math.a_{M-m+1}^T\right).Math.\cosh \left({\tilde{r}}_{M-m+2}^M.Math.s_{m-1}^T\right)$ where the synchronization marker, s=[s.sub.1, s.sub.2, . . . , s.sub.N], N denoting the length of the synchronization marker, the received sequence in the sliding observation window is denoted by r, r=[r.sub.1, r.sub.2, . . . , r.sub.N], and the acquisition sequence a=[a.sub.1, a.sub.2, . . . , a.sub.A], A denoting the length of the acquisition sequence.

13. The device according to claim 10, wherein the searcher circuit comprises a buffer of a first buffer length greater than a length of the synchronization marker length, and wherein the searcher circuit applies a peak detector to a sequence of symbols received in the buffer to find a most likely position of the synchronization marker first symbol and error detection indicators from a decoder of the receiver to avoid false dectections of the synchronization marker.

14. The device according to claim 13, wherein the peak detector comprises metric computing instructions configured to compute a metric .sub.LW(m) as ${}_{\mathrm{LW}}\left(m\right)=\ln .Math..Math.\cosh \left({\tilde{y}}_1^m.Math.a_m^T\right)+\ln .Math..Math.\cosh \left({\tilde{y}}_{m+1}^{m+N}.Math.s^T\right)+\underset{n=m+N+1}{\overset{B}{.Math.}}.Math..Math.\ln .Math..Math.\cosh \left({\tilde{y}}_n\right)$ where the sequence received in the buffer is denoted by y=[y.sub.1, y.sub.2, . . . , y.sub.B], the synchronization marker is denoted by s=[s.sub.1, s.sub.2, . . . , s.sub.N], the acquisition sequence is denoted by a=[a.sub.1, a.sub.2, . . . , a.sub.A], and m denotes a position of the synchronization marker (s) first symbol; and the peak detector finds the most likely position of the synchronization marker first symbol by maximizing the computed metric.

15. The device according to claim 14, further comprising a list decoder applied to a list of the computed metric .sub.LW(m) values, obtained in decreasing order for every possible position m from a set of indices n{1, 2, . . . , B}.

Description

DESCRIPTION OF THE DRAWINGS

[0043] For the purpose of aiding the understanding of the characteristics of the invention, according to a preferred practical embodiment thereof and in order to complement this description, the following figures are attached as an integral part thereof, having an illustrative and non-limiting character:

[0044] FIG. 1 shows the structure of a frame transmitted in a communication system, as known in prior-art.

[0045] FIG. 2 shows the structure of a frame to which the invention can be applied.

[0046] FIG. 3 shows the structure and position of an extended sliding observation window with respect to the frame, in accordance with a preferred embodiment of the invention.

[0047] FIG. 4 shows probabilities of missed detection, false alarm and frame synchronization error for the soft correlation and the LRT-A metrics with a length of extended observation window, in accordance with a possible embodiment of the invention.

[0048] FIG. 5 shows the frame synchronization error at a fixed signal-to-noise ratio, for hard correlation, soft correlation, the Massey-Chiani metric and LRT-A metrics, and for different lengths of the extended observation window, in accordance with another possible embodiment of the invention.

[0049] FIG. 6 shows the frame synchronization error for different signal-to-noise ratios, for hard correlation, soft correlation, the Massey-Chiani metric and LRT-A metrics, and for different lengths of the extended observation window, in accordance with another possible embodiment of the invention.

[0050] FIG. 7 shows the frame and buffer structure for peak detection, in accordance with a possible embodiment of the invention.

[0051] FIG. 8 shows a block diagram of the receiver architecture using frame synchronization, in accordance with a possible embodiment of the invention.

[0052] FIG. 9 shows a flow chart for frame synchronization using peak detection, in accordance with a possible embodiment of the invention.

[0053] FIG. 10 shows the frame synchronization error as a function of signal-to-noise, in accordance with a further possible embodiment of the invention, using multiple peak detection on a long observation window.

PREFERRED EMBODIMENT OF THE INVENTION

[0054] The matters defined in this detailed description are provided to assist in a comprehensive understanding of the invention. Accordingly, those of ordinary skill in the art will recognize that variation changes and modifications of the embodiments described herein can be made without departing from the scope and spirit of the invention. Also, description of well-known functions and elements are omitted for clarity and conciseness.

[0055] Of course, the embodiments of the invention can be implemented in a variety of architectural platforms, operating and server systems, devices, systems, or applications. Any particular architectural layout or implementation presented herein is provided for purposes of illustration and comprehension only and is not intended to limit aspects of the invention.

[0056] FIG. 1 illustrates transmitted data in a frame whose structure consists of: a sync marker (s) which is a known word of length N and indicates the beginning of the data (d) transmitted within a block of length D. The sync marker (s) can be denoted by s=[s.sub.1, s.sub.2, . . . s.sub.N]{1, 1}.sup.N. Before the sync marker (s), there is preceding sequence (a) with a known structure of length A, the length of the preceding sequence (a) being generally not known by the receiver. The preceding sequence (a) is typically used for time and frequency acquisition. For this reason, in the following and in the context of the invention, this sequence is called the acquisition sequence (a) and is denoted by a=[a.sub.1, a.sub.2, . . . , a.sub.A].

[0057] Some possible and relevant examples for the acquisition sequence (a) are: [0058] A sequence of alternating symbols: a.sub.n=(1).sup.n{1, 1} [0059] A constant signal: a.sub.n=a.sub.0, including the case a.sub.0=0

[0060] In prior art, a sliding observation window (W) of the same length N as the sync marker (s) takes N symbols out of the received noisy symbols stream to compute the metric (r) which is compared to a pre-defined threshold.

[0061] It is within the context of the invention, that various embodiments are now presented with reference to the FIGS. 2-10.

[0062] FIG. 2 presents an example of transmitted frame to be synchronized at the receiving side of a digital communication system in accordance with a possible embodiment of the invention. The formulation used in the following holds for all the above-mentioned three cases of a possible acquisition sequence (a): a sequence of alternating symbols, a void signal or a constant signal.

[0063] In order to better exploit the known properties of the preceding acquisition sequence (a), the use of an extended sliding window (x.sub.m) is proposed to compute a metric for frame synchronization. The sliding observation window (x.sub.m) is extended to a length MN, i.e., the observation window (x.sub.m) may be longer than the sync marker, as depicted in FIG. 2.

[0064] The entire noiseless sequence can be denoted by x=[h.sub.1a, h.sub.2s,d] (equation 13), where d denotes an unknown data sequence.

[0065] The random coefficients h.sub.1, h.sub.2 {1, 1} model the sign ambiguity of the received signal and the sign ambiguity of the acquisition sequence (a). Although it is assumed that at the receiving side, the sign ambiguity is the same for the entire received sequence, the two factors h.sub.1 and h.sub.2 are needed to account also for the uncertainty on whether the acquisition sequence (a) ends with a binary value equal to 1 or +1. This uncertainty could be easily removed at the transmitter side.

[0066] A noiseless extended sliding observation window (x.sub.m) at position m is defined as x.sub.m[h.sub.1.Math.a.sub.M+1m.Math.h.sub.2.Math.s.sub.m1] (equation 14), where m=1, 2, . . . , N+1.

[0067] FIG. 3 illustrates the meaning of the index m, which determines the position of the sliding window (x.sub.m) relative to the position of the sync marker (s). The upper part (A) of FIG. 3 shows the indexing of sliding window position, while the lower part (B) illustrates some examples of sliding window positions, i.e., possible values of index m.

[0068] With the indexing of FIG. 3, the two hypotheses can be reformulated as:

H.sub.0:m{1, 2, . . . , N}

H.sub.1:m=N+1

[0069] Table 1 shows the relation between indices n and m and the observed window (x.sub.m). The index m refers to the last symbol position of the sliding window (x.sub.m), counted from the last symbol of the acquisition sequence (a), whereas the index n refers to the first symbol of the sliding window (x.sub.m), counted from the start of the acquisition sequence (a). Both indices are related by the expression: n=AM+m. Only window positions in which the sliding observation window (x.sub.m) ends before or at the same bit interval as the sync marker (s) are considered, and therefore the random data sequence (d) has no effect.

TABLE-US-00001 TABLE 1 n m x.sub.m [00011]$1.Math..Math.\mathrm{.Math.}.Math..Math.A-M+1$ 1 h.sub.1 .Math. a.sub.M A M + 2 2 [h.sub.1 .Math. a.sub.M1, h.sub.2 .Math. s.sub.1] A M + 3 3 [h.sub.1 .Math. a.sub.M2, h.sub.2 .Math. s.sub.2] [00012]$\mathrm{.Math.}$ [00013]$\mathrm{.Math.}$ [00014]$\mathrm{.Math.}$ A M + N N [h.sub.1 .Math. a.sub.MN+1, h.sub.2 .Math. s.sub.N1] A M + N + 1 N + 1 [h.sub.1 .Math. a.sub.MN, h.sub.2 .Math. s]

[0070] The received signal (r) in the observation window (x.sub.m) is hence:

[00015]$r=x_m+w,w.Math..Math..Math.\left(0,\frac{N_0}{2}.Math.I_M\right)$

[0071] One of the key aspects when considering the acquisition sequence (a) is that, in contrast to a sync marker (s) preceded by random data, the mixed data case cannot be neglected. For this reason, all positions of the observation window (x.sub.m) for the null hypothesis are considered.

[0072] For the null hypothesis,

[00016]$\begin{array}{cc}p\left(r{H}_0\right)=\underset{\mathrm{.Math.}=1}{\overset{N}{.Math.}}.Math..Math.{}_m.Math.p\left(rm=\mathrm{.Math.}\right),& \left(\mathrm{equation}.Math..Math.15\right)\end{array}$

where .sub.P[m=] denotes the a priori probability that the sliding window (x.sub.m) is in position m=, assuming that

[00017]${}_{\mathrm{.Math.}}=\frac{1}{A+N-M-1}.Math.\{\begin{array}{c}A-M.Math..Math.\mathrm{for}.Math..Math.\mathrm{.Math.}=1\\ 1.Math..Math.\mathrm{for}.Math..Math.\mathrm{.Math.}=2,\mathrm{.Math.}.Math.,N\end{array}$

and the same probability for the four sign ambiguities, i.e.

[00018]$p\left(r|m=\mathrm{.Math.}\right)=\frac{1}{4}.Math.\underset{h_1,h_2}{.Math.}.Math..Math.p\left(r|m=\mathrm{.Math.},h_1,h_2\right)$

then

[00019]$\begin{array}{c}p\left(r|m,h_1,h_2\right)=.Math.\underset{n=1}{\overset{M-m+1}{.Math.}}.Math..Math.p\left(r_n|x_{\mathrm{mn}}=h_1.Math.a_n\right).Math.\\ .Math.\underset{n=M-m+2}{\overset{M}{.Math.}}.Math..Math.p\left(r_n|x_{\mathrm{mn}}=h_2.Math.s_{n-M+m-1}\right)\\ =.Math.K_M\left(r\right).Math.\underset{n=1}{\overset{M-m+1}{.Math.}}.Math..Math.\exp \left(h_1.Math.a_n.Math.{\tilde{r}}_n\right).Math.\\ .Math.\underset{n=M-m+2}{\overset{M}{.Math.}}.Math..Math.\exp \left(h_2.Math.s_{n-M+m-1}.Math.{\tilde{r}}_n\right)\end{array}$

and with {tilde over (r)}.sub.n.sup.m[{tilde over (r)}.sub.n, {tilde over (r)}.sub.n+1, . . . , {tilde over (r)}.sub.m], we can write

p(r|m,h.sub.1,h.sub.2)=K.sub.M.Math.exp(h.sub.1{tilde over (r)}.sub.1.sup.Mm+1a.sub.Mm+1.sup.T).Math.exp(h.sub.2{tilde over (r)}.sub.Mm+2.sup.Ms.sub.m1.sup.T)

and hence

[00020]$p\left(r|m\right)=K_M.Math.\cosh \left({\tilde{r}}_1^{M-m+1}.Math.a_{M-m+1}^T\right).Math.\cosh \left({\tilde{r}}_{M-m+2}^M.Math.s_{m-1}^T\right)$$\mathrm{and}$$p\left(r|H_0\right)=K_M.Math.\underset{m=1}{\overset{N}{.Math.}}.Math..Math.{}_m.Math.\cosh \left({\tilde{r}}_1^{M-m+1}.Math.a_{M-m+1}^T\right).Math.\cosh \left({\tilde{r}}_{M-m+2}^M.Math.s_{m-1}^T\right)$

[0073] For the other hypothesis, we obtain

p(r|H.sub.1)=K.sub.M.Math.cos h({tilde over (r)}.sub.1.sup.MNa.sub.MN.sup.T).Math.cos h({tilde over (r)}.sub.MN+1.sup.Ms.sup.T)

which leads to a metric of likelihood ratio test for the acquisition sequence, LRT-A,the A stands for the acquisition sequence (a)in logarithmic domain:

[00021]${}_{\mathrm{LRT}-A}\left(r\right)=\ln .Math..Math.\cosh \left({\tilde{r}}_1^{M-N}.Math.a_{M-N}^T\right)+\ln .Math..Math.\cosh \left({\tilde{r}}_{M-N+1}^M.Math.s^T\right)-\ln .Math.\underset{m=1}{\overset{N}{.Math.}}.Math..Math.{}_m.Math.\cosh \left({\tilde{r}}_1^{M-m+1}.Math.a_{M-m+1}^T\right).Math.\cosh \left({\tilde{r}}_{M-m+2}^M.Math.s_{m-1}^T\right)$

[0074] This expression simplifies slightly for M=N, but does not become identical to the equation 8 described in prior-art. The difference comes from the fact that here the mixed data case is explicitly taken into account.

[0075] The application of the standard LRT can lead to two types of error at every symbol position: [0076] i) a false alarm occurs if the presence of the sync marker (s) is indicated by (r) at another position than the true one, [0077] ii) a missed detection occurs if the observation window (x.sub.m) is at the true position but the metric (r) is below the threshold .

[0078] These error events can be distinguished by the window position given by the index n shown in Table 1. The probabilities for false alarm P.sub.fa(v) and missed detection P.sub.md are respectively given by

P.sub.fa(v)=P[, n=v], v=1, . . . , AM+N

P.sub.md=P[<, m=N+1](equation 16)

[0079] For the overall false alarm probability P.sub.fa, since the events {n=1}, {n=2}, . . . , {n=AM+N} are mutually exclusive, we have

[00022]$\begin{array}{cc}{\stackrel{\_}{P}}_{\mathrm{fa}}=\underset{v=1}{\overset{A-M+N}{.Math.}}.Math..Math.P_{\mathrm{fa}}\left(v\right)& \left(\mathrm{equation}.Math..Math.17\right)\end{array}$

[0080] Since in each failed synchronization attempt, either a false alarm or a missed detection occurs, the probability of a frame synchronization error, FSE, is hence given by the sum of both probabilities

P.sub.FSE=P.sub.fa+P.sub.md (equation 18)

[0081] The proposed methods are validated through computer simulations in the deep-space communication uplink and show significant performance gains compared to current solutions.

[0082] In the following, the system parameters for deep space telecommand in the uplink are used as a running example, being the most important aspect the length (N) of the sync marker (s). The sync marker (s) is defined in hexadecimal notation by the ECSS as the word EB90 and has a length of N=16 bits. For the acquisition sequence (a), the length (A) which is assumed in the example is A=512.

[0083] FIG. 4 shows missed detection, false alarm and frame synchronization error probabilities as a function of the detection threshold for the soft correlation (SC) and the LRT-A metrics with a length of extended observation window M=24. In FIG. 4, the false alarm and missed detection probabilities, denoted as P.sub.fa and P.sub.md respectively, as well as the resulting frame synchronization errorFSEprobability P.sub.FSE, are plotted as a function of the decision threshold for two metrics at E.sub.S/N.sub.0=0 dB. From the definition of the standard LRT, it is clear that the false alarm probability P.sub.fa is a decreasing function of the threshold , while the missed detection probability P.sub.md is increasing. The parameter of interest, however, is the FSE, which simplifies the problem of finding the optimum threshold to a simple one-dimensional minimization which can be solved numerically by simulation.

[0084] FIG. 5 shows the frame synchronization error (FSE) values at a fixed SNR, e.g., Es/N.sub.0=0, and for every metric which is considered here: Hard and Soft correlations, the Massey-Chiani metric and LRT-A for different lengths (M) of the extended sliding window, and the FSE is plotted as a function of the decision threshold . From these diagrams, the optimum threshold for each metric for a given SNR can be found. These values of the optimum decision threshold A for minimum FSE are listed in Table 2 for the four metrics and for several SNR values, in terms of energy per symbol to noise power spectral density ratio (Es/N.sub.0).

TABLE-US-00002 TABLE 2 Hard Soft Massey- E.sub.S/N.sub.0 Correlation Correlation Chiani LRT-A 3 dB 6 9 5 6 2 dB 6 8 4 6 1 dB 6 7 4 6 0 dB 6 7 4 6 1 dB 6 6 3 6 2 dB 6 6 2 6 3 dB 6 6 1 6 4 dB 6 6 0 6

[0085] From FIG. 5 and Table 2, it can be derived that, at least within this range, only the SC and the MC metrics depend on the SNR, while for the HC and the LRT-A the same threshold can be applied for all SNR values. This aspect is important in practical receivers where an accurate SNR estimation is often not viable.

[0086] FIG. 6 shows the achieved frame synchronization error (FSE) values for different values of SNR and for every metric which is considered here: Hard and Soft correlations, the Massey-Chiani metric and LRT-A for different lengths (M) of the extended sliding window, and the FSE is plotted as a function of the energy per symbol to noise power spectral density ratio (Es/N.sub.0). We can observe that, while soft correlation performs very poorly, the hard correlation metric comes comes close to the Massey-Chiani metric for high SNR. We can also see that the proposed LRT-A metric achieves a significant performance improvement for all SNR values, even without extending the window length. This gain comes from the exploitation of the structure of the acquisition sequence, in particular in the mixed data case. The performance improves slightly by extending the observation window from 16 to 24 bits, while a further extension to 128 bits does not lead to a further improvement.

[0087] In an alternative embodiment of the invention, the proposed method for frame syncronization uses, single or multiple, peak detection with a long observation window, i.e. a buffer of length BN, where N is the length of the syncronization marker (s).

[0088] For single or multiple peak detection based on the long observation window, a further assumption on the frame structure is that the sync marker (s) is followed by one or multiple codewords (c.sub.1, c.sub.2, . . . ) as depicted in FIG. 7. The incoming symbols stream is partitioned into overlapping sequences (b.sub.1, b.sub.2, . . . ) of length BN, which are buffered in storing means of the receiver at respective buffer positions (y.sub.1, y.sub.2, . . . ). The overlap (O) comprises at least N1 symbols, in order to avoid that the sync marker (s) falls between two consecutive buffer positions.

[0089] On the other hand, a condition which is given in many communication systems is that, at the receiving side, a channel decoder is capable to determine if a sequence of N, symbols corresponds to the first codeword after the sync marker (s). This is used in a possible embodiment of the invention to avoid false alarms, that is, to avoid that the frame synchronizer declares a sync marker detection although no sync marker is present. In this case, an error detection indicator needs to be available to the frame synchronizer. An illustrative example of a possible receiver (800) block diagram is depicted in FIG. 8. The input signal (In) from the ADC stage is processed by the signal adquisition (801) and the synchronization and tracking means (802) of the receiver (800). The, the adquired signal is demoduled and decoded, but it is needed a frame synchronizer (804) between the demodulator (803) and the decoder (805). The proposed frame synchronizer (804) uses the sync marker (s) and indicators (E) of the error detection by the decoder (805).

[0090] FIG. 9 illustrates the procedure of applying (multiple) peak detection using the long observation window determined by a buffer of length B. The buffer positions (y.sub.i) are filled (901) with symbols (b.sub.1, b.sub.2, . . . ) of length B from the received stream (900). Then, the most likely positions (n.sub.1, n.sub.2, . . . , n.sub.L) of the sync marker (s) are searched (902) in the buffer positions (y.sub.i), as explained below. The channel decoder (805) decodes (903) the N.sub.c symbols which follow a candidate sync marker. For each candidate position, the channel decoder (805) checks (903) if the N.sub.c symbols which follow the candidate sync marker correspond to a codeword (c.sub.1, c.sub.2, . . . ). If this is the case, the correct position is found (904). If not, the next candidate position is tested and if no valid codeword is found after testing all candidate positions, the search continues with the content of the next buffer.

[0091] While for one-shot detection of the sync marker (s), for every window position (m), a metric is compared to a threshold, as disclosed by Chiani in Noncoherent frame synchronization, for periodically inserted sync markers (s) with known periodicity, the receiver can search for the maximum metric within a frame by single peak detection and then there is no need to determine any threshold as disclosed by Massey in Optimum frame synchronization.

[0092] Nevertheless, peak detection even for a single sync marker can be applied with the following method: The incoming symbol stream is partitioned into long overlapping observation windows. The overlap is as long as the sync marker to avoid that this falls in between two windows. Then, peak detection is applied within the long observation window. This inevitably leads to false alarms in windows which do not contain the sync marker (s). These false alarms can be detected after decoding of the first code word after the sync marker (s), provided that the undetected error probability of the channel coding scheme is lower than the target FSE. This is an additional requirement which, however, is typically satisfied anyway.

[0093] It is assumed that the long observation window contains B=A+N+DN symbols and contains the acquisition sequence (a), the sync marker (s) and data (d), as depicted in FIG. 1. The entire noiseless sequence in the buffer of length B is given in equation 13 and the received sequence is denoted by y=x+x. The maximum likelihood rule to determine the index of the first bit of the sync marker (s) is given by:

[00023]$n^{*}=\arg .Math.\underset{m}{\max }.Math.\left\{p\left(y|A=m\right)\right\}+1$

[0094] Similar to the derivation for the extended observation window, we start with p(y|A=m)=1/4.sub.h.sub.1.sub.,h.sub.2p(y|A=m,h.sub.1,h.sub.2). Since we are considering the entire buffer, we factor the conditional probability of y as

[00024]$\begin{array}{c}p\left(y|m,h_1,h_2\right)=.Math.\underset{n=1}{\overset{m}{.Math.}}.Math..Math.p\left(y_n|h_1.Math.a_n\right).Math.\underset{n=m+1}{\overset{m+N}{.Math.}}.Math..Math.p\left(y_n|h_2.Math.s_{n-m}\right).Math.\\ .Math.\underset{n=m+N+1}{\overset{B}{.Math.}}.Math..Math.\frac{p\left(y_n|-1\right)+p\left(y_n|1\right)}{2}\\ =.Math.K_B\left(y\right).Math.\exp \left(h_1.Math.{\tilde{y}}_1^m.Math.a_m^T\right).Math.\exp \left(h_2.Math.{\tilde{y}}_{m+1}^{m+N}.Math.s^T\right).Math.\underset{n=m+N+1}{\overset{B}{.Math.}}.Math..Math.\cosh \left({\tilde{y}}_n\right)\end{array}$

which leads to

[00025]$p\left(y|A=m\right)=K_B.Math.\cosh \left({\tilde{y}}_1^m.Math.a_m^T\right).Math.\cosh \left({\tilde{y}}_{m+1}^{m+N}.Math.s^T\right).Math.\underset{n=m+N+1}{\overset{B}{.Math.}}.Math..Math.\cosh \left({\tilde{y}}_n\right)$

and, finally, the metric to be maximized .sub.LW(m) is defined as

[00026]$\begin{array}{c}{}_{\mathrm{LW}}\left(m\right).Math.\stackrel{}{=}.Math..Math.\ln \left(\frac{1}{K_B}.Math.p\left(y|A=m\right)\right)\\ =.Math.\ln .Math..Math.\cosh \left({\tilde{y}}_1^m.Math.a_m^T\right)+\ln .Math..Math.\cosh \left({\tilde{y}}_{m+1}^{m+N}.Math.s^T\right)+\underset{n=m+N+1}{\overset{B}{.Math.}}.Math..Math.\ln .Math..Math.\cosh \left({\tilde{y}}_n\right)\end{array}$

[0095] The most likely position of the first symbol of the sync marker (s) is then found by:

[00027]$n^{*}=\arg .Math.\underset{m}{\max }.Math.\left\{{}_{\mathrm{LW}}\left(m\right)\right\}+1$

[0096] In another possible embodiment of the invention, multiple peak detection on the long observation window can be used for frame syncronization. The fact that the sync marker (s) is followed by codewords can be further exploited, in the case that the code schema which is used provides sufficient error detection capability and multiple decoding attempts are affordable. These are rather mild assumptions, since the probability of undetected error is usually required to be significantly lower than the FSE. Furthermore, bit rates for telecommand operations are typically moderate, hence multiple decoding attempts within the observation window, which is at least as long as a codeword, are not unrealistic.

[0097] For multiple peak detection, the indices n{1, 2, . . . , B} are listed in decreasing metric order:

.sub.LW(m.sub.1).sub.LW(m.sub.2) . . . .sub.LW(m.sub.B)

and perform L successive decoding attempts for the indices m.sub.1, m.sub.2, . . . , m.sub.L. In coding theory, this approach is known as list decoding.

[0098] For L=1, we have the simple peak detection as described before, while for the unrealistic value L=B, the FSE is limited only by the undetected word error probability of the channel coding scheme.

[0099] FIG. 10 shows the achieved FSE with multiple peak detection (PD) for different list decoding lengths L. A short value of additional decoding attempts already provides very significant gains for frame synchronization. As a reference, the Massey-Chiani (MC) metric can also be applied, computed in a sliding window operation and with buffer of length B=64, but this MC metric suffers from an error floor which is due to false alarms which are unavoidable if the 16-bit sync marker appears in the data.

[0100] The proposed embodiments can be implemented as a collection of software elements, hardware elements, firmware elements, or any suitable combination of them.

[0101] Note that in this text, the term comprises and its derivations (such as comprising, etc.) should not be understood in an excluding sense, that is, these terms should not be interpreted as excluding the possibility that what is described and defined may include further elements, steps, etc.