HK1141371B - Method and system for processing communication signal - Google Patents

Description

Method and system for processing communication signal

Technical Field

The present invention relates to the field of wireless communication systems, and more particularly, to a method and system for extending frequency offset estimation range based on correlation of complex sequences

Background

Mobile communications have transformed the way people communicate, and mobile phones have transformed from a luxury item to an essential part of everyday life. Today, the use of mobile phones is controlled by social situations and not by geographical or technical constraints. Voice connections fulfill the basic requirements of communication, while mobile voice connections will penetrate deeper into everyday life. Mobile networks have become a popular source of everyday information and, of course, use simple, generic mobile access technologies to access such information.

Third generation (3G) and fourth generation (4G) cellular networks are specifically designed to meet future mobile network requirements. With the popularity and use of these services, factors such as cost-effective optimization of network capacity and quality of service (QoS) will become more important to cellular operators than today. These factors can be achieved through careful network planning and operation, improvement of transmission means, and improvement of reception technology level. Finally, carriers need technologies that can enhance their downlink capabilities.

Other drawbacks and disadvantages of the prior art will become apparent to one of ordinary skill in the art upon examination of the following system of the present invention as described in conjunction with the accompanying drawings.

Disclosure of Invention

A method and/or system for extending a range of frequency offset estimation based on correlation of complex sequences, substantially as shown in and/or described in connection with at least one of the figures, as set forth more completely in the claims.

According to an aspect of the invention, the invention proposes a method of processing a communication signal, comprising:

splitting each received sample sequence and local sample sequence replica (duplicate sample sequence) into three or more contiguous sample subsequences of similar length;

for each of the three or more similar-length consecutive sub-sequences of samples, determining a correlation coefficient between the local sample sequence replica and the corresponding sub-sequence of samples of the split received sample sequence;

determining a plurality of phase differences based on neighboring (adjacent) correlation coefficients among the determined correlation coefficients; and

averaging the determined plurality of phase differences to generate a frequency offset estimate.

Preferably, the communication system conforms to a wireless standard.

Preferably, the wireless standard includes UMTS EUTRA (LTE), WiMAX (IEEE802.16), and/or WLAN (IEEE 802.11).

Preferably, the subsequences are of equal length.

Preferably, the method further comprises calculating the plurality of phase differences by calculating a phase difference of two numbers (two times), any one of the two numbers being from a continuous set (contiguous set) of the determined correlation coefficients, the two continuous sets being mutually exclusive.

Preferably, the two joint continuum sets comprise a continuum set of the determined correlation coefficients.

Preferably, the method further comprises deriving a sample mean from the determined phase difference for the averaging.

Preferably, the method further comprises increasing a range of steerable frequency offset estimates by adding a plurality of consecutive sample sequences.

Preferably, the received sampling sequence and the local sample sequence replica are derived from a pseudo-random sequence.

Preferably, the method further comprises determining the phase difference by successive approximation (approximation).

According to yet another aspect of the present invention, there is provided a system for processing a communication signal, comprising:

one or more circuits to:

splitting each received sample sequence and local sample sequence replica into three or more contiguous sample subsequences of similar length;

for each of the three or more similar-length consecutive sub-sequences of samples, determining a correlation coefficient between the local sample sequence replica and the corresponding sub-sequence of samples of the split received sample sequence;

determining a plurality of phase differences based on adjacent correlation coefficients among the determined correlation coefficients; and

averaging the determined plurality of phase differences to generate a frequency offset estimate.

Preferably, the communication system conforms to a wireless standard.

Preferably, the wireless standard includes UMTS EUTRA (LTE), WiMAX (IEEE802.16), and/or WLAN (IEEE 802.11).

Preferably, the subsequences are of equal length.

Preferably, the one or more circuits calculate the plurality of phase differences by calculating a phase difference of two numbers (two times), either of the two numbers being from a consecutive set (contiguous set) of the determined correlation coefficients, the two consecutive sets being mutually exclusive.

Preferably, the two joint continuum sets comprise a continuum set of the determined correlation coefficients.

Preferably, said one or more circuits derive a sample mean from said determined phase difference for said averaging.

Preferably, the one or more circuits increase a range of steerable frequency offset estimates by adding a plurality of consecutive sample sequences.

Preferably, the received sampling sequence and the local sample sequence replica are derived from a pseudo-random sequence.

Preferably, the one or more circuits determine the phase difference by successive approximation (approximation).

Various advantages, aspects and novel features of the invention will become apparent from the following detailed description of specific embodiments when considered in conjunction with the drawings.

Drawings

FIG. 1 is a diagram of a preferred wireless communication system in accordance with an embodiment of the present invention;

FIG. 2 is a diagram of a preferred correlator for frequency offset estimation in accordance with one embodiment of the present invention;

fig. 3 is a bode plot of preferred EUTRA frequency acquisition characteristics under different SNR conditions in accordance with an embodiment of the present invention;

fig. 4 is a flow diagram of a preferred frequency offset estimation protocol in accordance with an embodiment of the present invention.

Detailed Description

The invention provides a method and a system for expanding a frequency offset estimation range based on the correlation of complex sequences. Aspects of a method and system for extending the range of frequency offset estimation based on correlation of complex sequences include splitting each received sample sequence and local sample sequence replica into three or more contiguous sample subsequences of similar length. For each of the three or more similar-length consecutive sub-sequences of samples, a correlation coefficient between the local sample sequence replica and the corresponding sub-sequence of samples of the split received sample sequence is determined. Determining a plurality of phase differences based on neighboring determined correlation coefficients; and averaging the determined plurality of phase differences to generate a frequency offset estimate.

The communication system conforms to a wireless standard, comprising: UMTS EUTRA (Universal Mobile telecommunications System; evolved Universal Terrestrial Radio Access) (LTE, long term evolution, long-term-Terrestrial), WiMAX (Worldwide Interoperability for microwave Access) (IEEE802.16), and/or WLAN (Wireless local area network) (IEEE 802.11). The subsequences are of equal length. The plurality of phase differences are calculated by calculating the phase difference of two numbers (two times), any one of the two numbers being from a continuous set (contiguous set) of the determined correlation coefficients, and the two continuous sets being mutually exclusive. The two joint continuum sets comprise a continuum set of the determined correlation coefficients. The averaging is performed by deriving a sampled average from the determined phase difference. A steerable frequency offset estimation range is increased by adding a plurality of consecutive sample sequences. The received replica of the sampling sequence and the local sampling sequence are taken from a pseudo-random sequence. In some cases, the pseudo-random sequence includes complex sequence elements. The phase difference is determined by a linear approximation technique.

Fig. 1 is a diagram of a preferred wireless communication system in accordance with an embodiment of the present invention. Referring to fig. 1, there is shown an access point 112b, a computer 110a, a router 130, the internet 132, and a web server 134. The computer or host device 110a includes a wireless transceiver 111a, a main processor 111c, and a main memory 111 d. A wireless connection between the wireless transceiver 111a and the access point 112b is also shown.

The access point 112b may comprise suitable logic, circuitry, and/or code that may enable data communication using, for example, the wireless transceiver 111a to transmit and receive Radio Frequency (RF) signals. The access point 112b is also used to communicate over a wired network, for example, with a router 130. The wireless transceiver 111a may comprise suitable logic, circuitry and/or code that may enable communication with one or more other wireless communication devices over a radio frequency wave (rf wave). The wireless transceiver 111a and the access point 112b are compliant with one or more communication standards, such as GSM, UMTS EUTRA (LTE), CDMA2000, Bluetooth, WiMAX (IEEE802.16), and/or IEEE802.11 wireless LANs.

The main processor 111c may comprise suitable logic, circuitry, and/or code that may enable generation and processing of data. The main memory 111d comprises suitable logic, circuitry, and/or code that may be operable to store and retrieve data for various system components and functions of the computer 110 a.

The router 130 may comprise suitable logic, circuitry, and/or code that may enable communication with a communication device. The communication device is communicatively coupled to router 130, such as via access point 112b and/or one or more communication devices coupled to internet 132.

The internet 132 comprises suitable logic, circuitry, and/or code that may be operable to provide interconnection and exchange data for a plurality of communication devices. The web server 134 may comprise suitable logic, circuitry and/or code that may enable communication with a communication device communicatively coupled to the web server 134 via, for example, the internet 132.

The various computer and communication devices include hardware and software that can communicate using one or more wireless communication standards and/or protocols. For example, a user of a computer or host device 110a accesses the internet 132 to be able to consume (consume) streaming content (streamcontent) from a web server 134. Thus, the user would establish a wireless connection between the computer 110a and the access point 112 b. Once established, the connection receives the data stream content from the web server 134 via the router 130, the access point 112b, and the wireless connection for consumption by the computer or host device 110 a.

In many communication systems, it is desirable to enable synchronization between a receiver, such as wireless transceiver 111a, and access point 112 b. Synchronization may be achieved by transmitting a known data sequence from the transmitter to the receiver. These data sequences can be regarded as navigation signals (pilot signals), synchronization signals and/or reference signals. Timing information and frequency offset information are obtained through timing reception and frequency offset measurements of the navigation signal, synchronization signal, and/or reference signal (e.g., through correlation of local signal replicas). It is desirable to use a low complexity synchronization protocol to achieve a large dynamic frequency offset range. In accordance with various embodiments of the present invention, a subsequence of local signal replicas is correlated with a received signal subsequence. A plurality of phase delays (lag) is calculated from the plurality of pairs of correlation coefficients based on adjacent pairs of sub-sequence pairs. The frequency offset is determined based on, for example, averaging a plurality of phase delays located at one or more timing delays in the correlation process where amplitude peaks of the correlation process occur.

Fig. 2 is a diagram of a preferred correlator for frequency offset estimation in accordance with an embodiment of the present invention. Referring to fig. 2, a plurality of adders 202, 208, 210, 212, 214, 216, a weighting block 204, a memory 206, a plurality of phase identification (discrimination) modules 218, 220, 222, and 224, and an averaging module 226 are shown. Also shown is a correlation input (correlation input), an output of the adder 202 (e.g., time synchronized), and an output to an averaging block 226 of the frequency controlled phase locked loop.

The adder 202 may comprise suitable logic, circuitry, and/or code that may enable generation of an output signal. The output signal is proportional to the sum of the plurality of input signals. Adders 208, 210, 212, 214, 216 are substantially similar to adder 202.

The weighting module 204 may comprise suitable logic, circuitry, and/or code that may enable generation of a plurality of weighted output signals. In this regard, each output signal includes one of a plurality of weighted output signals. Thus, the weighting module 204 is used for the input signal.

The memory 206 may comprise suitable logic, circuitry, and/or code that may be operable to receive and store a plurality of correlation coefficients (e.g., N correlation coefficients). The correlation coefficients are received, for example, at a wireless transceiver 111a, the wireless transceiver 111a including a plurality of sub-sequence correlators. A plurality of sub-sequence correlators are used to provide sub-correlation results. For example, for a full length reference or correlation sequence, the results are set to be contiguous.

The phase identification module 218 may comprise suitable logic, circuitry, and/or code that may enable generation of an output signal that may include a phase difference that may be proportional, for example, to a frequency offset between a synchronization signal (received via a wireless transceiver link) and a local reference signal replica. The phase identification modules 220, 222, 224 are completely similar to the phase identification module 218.

The averaging module 226 may comprise suitable logic, circuitry, and/or code that may enable generation of an output signal that is proportional to a sampled average of a plurality of input signals.

The complex random sequence and/or the navigation signal are used to assist in synchronization acquisition of the communication system. These complex sequences are also used to estimate the frequency offset between, for example, the transmission carrier frequency of the base station (e.g., access point 112b) and the receiver local oscillation frequency of the mobile terminal (e.g., host 110 a). Due to inaccuracies caused by crystal oscillators, manufacturing tolerances, and/or other factors, the mobile terminal receiver oscillation frequency may deviate (offset) from the transmission carrier frequency of the base station transmitter. By performing oscillator frequency synchronization during time and/or frequency synchronization, the likelihood (likelihood) that the receiver will successfully complete the initial operations associated with the synchronization is increased. In addition, the frequency synchronization acquisition capability early in the signal acquisition process enables synchronization to be successfully achieved under difficult conditions, for example, when the signal-to-noise ratio (signal-to-noise) is reduced.

For example, the complex synchronization sequence includes an M complex valued part (complex valued element). The complex sequence may be split into, for example, two partial sequences (two partial sequences). In order to be able to obtain an initial frequency offset estimate based on the autocorrelation of the partial sequences, two averaged portions (two hashes) of the reference sequence are correlated with the two partial sequences. Estimating a frequency offset by calculating a complex angular increment (complex angular increment) between two partial correlation results based on the two partial correlation results for each of the two sequence portions.

According to various embodiments of the present invention, frequency offset and/or frequency synchronization can be successfully achieved over a steerable frequency range that can be extended by performing partial correlation of multiple partial complex sequences. Then the number of complex sequence segments/portions will be increased, enabling to perform more partial correlations in a smaller number of sequence elements, and to determine the angular increment between successive synthesized partial correlation results. In accordance with various embodiments of the present invention, the method may extend the frequency offset range to achieve time synchronization.

A sequence of discrete complex values s [ n ], of length M, may be transmitted as a time reference sequence. At the receiver end, e.g. a mobile terminal, which desires to establish synchronization with the transmitter, M samples of the received signal r n are correlated with a reference synchronization sequence s n (corrected acquisition). The correlation output may be given by:

where R τ represents the correlation coefficient at the offset τ, and represents the complex conjugate (complex conjugate). For establishing a time reference (e.g. received sequence r n]And a reference sequence s [ n ]]Time offset between), it is expected that max (| R τ |), τ ≧ 0, can be found. When the receiver frequency offset is f_oThe received signal may be described by:

where r' n represents the r n signal imparted with the frequency offset.

In the case of frequency offset, the correlation coefficient R τ is distorted when compared to the ideal correlation coefficient without frequency offset. Then the maximum of the correlation amplitude will appear at a different position when compared to the corresponding maximum in the absence of the frequency offset. When this occurs, an incorrect synchronization time is determined, and when this incorrect synchronization time is used to estimate the frequency offset, an undesirable frequency offset estimate results.

In accordance with various embodiments of the present invention, it is desirable to establish proper time synchronization, particularly in the presence of frequency offsets. To increase the likelihood that the maximum amplitude of the correlation process coincides with the correct head time, the overall correlation process is broken down into several short correlation processes and the resulting amplitudes are combined.

For example, a complex-valued discrete sequence s [ n ]]＝{s[0]，s[1]，…，s[M-1]Can be transmitted as a time reference. Time synchronization may provide a correlation to establish. In this embodiment, instead of the coherent execution of M samples as described earlier, the correlation of the received sequence and the locally generated reference sequence copy may be divided into N segments, each segment comprising p elements, i.e. N ═ M/p. The sub-sequence of local replica samples is correlated with the sub-sequence of received samples to generate a sequence of correlation coefficients R'_k. Sequence R'_k(k-0, 1, …, N-1) is stored in the memory 206 for use in the processing of the plurality of adders 208 and 216. The correlation amplitude is given, for example, in accordance with the following equation:

l adjacent correlation coefficients R'_kAdded by adder 208-216 to generate, for example, y n]. For example, as shown in FIG. 2, adder 216 generates y [0 ]]Adder 214 generates y [ 1]]。

In various embodiments of the present invention, N/L correlation results y [ k ] for a correlation build determine N/L-1 phase increments through the full correlation length (M). However, depending on the required frequency offset range, the N/L number of correlated sub-segments means that the sampling frequency is strongly correlated with the desired offset range. This results in a small angular increment estimate (which in turn affects the dynamics of the frequency controlled phase locked loop).

As shown in FIG. 2, the angular difference between two consecutive correlation results (e.g., between y [ n ] and y [ n +1 ]) is estimated by the following equation, as shown by the preferred phase identification modules 218, 220, 222, 224:

Δθ_n＝arctan(Im(y[n+1]y^*[n])/Re(y[n+1]y^*[n]))，n＝0，1，…，N/L-1.

in some cases, the phase difference between y [ n ] and y [ n +1] may be approximated by a linear approximation arctangent function (arctan).

Increment of mean angleThe estimation can be done from the N/L estimates by:

where the N/L phase increments may be averaged by averaging module 226 to produce an averaged angle increment.

In accordance with various embodiments of the present invention, it is desirable that the sum of the amplitudes of the short coherent correlation segments establish the correct time, and that longer coherent correlation segments be desirable because the angle increment estimates are from longer coherent correlation segments. This allows for efficient frequency control dynamics, resulting in a large frequency control range. To overcome these potentially conflicting criteria, both need to be implemented together. The received signal includes a pseudo-random sequence.

Fig. 3 is a preferred EUTRA frequency acquisition characteristic bode plot under different SNR conditions showing an SNR10dB bode plot 302, an SNR 0dB bode plot 304, and an SNR-10dB bode plot 306, in accordance with an embodiment of the present invention. The abscissa represents the number of slots and the ordinate represents the frequency offset.

According to a preferred embodiment of the present invention, Primary Synchronization Signals (PSS) are defined in the E-UTRA (LTE) standard. The complex signal sequence may be embodied as a Zadoff-Chu sequence, e.g. of length 63, the (punting) middle most point of the puncturing sequence. These sequences are again mapped to, for example, 32 subcarriers on either side of DC. At the base rate (fundamental) of the signal, this is consistent with a time domain sequence of length 63. However, in order to be able to obtain the desired sampling characteristics (e.g. frequency offset estimation and/or frequency offset range extension) for acquisition of the primary synchronization or to perform channel estimation for detection of the Secondary Synchronization Signal (SSS), the time domain representation (representation) of the signal is oversampled. A preferred oversampling factor of 2 makes it possible to generate 128 sampled copies of the primary synchronization signal, i.e. the reference signal for which the primary synchronization is performed comprises 128 complex components. For example, in the parameters (numerology) specified for E-UTRA, this means that the base (fundamental) sampling rate is 1.92 MHz.

In accordance with one embodiment of the present invention, for a carrier frequency of, for example, 2GHz, the PSS can still be successfully acquired when the frequency offset reaches + -15 ppm or more, and the preferred parameters of the above-mentioned synchronization strategy are shown in the following table.

M	128
		N	16
P	8
		L	4

The achievable frequency offset acquisition range can be varied by appropriate selection of the above parameters, but with separate tradeoffs for cost/benefit, reduced/enhanced primary synchronization, high/low SNR (signal-to-noise ratio),

the SNR10dB bode plot 302 illustrates a fast convergence (convergence) to 0 frequency offset, in accordance with various embodiments of the present invention. The SNR 0dB baud plot 304 shows a slower convergence situation requiring more gaps to achieve the 0 frequency offset. Accordingly, the SNR-10dB bode plot 306 shows the slowest convergence among the bode plot 302, the SNR bode plot 304, and the SNR bode plot 306. Thus, the higher the SNR, the faster the frequency offset acquisition.

Fig. 4 is a flow diagram of a preferred frequency offset estimation protocol in accordance with an embodiment of the present invention. After initializing step 402, step 404 generates a correlation coefficient R'_k(generated from the received signal, as shown in fig. 2). In step 406, the coefficient of correlation R'_kSplit into N/L groups of p elements each. For each group, processing the correlation coefficient R'_kTo generate output signals such as adder 208 and 216Number set { y [ n ]]}. In step 408, the output signal of the adder is processed to generate N/L-1 phase change parameters (term) { Δ θ {_nAs shown in fig. 2. In step 410, the phase variation parameter is averaged to generate an angle delta estimate

In some cases, the subsequence that results in output { y [ n ] } is of arbitrary length, which is determined independently for each output, in accordance with various embodiments of the present invention. In some cases, calculating the phase change quantity includes a non-linear function. In those cases, a linear approximation, e.g. a first order approximation, of the phase change is required. This need is even more pronounced for small phase change parameters.

In accordance with various embodiments of the present invention, a method and system for extending the range of frequency offset estimation based on correlation of complex sequences includes concatenating each received sample sequence r [ n ]]And local sample sequence replica s^*[n]Split into three or more contiguous sub-sequences of samples of similar length as shown in fig. 2. For each of the three or more consecutive sub-sequences of samples of similar length, determining a correlation coefficient y [ n ] between the corresponding sub-sequence of samples of the split received sequence of samples and the local copy of the sequence of samples]. Determining a plurality of phase differences, e.g. delta theta, based on adjacent ones of said determined correlation coefficients_iAveraging the determined plurality of phase differences to generate a frequency offset estimateAs shown in fig. 2.

The communication system conforms to wireless standards including UMTS EUTRA (LTE), WiMAX (IEEE802.16), and/or WLAN (IEEE 802.11). The subsequences are, for example, of equal length. The phase difference is calculated by calculating the phase difference of two numbers (two times), either of which is from a continuous set (contiguous set) of the determined correlation coefficients, and which are mutually exclusive. For example, two numbers areAndand generates a phase difference Δ θ₀As shown in fig. 2. The two joint continuous sets comprise a continuous set of the determined correlation coefficients, e.g. { R'₀，…，R’_2L-1}。

For averaging, such as averaging module 226, a sample average is derived from the determined phase difference Δ θ i.

A steerable frequency offset estimation range is increased by adding a plurality of consecutive sample sequences, as shown in fig. 2. The received sampling sequence and the local sample sequence copy are taken from a pseudo-random sequence. In some embodiments, the pseudo-random sequence comprises complex sequence elements. The phase difference is determined by a linear approximation technique, as shown in fig. 2 and 4.

Another embodiment of the present invention provides a machine and/or computer readable storage and/or medium, having stored thereon a machine code and/or a computer program comprising at least one code segment executable by a machine and/or a computer, to cause the machine and/or computer to perform the steps of the method and system for extending a frequency offset estimation range based on correlation of complex sequences described herein.

In general, the invention can be implemented in hardware, software, firmware, or a combination thereof. The present invention can be realized in an integrated manner in at least one computer system or in a separate manner by placing different components in a plurality of interconnected computer systems. Any kind of computer system or other apparatus adapted for carrying out the methods described herein is suited. A typical combination of hardware, software, and firmware may be a specialized computer system with a computer program that, when being loaded and executed, controls the computer system such that it carries out the methods described herein.

The present invention can also be embedded in a computer program product, which comprises all the features enabling the implementation of the methods described herein. Once loaded in a computer system, the article of manufacture is capable of performing these methods. The computer program in the present invention may be in any form, language, code or notation, having a set of instructions intended to cause a system having an information processing capability to perform a particular function either directly or after either or both of the following: a) conversion to another language, code or notation; b) reproduced in different material ways. However, other forms of computer programs, as would be understood by one of ordinary skill in the art, are also contemplated by the present invention.

While the invention has been described with reference to certain embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof without departing from the spirit and scope of the invention. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the invention without departing from the essential scope thereof. Therefore, it is intended that the invention not be limited to the particular embodiment disclosed, but that the invention will include all embodiments falling within the scope of the appended claims.

Claims (8)

1. A method of processing a communication signal, comprising:

splitting each received sample sequence and local sample sequence replica into three or more contiguous sample subsequences of similar length;

for each of the three or more similar-length consecutive sub-sequences of samples, determining a correlation coefficient between a respective sub-sequence of samples of the split received sequence of samples and a respective sub-sequence of samples of the local copy of the sequence of samples;

calculating a plurality of phase differences by calculating the phase difference of two numbers, any one of the two numbers being from a continuous set of the determined correlation coefficients, the two continuous sets being mutually exclusive; and

averaging the determined plurality of phase differences to generate a frequency offset estimate.

2. The method of processing a communication signal of claim 1, wherein the method of processing a communication signal complies with a wireless standard.

3. The method of processing a communication signal of claim 2, wherein the wireless standard comprises UMTS EUTRA LTE, WiMAX IEEE802.16, and/or wlan IEEE 802.11.

4. The method of processing a communication signal of claim 1, wherein the subsequences are of equal length.

5. A system for processing a communication signal, comprising:

a first module: for splitting each received sample sequence and local sample sequence replica into three or more contiguous sample subsequences of similar length;

a second module: for each of the three or more similar-length consecutive sub-sequences of samples, determining a correlation coefficient between a corresponding sub-sequence of samples of the split received sequence of samples and a corresponding sub-sequence of samples of the local copy of the sequence of samples;

a third module: for calculating said plurality of phase differences by calculating the phase difference of two numbers, either of which is from a consecutive set of said determined correlation coefficients, and which are mutually exclusive; and

a fourth module: for averaging the determined plurality of phase differences to generate a frequency offset estimate.

6. The system for processing communication signals according to claim 5, wherein said system for processing communication signals complies with a wireless standard.

7. The system for processing communication signals according to claim 6, wherein the wireless standard comprises UMTS EUTRA LTE, WiMAX IEEE802.16, and/or WLAN IEEE 802.11.

8. The system for processing a communication signal of claim 5, wherein the subsequences are of equal length.