Method and apparatus for range and coverage extension in a heterogeneous digital chaos cooperative network
10069522 ยท 2018-09-04
Inventors
Cpc classification
H04B1/7136
ELECTRICITY
H04W52/244
ELECTRICITY
H04W16/26
ELECTRICITY
Y02D30/70
GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
H04W12/068
ELECTRICITY
H04W4/70
ELECTRICITY
H04B1/0475
ELECTRICITY
International classification
H04L25/03
ELECTRICITY
H04B1/7136
ELECTRICITY
H04W16/26
ELECTRICITY
H04W12/04
ELECTRICITY
H04W40/24
ELECTRICITY
H04W4/70
ELECTRICITY
Abstract
The present invention teaches a system and method for improved signal recovery for range and coverage extension in a heterogeneous cooperative network of digital chaos transmissions with OFDM component signal transmission. The invention improves upon the state of art in side channel information from the transmit side containing information on the clipped amplitude. In-band transmission of the side information is achieved by exploiting the sparsity of the resulting clip amplitude position with improved levels of compression over the prior art using Gabor Transform Multiple Symbol Encoding transmitter. The information rate of the clipped amplitude is sub-Nyquist relative to the original OFDM component signal transmission, which allows very low power spreading by a cooperative digital chaos sequences at a transmit side and recovery of the clipped amplitude at a receive side. Further, an improved noise resistance side channel performance is achieved by decoding Gabor Transform symbols for symbol recovery.
Claims
1. A method of compensating for in-band distortion using signal recovery of clipping amplitudes of a primary user in a cooperative heterogeneous network of secondary users, wherein the secondary users comprise digital chaos signals, wherein said primary and secondary users are wirelessly transmitted, the method comprising: measuring the instantaneous amplitude envelope of a primary user, the instantaneous amplitude envelope including multiple measured instantaneous amplitudes, wherein the primary user contains at least one group of Orthogonal Frequency Division Modulation (OFDM) signal components, wherein said instantaneous amplitude envelope is measured at a rate of at least four times the base rate of the OFDM signal components; clipping at least one of the multiple measured instantaneous amplitudes when the at least one of the multiple measured instantaneous amplitudes exceeds a predetermined threshold, said clipping to reduce said instantaneous amplitude envelope to a value no more than the predetermined threshold, wherein the predetermined threshold is derived from the maximum allowable power according to a peak-to-average ratio (PAPR) constraint specified at a transmit side; collecting multiple clipped instantaneous amplitudes values into a sparse vector, wherein the sparse vector has a nonzero value and a corresponding nonzero value position location, wherein said nonzero value and said nonzero value position location are aligned with instants of clipping for a frame data as defined by the international protocol standard for the primary user; processing the sparse vector into a smaller vector, the smaller vector containing a vector of non zero values, the processing of the sparse vector comprising Gabor Transform clipped amplitudes and position location to produce Gabor transformed compressed samples; transmitting the nonzero values as the payload of an extremely low powered digital chaos secondary user, wherein the payload of the digital chaos secondary user is transmitted in-band with a primary user payload, wherein the amplitude of the digital chaos secondary user is less than the amplitude primary user according to the error vector magnitude (EVM) requirements of the regulatory requirements; receiving said digital chaos secondary user payload and said primary user payload at a receive side; processing said digital chaos secondary user payload in the presence said primary user payload to produce the nonzero value and the nonzero value position; using said nonzero value and the nonzero value position to produce an estimate of the sparse vector; and using the estimated sparse vector to compensate for distortion created by clipping the at least one of the multiple measured instantaneous amplitude.
2. A method of claim 1, wherein the step of clipping at least one of the multiple measured instantaneous amplitudes comprises polar clipping, and wherein the amplitude of instantaneous amplitude envelope is reduced to the predetermined threshold, but the phase of the instantaneous amplitude envelope is preserved.
3. A method of claim 1, wherein the step of clipping at least one of the multiple measured instantaneous amplitudes comprises rectangular clipping, wherein the amplitude of the sample is reduced to the threshold, but the phase of the sample is not preserved.
4. A method of claim 1, further including modulating said sparse vector with a digital chaos sequence as part of a secondary user transmission.
5. A method of claim 1, wherein the digital chaos secondary user includes a power level, wherein the digital chaos secondary user power level is determined from an error vector magnitude (EVM) caused by the sparse vector compared to that which is allowable by the regulatory standard protocol to which the primary user signal is a compliant.
6. A method of claim 1, further comprising decoding and demodulating of Gabor Transformed compressed samples to improve detection of the clipped amplitude.
7. A method of claim 6, wherein decoding Gabor Transformed compressed samples comprises using a dynamic programming algorithm (DPA).
8. A method of claim 1 further including mapping said sparse vector nonzero value and said sparse vector position location using a hash function having a load factor, said hash function for producing multiple hash values, wherein the number of hash values equals the number of samples contained in the baseband frame of the primary user and the load factor for the hash is an order magnitude greater than the Complementary Cumulative Distribution Function (CCDF) threshold requirement of the PAPR constraint for the primary user signal, wherein said baseband frame of the primary user includes said instantaneous amplitude envelope measured at a rate of at least four times the base rate of the OFDM signal components.
9. A method of claim 8, wherein said digital chaos sequence comprises a maximum spreading factor and a frame length, wherein the maximum spreading factor is determined by floor operation of the ratio of the frame length to the number of hash values.
10. A method of claim 5, further including the step of mapping the clipping amplitudes to a scaled version of digital chaos sequences stored on the device.
11. A method of claim 8, further including a step of updating the digital chaos sequence for use in signal amplitude recovery, and further using beacon frames with an update clip and a reset clip field element in a beacon frame signal field.
Description
BRIEF DESCRIPTION OF DRAWINGS
(1) A more complete understanding of the present invention may be derived by referring to the various embodiments of the invention described in the detailed descriptions and drawings and figures in which like numerals denote like elements, and in which:
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DETAILED DESCRIPTION
(30) The description of exemplary embodiments and best mode of the invention herein makes reference to the accompanying drawings and flowcharts. While these exemplary embodiments are described in sufficient detail to enable those skilled in the art to practice the invention, it should be understood that other embodiments may be realized and that logical and mechanical changes may be made without departing from the spirit and scope of the invention. Thus, the description herein is presented for purposes of illustration only and not of limitation. For example, the steps recited in any of the method or process descriptions may be executed in any order and are not limited to the order presented.
(31) The present invention may be described herein in terms of functional block components and various processing steps. It should be appreciated that such functional blocks may be realized by any number of hardware and/or software components configured to perform the specified functions. For example, the present invention may employ various integrated circuit (IC) components (e.g., memory elements, processing elements, logic elements, look-up tables, and the like), which may carry out a variety of functions under the control of one or more microprocessors or other control devices. Similarly, the software elements of the present invention may be implemented with any programming or scripting language such as C, C++, java, COBOL, assembler, PERL, or the like, with the various algorithms being implemented with any combination of data structures, objects, processes, routines or other programming elements. Further, it should be noted that the present invention may employ any number of conventional techniques for data transmission, signaling, data processing, network control, and the like. Still further, the invention could be used to detect or prevent security issues with a scripting language, such as JavaScript, VBScript or the like. For a basic introduction of cryptography, please review a text written by Bruce Schneider which is entitled Applied Cryptography: Protocols Algorithms, And Source Code In C, published by john Wiley & Sons (second edition, 1996), which is hereby incorporated by reference.
(32) It should be appreciated that the particular implementations shown and described herein are illustrative of the invention and its best mode and are not intended to otherwise limit the scope of the present invention in any way. Indeed, for the sake of brevity; conventional wireless data transmission, transmitter, receivers, modulators, base station, data transmission concepts and other functional aspects of the systems (and components of the individual operating components of the systems) may not be described in detail herein. Furthermore, the connecting lines shown in the various figures contained herein are intended to represent exemplary functional relationships and/or physical couplings between the various elements. It also should be noted that many alternative or additional functional relationships or physical connections may be present in a practical electronic transaction or file transmission system.
(33) As will be appreciated by one of ordinary skill in the art, the present invention may be embodied as a method, a data processing system, a device for data processing, and/or a computer program product. Accordingly, the present invention may take the form of an entirely software embodiment, an entirely hardware embodiment, or an embodiment combining aspects of both software and hardware. Furthermore, the present invention may take the form of a computer program product on a computer-readable storage medium having computer-readable program code means embodied in the storage medium. Any suitable computer-readable storage medium may be utilized, including hard disks, CD-ROM, optical storage devices, magnetic storage devices, and/or the like.
(34) To simplify the description of the exemplary embodiment, the invention is described as being able to be used with single-input-single-output (SISO) and multiple receive antenna systems, such as, single-input-multiple-output (SIMO), multiple-input-single-output (MISO), and multiple-input-multiple-output (MIMO) wireless transmission systems. For example, the invention may be used with a SISO DSSS systems and MIMO DSSS systems as well.
(35) It will also be appreciated that many new applications of the present invention could be formulated. For example, the present invention could be used to facilitate any conventional wireless communication medium. Further, it should be appreciated that the network described herein may include any system for exchanging data or transacting business, such as the Internet, an intranet, an extranet, WAN, WLAN, WPAN, HAN, Ad hoc Networks, mobile ad hoc networks (MANET), satellite communications (SATCOM), and/or the like.
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(37) The multiple chaos modulated data source signals may then be spatially mapped (e.g., spread over multiple spatial channels) by spatial mapper 110. The spatially mapped multiple chaos modulated data source signals may then be provided to multiple radio frequency oscillators systems 112a-n prior to transmitting the spatially mapped multiple chaos modulated data source signals over the multiple spatial communication channels 116 via multiple antennas 114a-n.
(38) The spatially mapped multiple chaos modulated data source signals may be received by receiver 104 at multiple antennas 118a-n. The spatially mapped multiple chaos modulated data source signals may be recovered from the channel 116 using multiple radio frequency receiving systems 120a-n. RF receiver system 120a-n may recover the summed chaos modulated data source signal from the signal transmitted over channel 116. For example, RF receiver system 120a-n may recover the summed chaos modulated data source signal from the signal transmitted over channel 116 using any conventional methods for recovering a data signal from a wireless channel as are found in the art. For example, RF receiver system 120a-n may recover the transmitted signal by down converting the transmitted signal to baseband analog format and converting the baseband analog signal to baseband discrete signal.
(39) Receiver 104 may further include a MIMO equalizer 122 for separating the spatially mapped multiple chaos modulated data source signals produced by the channel. MIMO equalizer 122 may separate the channel signals according to estimates of each channel amplitudes and phases characteristics associated with each path traverse by the spatially mapped modulated data source signal to produce received baseband modulated signals. The received baseband modulated signals may then be chaos demodulated by multiple chaos demodulators 124a-n according to data source signal channel. The multiple chaos demodulated data source signals may then be decoded by multiple decoders 126a-n. The multiple decoded chaos demodulated data source signals may then be merged by a signal merger 128 for combining the multiple data source signals into a single merged signal. In one embodiment, the merged signal may be a copy of the data source 101. Receiver 104 may provide the merged signal to a data sink 130.
(40) Splitter 104, encoders 106a-n, spatial mapper 110, MIMO equalizer 122, decoders 126a-n, signal merger 128, and RF oscillator systems 112a-n, RF receiving system 120a-n may be of conventional construction and operation as is found in the art. The operation and construction of chaos modulators 108 an and demodulators 124a-n are discussed more fully below.
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(42) The multiple chaos modulated data source signals may then be summed at a signal summer 210 prior to being provided to a RF oscillator system 212. Transmitter 202 may then transmit the summed chaos modulated data source signal via an antenna 214. Transmitter 202 may transmit the summed chaos modulated data source signal via a communication channel 216. The chaos modulated data source signal may be received by receiver 104 at antennas 118a-n. The summed chaos modulated data source signal may be received by multiple RF receiver system 120a-n. RF receiver system 120a-n may recover the summed chaos modulated data source signal from the signal transmitted over channel 216, in similar manner as discussed with respect to
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(44) In alternate embodiments, receiver 304 may comprise multiple independent receivers where each receiver may include a chaos demodulator 124. Similarly, transmitter 202 may comprise multiple independent transmitters, where each transmitter includes a chaos modulator 208a-n.
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(46) According to
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(49) Transmitter 102 receives data source signal 101 and channel encodes the sequence at channel encoder 106. Data source signal 101 may be bits, symbols, or sampled analog waveforms. A chaos spreading code sequence, the construction of which is described below with respect to
(50) In accordance with the present invention, chaos modulator 108 uses the chaos spreading sequence in modulation to generate a data payload having pre-ambles and mid-ambles. The pre-ambles and mid-ambles may be constructed so that multiple embedded signals can be detected at one or more locations without interference from the native performance of each constituent signal. In one particular embodiment, the data payload may be comprised of at least one chaos modulated signal and at least one other signal (either chaos modulated or not) signal that is part of a cooperative network protocol. The pre-amble and mid-amble may also be constructed by repeating the digital chaos sequence of sign flipping a copy of the digital chaos sequence in the next extended symbol period.
(51) In one exemplary embodiment, the data payload includes pre-ambles and mid-ambles that may be constructed so that the data payload may be augmented for the inclusion of a signal field and a symbol delimiter within each of aggregated digital signals. The augmented data payload may include digital information within multiple digital chaos waveforms so that the time of arrival of each constituent signal, part of the aggregated digital signals can be identified accurately and reliably. A signal field portion instructing the receiver of at least one length information of the digital signal and data rate scheme information for the remaining payload. Further, the signal field may contain parity information for protection against and detection errors of other information within the signal field.
(52) During operation of chaos modulator 108, the data source signal is spread with the chaos spreading sequence stored in chaos sequence memory 606 using, for example, spreader 602. The chaos spreading sequence may be used in the generation of the pre-amble 608 and the mid-amble 610. The payload generated by chaos modulator 108 may be augmented to include the symbol delimiter 612 and signal field 614 as is described with respect to
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(54) During operation, transmitter 102 receives a data source signal at encoder 106 which channel encodes the data source signal. The data source signals may be any information bearing signals such as bits, symbols, or sampled analog waveforms.
(55) A chaos spreading sequence, the construction of which is described below with respect to
(56) The digital chaos sequences stored in chaos sequence memory 606 are constructed using, for example, the digital chaos sequence generation method 800 of
(57) An irregular sampling interval according to the invention may be, for example, determined by modulo counting of a known sequence generator such as Fibonacci numbers, Lucas numbers, Perrin numbers or any pseudo random number generators. For implementation ease with semiconductor technologies for digital system, the amplitudes may be quantized to finite levels based on the maximum allow cross-correlation (.sup.L), where is L is the number of bits used to represent by each sample amplitude) between code sequences. Independent segments of the digital chaos sequences are grouped together to form a vector span for transmitting the information-bearing communication signals or training signals. It is well-known in mathematics that any signal in an n-dimensional subspace can uniquely represented an n-tuple of scalar corresponds to the projection of the signal onto the orthonormal bases of the n-dimensional. The final step of the digital chaos process is to convert the independent digital chaos segments into a group of orthonormal sequences spanning the same subspace as the original segment. This process may be performed using the Gram-Schmidt orthogonalization process.
(58) The chaos sequence memory 606 (and the chaos replica memory 706 of
(59) Once the chaos sequence memory 606 is fully populated with digital chaos spreading sequences, the entire memory 606 may be subjected to Gram-Schmidt processing. The entire memory 606 may be subjected to an orthonormalization process. In alternate embodiments, independent digital chaos segments may be converted into a group of orthonormal sequences spanning the same subspace as the original segment.
(60) A preferred embodiment of the invention for the packet formation is shown in
(61) A super-frame consists of several frames transmitted in succession with 2 ms gap spacing between frames. Each frame to be transmitted consists of a preamble training sequence, mid-amble training sequence, and data payload. The flexibility of frame structure can accommodate many other embodiments to specific applications. In this embodiment, sufficient training information is included to securely and reliably.
(62) As is well known, the key to a successful wireless design is to incorporate sufficient training information to recognize the arrival of packets, align symbol boundaries, estimate channel characteristic and correct for frequency offset. In one embodiment of the invention utilizes a header field. The header field comprises a ten symbol preamble and 48 symbol signal field that defines the configuration state for the receiver. The training sequences are modulated using differential chaos shift keying (DCSK) and repeated predetermine number of times; nine times is used in
(63) As previously noted, the present invention addressed problems in traditional MIMO WLAN transmission. Namely, prior art systems such 802.11x compliant system are more susceptible to interference, wireless collisions, and interception by unintended parties. The present invention addresses these problems by providing a system and method for aggregating and embedding multiple information-bearing communication signals within digital chaos communication waveforms occupying the same frequency channel bandwidth transmitted with a multiple antenna system. Digital chaos may be a waveform generated by sampling a chaos signal, where chaos signals are determined by deterministic nonlinear dynamics. Digital chaos sequences generated according to the invention as described below, are used as a spreading sequence in accordance with various embodiments of the invention.
(64) The signal transmitted by transmitter is received by a receiver 104 of
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(66) Receiver 104 receives the transmitted signal to recover the embedded data from the signal. It should be noted that there may be two common receiver modes in preferred embodiments. In the first mode, the high-speed multiplication with chaos replica memory 706 occurs directly after operation of A/D 704. This embodiment is preferred when a sampled analog waveform is the information-bearing signal. In the second mode, the high-speed multiplication with chaos replica memory 706 occurs prior symbol detect 716 and after Doppler Correction 714 and channel estimation 712 operations. This embodiment is best suited when the information-bearing signal, bits or symbols. Either configuration works for the information-bearing signals in the form of bits or symbol. However, the second mode has the best performance and the first mode has the lower power consumptions. After despreading the high-speed digital chaos sequence, the receiver operations are typical of those performed by commercially standard receivers for 802.11x, WCDMA, or CDMA 2000, the description of which is omitted for the sake of brevity.
(67) The chaos modulator 108 and demodulator 124 may be implemented as part of a wireless local area network (LAN), wireless personal area network (PAN), wireless home area network (HAN) or metropolitan area network (MAN) system, a cellular telephone system, or another type of radio or microwave frequency system incorporating one-way or two-way communications over a range of distances. The invention may employ various signal modulation and demodulation techniques, such as single-carrier frequency domain equalization (SCFDE), direct sequence spread spectrum (DSSS) or orthogonal frequency division multiplexing (OFDM), for example. However, throughout this description, references are made with respect to a SIMO and MIMO communication systems or a system including a transmitter and receiver merely to facilitate the description of the invention. All the similar components of the wireless channels 711 will also have similar descriptions to each other.
(68) The transmitters of the present invention may transmit different signals from each antenna in transmit antenna array so that each signal is received by the corresponding antenna in a receiving antenna array at the receive side. Various transmitters described herein may transmitted the data source signal as an aggregate signal and received as an aggregation of all the transmit signals, or an aggregation of parts of the signal. All signals are transmitted once and the receiver demodulates the aggregate signal using a replica of the chaos spreading sequence spreading code stored in chaos replica memory at the receiver.
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(71) The digital chaos systems and methods of the present invention are suitable for operation in wireless transmissions desiring coordinated transmissions to enhance network capacity. Such systems often require multiple transactions between tightly coordinated nodes or access points. By coordinated, what is meant is that the transmission protocol of each node (receiver) in a network is organized into a relationship with a second receiving node in the network to ensure that subsequent transmissions are efficient according to the requirements of the network. By efficient, what is meant is that the node to node transfer is optimized according to the requirements of the node or the requirements of the transmission medium. In one instance, improving efficiency may include improving the throughput of the network. Coordinated nodes may be such that one node, or a group of nodes may include a transmission protocol that depends on the transmission received from one node in the network or the group of nodes. In the instance where multiple nodes depend on a transmission received, and the transmission protocol of a multiple of nodes may cooperatively communicate to ensure optimization of the network or transmission medium.
(72) One transmission protocol that can require coordination is adaptive changing of channel by a group of nodes. By channel, what is meant is an available time slots, hopping frequency, independent spatial path, or distinct digital chaos sequence at a transmitting side. By time slot, what is meant is the next transmission opportunity (Txop) after a channel reservation request expires, the channel is idle for a specified period of the time including time requirement for a delay and disruption tolerant protocol known at the receiving and transmitting side, or the channel is busy and the number of digital chaos signals are less than the multi-user limit for simultaneous transmission. By hopping frequency, what is meant is any of the tunable center frequencies of capable by the equipment that is permitted in a hopping sequence; whereby the minimum spacing between center frequencies is equal to the chipping rate of a generated digital chaos sequences at the transmitting side. By independent spatial path, what is meant is that separate paths arriving at the receive side wherein the cross-correlation between paths are sufficiently small such that low to ensure the transmission of the information at the rate and with the quality required under specified conditions. And distinct digital chaos sequence at a transmitting side may originate from the same source or separate sources. In the case wherein they originate from the same antenna, the distinct digital chaos sequences are orthogonal by construction and hence meet the requirement to be considered separate channels. In the case wherein distinct digital chaos sequence at a transmitting side originate from difference antennas, results in sufficient differential signal attenuation for different arriving paths at the receive side coupled with the cross-correlation between distinct digital chaos sequences to ensure each transmission of the information at the rate and with the quality required under specified conditions. Determination that the channel of the wireless medium is busy or currently in use is achieved by sensing the physical channel using one of several method techniques taught in the prior art (referred to as detectors) and comparing against a predetermined threshold. Some of these detectors can be applied directly to our circumstances; others have to be adapted to exploit the unique properties of the digital chaos. If the channel metric measured exceeds the predetermined threshold, clear channel assessment (CCA) is set false. For instance, the prior art teaches energy detection as a means of determining assessing CCA for many wireless protocol as a failsafe. An energy detector does not exploit a signal structure or property of the incoming signal at the receive side thus can be applied to any signature; however, some signals such as the digital chaos signals are constructed to reduce the probability of detection by these energy detectors. Other physical channel sensing methods exploits the construction of the signal such as cyclical detectors. Most communication systems exhibit some known periodicity to its structure such as periods of the symbol clock, sample rate clock for intermediate frequency (IF) carrier or RF carrier or even repetition of sequences for training purposes. These known periodicities can be incorporated in a cyclical detector by correlating different segments separated by the known periods and computing the energy over the window of data for which cyclostationary property is valid. For instance, differential chaos shift keying (DCSK) shown in
(73) In the instance of multiple transmissions, as noted above, multiple transmissions may create increased opportunities for compromised data transmission or collisions of data transmission. In one embodiment of the invention, the coordinated nodes may include knowledge of the transmission protocol one or more of the other nodes in the network. Alternative, the coordination of the transmissions from one node, or a group of nodes, may depend on the transmission received from a node outside the network or group. In another embodiment, coordinated nodes or coordinated transmission over a wireless medium may mean that transmission from one node coordinated with another node may occur at the next transmission opportunity (Txop) or within the time specified by a delay and disruption tolerant protocol known at the receiving side.
(74) The digital chaos waveform described herein may be used to secure the data transmissions while improving network throughput. For example, coordinated multi-point transmission and reception over heterogeneous wireless networks comprise a set of disparate transmission points, access points or nodes operating in the same cell (e.g., group), overlaps cells, or mutually exclusive cells, simultaneously or in a coordinated fashion. Coordinated multi-point transmission may be used to utilize to increase throughput and service quality in wireless networks, particularly at or near the edge of a given cell in a cellular network or group of nodes, access points or users.
(75) A typical cooperative network that may be used with this invention is the Internet of Things (IoT). The IoT refers to interconnection and autonomous exchange of data among devices which are machines or parts of machines. IoT may typically be used to support, for example, Machine-to-Machine (M2M) communication. M2M is defined as data communication among devices without the need for human interaction. This may be data communication between devices and a server, or device-to-device either directly or over a network. Examples of M2M services include security, tracking, payment, smart grid and remote maintenance/monitoring. Consequently, a coordinated network according to the invention may include the autonomous exchange of data among devices nodes or members of the coordinated network.
(76) As used herein, nodes belonging to a single cell may be described as members of a single group. In some instances, to facilitate the coordination of wireless transmission, members may be described as members belonging to one group, or to more than one group. Signals received by a specific member may be further processed according to the signal preamble or mid-amble information. Membership to a group requires first a request to join a group by node. The process of joining is characterized by three distinct states: {unauthenticated, unassociated}, {authenticated, unassociated}, and {authenticated, associated}. In one embodiment of this invention, authentication is performed by unique preloaded authentication digital chaos sequences associated with unique identifiers for communicating device. The coordinator for the group has access to a repository of all complementary authentication digital chaos sequences for other authorized devices. These complementary authentication digital chaos sequences are used in the handshaking exchange for response queries between the requesting node and the coordinating node. Analogous to the cryptography exchange procedure wherein a node A desiring to communicate to a node B, send it message encrypted with node B public key. Node B uses it private key and the incoming message to decrypt the package. In this case, Node B demodulates the digital chaos sequences using its complementary authentication digital chaos sequences along with its private unique authentication digital chaos sequences. Node B uses its private unique authentication digital chaos sequences or derivative of to encapsulate any response frame including an acknowledgement frame. In yet another embodiment, after a node has been authenticated it transitions to state two within the coordinating node and an association to a specific group is started. Association to group includes but not limited to exchanges of capability information to the coordinator and verification of the coordinator of a set of rates, digital chaos sequences for data frames, beacon frames, request-to-send (RTS) frames, clear-to-send (CTS) frames and group acknowledgement frames. Completion of this step transitions the state of the node to membership granted status as the coordinator node. The coordinator node provides in one of its data payload of beacon frame information containing a temporary local ID for subsequent communications as well as informs other members of the group of the new member credentials for communicating. Membership to a group is not permanent and maybe voluntarily terminated by the any member group. In additional, the network manager or coordinator may terminate the membership for any member deem detrimental to operation of the network. For example, a rogue node may temporarily gain access to the network but based on its traffic pattern but later kick out of group membership whereby not member will engage in future transmission with that node.
(77) In one embodiment of this invention, authentication digital chaos sequences can share the same level of difficulty to securely update, particularly without exposure to unauthorized listeners or distribute to a large number of users based on a similar process central authority called the certificate authority (CA) in key management for public-key cryptography. Strong cryptography designs strictly adhere to Kerckoffs's Principle in design good encryption scheme; that is, the security of the encryption scheme must depend only on the secrecy of the key and not on the secrecy of the algorithm. The rationale behind the rule is that algorithms are hard to change since they are normally built into software or hardware, which can be difficult to update. In the present invention, the network coordinator that provides some CA functionality for private unique authentication digital chaos sequences.
(78) As used herein, the coordinated multi-point system may be a MIMO system, wherein the members may use multiple antennas at both the transmitter and receiver. The present invention may be also useful multi-user multiple-input-multiple-output or MU-MIMO systems. As used herein MU-MIMO systems are wireless communication systems in which available antennas are spread over a multitude of independent group members, access points and independent radio terminals, wherein each member has one or multiple antennas. The present invention may also be used with conventional SISO (single input-single output), SIMO (single input-multiple output), MISO (multiple input-single output) systems, or other similar systems as is known in the art.
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(81) Group arrangement 1300 further depicts the wireless transmissions that occur when one digital chaos signal is transmitted between members. For example, member A6 may transmit digital chaos signals to member A2, A5 or An; member C1 may transmit digital chaos signals to C8; B3 may transmit digital chaos signals to B1, B4, or B9 depending on how the digital chaos signal is addressed in the digital chaos preamble. In the instance where the digital chaos is received by a multi-group member, the receiving member may transmit the digital chaos signal to the corresponding group member to which the receiving member belongs. This may be true even when the intended group member belongs to a separate overlaps member. By overlaps, what is meant is that more than one group shares at least one group member. In the group arrangement 1300 shown, group A overlaps with group C, and group A overlaps with group B.
(82) It should be noted that the digital chaos signals discussed with respect to the embodiments in
(83) In a typical coordinated transmission according to the present invention, group members operate in a coordinated fashion to improve the overall network capacity for all members sharing the wireless medium. By coordinated fashion what may be meant is that signals are processed together to combat the distortive effects of the wireless medium and mutual-interference to improve the detection for all active distinct user data signals. The group members process the extracted distinct user data signals according to membership or non-membership to a specific group. The group member may process the extracted distinct user data signals according to membership or non-membership to a particular group wherein said extracted distinct user data signals not addressed to the receiving side (e.g., receiving member) are aggregated, time aligned, and retransmitted over the wireless medium at the next transmission opportunity (Txop) or time specified by a delay and disruption tolerant protocol known at the receiving side. For example, the delay and disruption tolerant protocol may be such that the network operates effectively over extreme distances such as those encountered in space communications or on an interplanetary scale. On the other hand, where a digital chaos signal is received by a receiving group member to which it is not addressed, the receiving group member may terminate the signal and not forwarded it at all.
(84) In a typical example, using
(85) In some instances, where group members of different groups are in proximity to each other, a receiving group member may receive a first fragment of the received signal, and time delay transmission of the received signal until a second fragment of the received signal is received by the receiving group member.
(86) It should be appreciated by one skilled in art, that the present invention may be utilized in any device that implements the DSSS encoding scheme. The foregoing description has been directed to specific embodiments of this invention. It will be apparent; however, that other variations and modifications may be made to the described embodiments, with the attainment of some or all their advantages. Therefore, it is the object of the appended claims to cover all such variations and modifications as come within the true spirit and scope of the invention.
(87) In another example, the keys for dual level network access is shown using
(88) A preferred embodiment of an exemplary diagram of a heterogeneous transceiver 1500 according to the present invention is shown in
(89) Since both the signal produced by (DUC, DAC) 1506a and the signal produced by (DUC, DAC) 1506b are modulated on the same RF carrier, the two signals appear spectrally in-band relative to each other. The resulting RF modulated signal may be transmitted out at least one antenna 1508.
(90) Ata receiving side, at least one antenna 1510 may receive the RF modulated signal transmitted by antenna 1508. The RF modulated signal received at antenna 1510 may be provided to a downconverter system 1512 including an analog-to-digital converter (ADC) for converting the signal to a digital signal, and a downconverter (DDC) for down-converting the digital signal. The down-converted signal at downconverter system 1512 may be split into two paths by a splitter (not shown). A first signal path may be provided to a digital chaos demodulator system 1504b for producing an estimate of the sparse data info samples. For example, the first signal path may be provided to a digital chaos demodulator for demodulating the downconverter system 1512 signal. The demodulated signal may then be despreaded by a chaos despreader to recover the sparse baseband clipping signal.
(91) The signal recovered by digital chaos demodulator system 1504b may be sampled to produce the sparse data information samples 1513 of the sparse clipping baseband clipping signal 1505. In another embodiment, the signal recovered by digital chaos demodulator system 1504b may be sampled to produce the recovered clipped amplitudes of the sparse clipping baseband clipping signal 1505 (i.e., a sparse clipped amplitude vector 1513), in which case the recovered signal is sparsely distributed in the estimated time positions of the clipping event within the original frame of the LTE or Wi-Fi baseband receive signal.
(92) A second signal path provided by down-converter system 1512 is signal conditioned to produce low PAPR soft data samples 1511. In one example, the low PAPR soft data samples 1511 and the sparse clipping baseband clipping signal 1513 may be subjected to a signal recovery algorithm 1514. The signal recovery algorithm 1514 processes the low PAPR soft data samples 1511 and recovered sparse clipped amplitudes vector 1513 to produce a received baseband signal substantially void of clipping distortion for final processing at the primary user demodulator 1516. For example, such baseband signals substantially void of clipping distortion are typically required to decode LTE or Wi-Fi compliant signals.
(93) The present invention describes an improvement in wireless side-channel feedback information using specialized data compression and extraction processing. In the prior art, the wireless side-channel feedback information is either sent on a separate signaling channel or in-band signaling in lieu of some data samples. Both situations lead to increase overhead for the transport of the intended information. Others have sought to quantize side-channel information and restrict the number of bits per side-channel sample (e.g. 3 bit quantization) to reduce the overhead burden but that leads to performance degradation due to the higher quantization error resulting from lower bit resolution of the side-channel sample. When the side-channel information is the result of computed errors resulting from transmitter function, not only are the value of the errors required but the location of those errors are needed as well. In the present invention, we exploit the properties of the Gabor Algorithm (GA) to compress the error values and locations and zero position in the error signal into a lower rate signal comprising all non-zero values. This reduces the amount of information that is need to be sent over channel without the associated degradation in performance experienced in the prior art. In a preferred embodiment of the present invention, these lower rates side-channel information is transmitted cooperatively using Digital Chaos in-band signaling with the original undistorted signal.
(94)
(95) As discussed below, the exemplary transceiver 1900 and the methods described according to the invention minimizes PAPR. The PAPR may be minimized at the transmitter and received (i.e., measured) at a receiver. Transceiver 1900 does not necessarily require knowledge of the location and amplitudes of a sparse signal such as described with respect to
(96) Exemplary transmitter 1902 may include a compressive sampling unit 1906 for compressing and sampling the clipped error samples. Compressive sampling unit 1906 may compresses the clipped error samples for data aggregation. Compressive sampling unit 1906 may comprise, for example, address hashing, a finite rate innovations (FRI) encoder, or a compressive sensing encoder.
(97) Where compressive sampling unit 1900 use an FRI, the method compresses sparse signals to a small number of compressed samples that can be reconstructed at the receive side. Where the compressive sampling unit 1900 uses a compressive sensing encoder, the method used is a non-parametric technique to improve robustness. Additionally, where compressive sampling unit 1900 uses address hashing, the transceiver may perform further processing of the clipped error samples with a second stage of sample compression using spherical modulation, which may improve noise immunity at the receiver.
(98) Transmitter 1902 may further include a spherical encoder and modulation unit 1908 for receiving the compressed and sampled clipped error samples from compressive sampling unit 1906. Spherical encoder and modulation unit 1908 may provide additional compression of the already compressed and sampled clipped error samples. In one instance the spherical encoder and modulation unit may 1908 may map the amplitude of the compressed and sampled clipped error samples to the phase of the compressed and sampled clipped error samples to improve receiver signal to noise ratio (SNR) performance for reconstructing compressed samples.
(99) Transmitter 1902 may further include a chaos waveform spreader 1910 for receiving and the spreading the spherically encoded and modulated clipped error samples using the chaos spreading sequences as described in accordance with various embodiments of the invention. In preferred embodiments of the invention, chaos waveform spreading unit 1910 performs spreading for improved multiple access interference resistance. Digital chaos waveforms and waveform classes are configurable to many spreading factors and lengths. As shown, of both clipped IDFT signals (x.sub.n) and clipped error (c.sub.n) are summed at summer 1912, preferably at the sampling rate of clipped signals. In which case, both signals may be transmitted in-band multiple access transmission.
(100)
(101) For example, receiver 1904 may include a chaos waveform despreader and rake receiver unit 1916 for receiving the signal transmitted by transmitter 1902. Chaos waveform despreader and rake receiver unit 1916 may despread the received signal for example, to restore the spherically modulated sample through processing gain. The rake receiver of unity 1916 may be used for combining multipath signals in a fading wireless channel, thereby enhancing the signal decoding process, such as performed by a spherical demodulator and decoder unit 1918. Spherical demodulator and decoder unit 1918 may use the same compression sensing algorithms used by spherical encoder and modulator unit 1908 to demodulate and decode the despreaded signal and thereby recover the compressed sparse signals discussed with respect to the output of compressive sampling unit 1906.
(102) Sparse clipped error signals may be reconstructed to restore sparse clipped error signals using the said compression sensing algorithms. For example, a sparse reconstruction unit 1920 able to perform one of re-hashing, FRI, or BPDN on the signal from spherical demodulator and decoder 1918.
(103) The original transmitted signal received by receiver 1904 may then be recovered by summing the estimates of the clipped signal to the estimates of the clipped error.
(104)
(105) In a typical example, M<<N for compressive sensing reconstruction may ordinarily be accomplished with M>2*m, where m is the number of sparse samples in a sparse signal. Consequently, M>2*m/N of 10%-20% of N.
(106)
[].sub.MN=[.sub.1.sub.2.sub.3 . . . .sub.N1.sub.N],.sub.i=[.sub.i,1.sub.i,2.sub.i,3 . . . .sub.i,M].sup.T [g].sub.N1=[].sub.MNe,e=[e.sub.1e.sub.2e.sub.3. . . e.sub.N1.sub.N].sup.T, Equation 1
(107)
(108)
(109) Let u.sub.i=[0 . . . u.sub.i,k.sub.
(110) u.sub.i,I=[0 . . . u.sub.I,58 0 0].sup.T, u.sub.i,Q=[0 . . . u.sub.Q,16 0 0].sup.T for I,Q samples at time (i), for 6-bit quantizer N=64.
(111) For I,Q samples each sparse vector is stacked to form NM1, where each N1
(112)
(113)
(114) In one examplary embodiment, the permutation table used in premutation group product mapper at Step 2208 may be defined for 2 elements as such:
(115) Let permutation table be defined for 2 elements
(116) u.sub.i,I=[0 . . . u.sub.i,58 0 0].sup.T, u.sub.i,Q=[0 . . . u.sub.i,16 0 0].sup.T
(117) then v.sub.i=u.sub.i,I+u.sub.i,Q=[0 . . . u.sub.i,16 0 . . . 0 u.sub.i,58 . . . 0].sup.T
(118) .sub.k is an atom of the constructed dictionary and now 2-vectors are selected from the dictionary. For 2-elements, a permuation group multiplication table using standard cycle construction can be defined as
(119)
(120) One skilled in the art will recognize this as a swap wherein the vector has (I,Q) swapped in the vector sum, and both sparse samples are multiplied by (1) in the sparse vectors u.sub.i,I,u.sub.i,Q. Consequently, when the vector has unswapped (I,Q) in the vector sum, then vector sum elements u.sub.i,I,u.sub.i,Q are multiplied by (+1) or they are unchanged.
(121) These encoded samples are then used in joint I, Q sample spherical modulation in accordance with Equation 2 to encode samples sent to chaos waveform spreader 1910. Joint I, Q sample spherical modulation may be performed, for example by a spherical encoder/modulation unit 1908.
(122) Equation 4 shows the additional encoding step, such as joint I,Q Sample Spherical Modulation 2220 for multiple (I,Q) Spherical Modulation Encoding. The Spherical Modulation Encoding assigns values to 3 sparse samples in the vector sum according to whether the 3 values need to be swapped. The more likely case is 4 sparse, (I,Q) samples but this example indicates how the procedure works for more samples, without burdensome algebra.
(123) For example, multiple symbols can be encoded for multiple (I,Q) samples when the (I,Q) ordering is not preserved but new ordering is an element of a permutation group, with 6-elements in the permutation group S.sub.n, n=3!=6. In this particular example, the 3 sparse vectors with 3-sparsity elements can be binary coded to an element of the permutation group. Permutation element (13) represents, the swapping of first and third vector elements of u.sub.1,u.sub.3 while u.sub.2 is not swapped. Each vector u.sub.1,u.sub.2,u.sub.3 is multiplied by (+1,1,+1) or vectors become u.sub.1,u.sub.2,u.sub.3 respectively from the binary encoding of the permutation group elements.
(124) Let permutation table be defined for 3 elements
(125) u.sub.1=[0 . . . u.sub.i,58 0 0].sup.T, u.sub.2=[0 . . . u.sub.i,23 0 0].sup.T, u.sub.3=[0 . . . u.sub.i,16 0 0].sup.T
(126) then [u.sub.1+u.sub.2+u.sub.3]=[0 . . . u.sub.i,16 0 0 u.sub.i,23 0 . . . u.sub.1,58 . . . 0].sup.T.sub.MN1,
(127) .sub.k is M1 atom of algebraically constructed dictionary
(128) For 3-elements permutation group multiplication table using standard cycle notation can be defined as
(129)
(130) As shown in
(131)
(132) The jointly encoded (I,Q) samples from Step 2206 are recovered from the inputs from the chaos waveform despreader and RAKE receiver 1916 by using the same sparse recovery algorithms discussed with respect to
(133) As discussed in the above example with respect to Equation 3, where (I,Q) sequence ordering is not preserved, new ordering may be an element of a permutation group, with 2-elements in the group. For this example, the 2 sparse I, Q vectors with 2-sparsity elements have been binary coded to an element of the permutation group (e.g., at Steps 2204 and 2208 above). One skilled in the art, will recognize this as a swap wherein the I and Q components of the vector are swapped in the vector sum, and wherein both sparse I and Q samples are multiplied by (1) in the sparse vectors u.sub.i,I,u.sub.i,Q. Likewise when the sparse I and Q samples of the vector are unswapped (I,Q) in the vector sum, then vector sum elements u.sub.i,I,u.sub.i,Q are multiplied by (+1). In some instances, the vector sum elements u.sub.i,I,u.sub.i,Q remain unchanged. For example,
(134) Let permutation table be defined for 2 elements which has encoded 2-samples as below
(135) u.sub.i,I=[0 . . . u.sub.i,58 0 0].sup.T, u.sub.i,Q=[0 . . . u.sub.i,16 0 0].sup.T
(136) then v.sub.i=u.sub.i,I+u.sub.i,Q=[0 . . . u.sub.i,16 0 . . . 0 u.sub.i,58 0].sup.T
(137) .sub.k is an atom of the constructed dictionary and now 2-vectors are selected from the dictionary. For 2-elements, a permuation group multiplication table using standard cycle construction can be defined as
(138)
(139) For decoding one must either swap or not swap the encoded samples to get the correct ordering. For example ab=1, for and encoded vector of (1,1) at the appropriate locations, the a=(12) from the permutation table, then the inverse element is b==(12).
(140) Equation 5 shows the inverse operators (12) used to swap both sparse I and Q samples are multiplied by (1) in the sparse vector, such that I and Q elements are in correct sequence. Once the swapping is complete, the ordered sparse vectors u.sub.i,I,u.sub.i,Q are sent to a D/A converter (6-bits) for example to generate compressive sensing sample estimates for reconstruction of clipped error sparse signal estimates processed by compressive sampling unit 1906.
(141)
(142) In a typical example of the invention, cross-correlation of input (y.sub.n) with a chaos sequence (C) may occur according to the following:
(143)
is length of chaos waveform (C), w.sub.n is the resulting correlation surface There can be multiple peaks on the correlation due to multipath returns [w(n.sub.1T) w(n.sub.2T) w(n.sub.2T) . . . w(n.sub.m)]=FindPeaks (w.sub.n), determines all the potential peaks Create Sorted list of peaks from highest to lowest are
[w(j.sub.iT)>w(j.sub.2T)>w(j.sub.3T) . . . >w(j.sub.mT)]=Sort[[w(n.sub.1T)w(n.sub.2T)w(n.sub.2T) . . . w(n.sub.m)]] Equation 6
(144) As shown in
(145)
(146) In some examples, it may be desired to provide an additional level of compression of the compressed samples received from compressive sampling unit 1906. By adding the additional level of compression, more bandwidth becomes available for chaos spreading. As shown by
(147) It should be noted that, the compressed samples may undergo an A/D quantization process (Step 2500) similar to the A/D quantizer discussed with respect to Step 2202 of
(148) In contrast to symbol-by-symbol encoding/decoding for spherical modulation, the Gabor Transform Encoder described in Step 2510 also reduces time computational complexity at the receiver by exploiting sparse recovery algorithms. The sparse (I,Q) vectors are encoded to time/frequency elements by the Gabor transform. Each of these 2-D matrices are multiplied by a sensing vector (e.g. Alltop sequence) to map the matrix to a 1-D vector representing the time/frequency sparse element.
(149) For example for (N=64)-(I,Q) samples of the sparse vector, the Gabor transform dictionary has at least (N.sup.2=4096)-elements. For reconstruction of a K-sparse signal, K<({square root over (N)}+1) or K<({square root over (64)}+1)=4.5 sparse quantized samples can be reconstructed with N=64 compressed samples. Therefore K=4 sparse quantized samples, can be jointly encoded using the Gabor Transform encoder. Joint encoding enhances noise immunity at the receiver. The overall sample rate of the incoming samples is decreased by a factor of 4, which means there is more chaos waveform spreading per symbol.
(150) Gabor frames are used to model entries in range-Doppler maps (RDM) in radar or symbol-timing/frequency offset for wireless communications receivers. For example, let (H) be unknown matrix (e.g. RDM) of size (M, N) and assume that it can expanded in an orthonormal set of basis functions (H.sub.i), matrices. Then, when M=N, the Gabor frame for matrix (H) is shown in Equation 3 where each matrix is (NN) in size. In such case, the matrices are also orthonormal and given by:
(151)
(152) Consequently, each matrix is formed as follows in Equation 8 where each matrix is a time/frequency matrix.
(153)
Compressed measurements are formed as (y) that is size N column vector, N.sup.2 is size of sparse vector (s)
(154)
where (f) is a probe signal (e.g. Alltop) sequence and .sub.i are the atoms of a compressed sensing measurement dictionary. Usually the vector (f) is the randomization function which generates a dictionary with underlying coherency properties (e.g. Reciprocal Isometry Property (RIP)) but (f) can also inject knowledge about signal-of-interest (SOI) into the over-determined bases. Equation 11 shows the definition of the Alltop sequence according to this invention.
(155)
(156) After A/D quantizing to unique position element in a sparse vector for both real and complex components (I,Q) at Step 2500, the Gabor Transform Encoder used at Step 2510 encodes each CS sample. Equation 1212 is an example encoding method that may be used for each sparse (I,Q).
(157) As shown, Each (N1) time ordered sparse vector is stacked to form a Gabor domain (s) (N.sup.21). Let u.sub.i=[0 . . . u.sub.i,k.sub.
(158) For K=4<<N.sup.2, CS samples of each sparse vector are stacked to form N.sup.21 vector. Note that since N must be a prime number for dictionary construction that is a property of the Alltop sequence, then N=67. Each N1 sample vector has an extra 0 at end. For this K, vectors are stacked in the Gabor Transform sparse vector.
(159)
The time ordered sparse vectors u.sub.i results in time ordered selection of Gabor dictionary atoms. Since K<N, there is no modulo-N arithmetic to be concerned with. The compressed sample vector b from Gabor Transform encoder (Step 2510) is sent to chaos waveform spreading (Step 2520) performed for example by chaos waveform spreader 1910. After spreading, the samples are sent by the transmitter.
(160)
(161)
(162)
(163)
(164) In accordance with the DPA processing, each recovered sparse vector has 64 positions which could include noise positions along with the 2 clipped error samples of interest, where one sequence of sparse vectors through the trellis is designated as path-1 and other sequence designated as path-2. The sequence of symbols then form a path through each trellis node (trellis node 1-250) for each path. Each trellis node is fully connected to all other nodes in the trellis. The DPA uses forward and backward processing to determine optimal paths through the trellis for each of the 64 positions of each recovered sparse vector. A measurement for each set of trellis nodes at each time is the sparse vector reconstructed using sparse recovery, such as is performed by sparse reconstruction unit 1920, during the same time epoch. A cost metric is computed at each trellis node to find the best match of measurement to hypothesis (+1,1,+2) since those are 2 possibilities for a sparse symbol for 2 signals present. Otherwise each vector is 0 or 2 at locations when no signals are present or both signals are the same for the vector sum respectively.
(165) Equation 13 shows exemplary processing that may be used for computing a cost metric for each trellis node in accordance with the present invention, wherein each node provides a sparse recovered vector sample at an identified point in time. The cost metric is approximated using the Turbo code approximation for reducing computational complexity. This metric identifies the most likely pairing of the measurement at a node with the most likely possible hypothesis. The term .sup.2 is the expected noise variance associated with each measurement. The cost metric is a standard normal probability density function to account whereby the signal power is the mean for the normal density function. Each trellis node is a tuple that has both metric score and hypothesis that resulted in that score.
(166) For each trellis node (i) at time t.sub.k compute cost metric
(167)
Equation 14 shows epoch how a cumulative score is computed for each node at time based on all possible previous nodes for the next time. As shown, a cumulative path metric to each current node is stored to track of optimal path to the current node. Equation 14 also shows the computations involved in calculating cumulative score and cumulative path from the previous node that yields the top score. A directed edge is formed for each node at time (k) and the previous node that resulted in the maximum score with index (J).
(168)
At each time epoch, each SOFT measurement is used to update cumulative scores and the cumulative paths, for each path. At the last time epoch, there will be a cumulative score and a cumulative path defined for the last set of nodes in the forward path.
(169) The backward path processing when the paths have no path nodes in common is as follows: Given all cumulative scores at the last set of nodes in the trellis, they are ranked in descending order. The maximum scores define the end nodes for all paths through the trellis, A backward trace is formed to define the optimal paths to the nodes with top scoreswhich has been defined during forward processingand the hypothesis associated with each path node to get to the final node. Equation 15 shows the explicit steps mathematically.
C.sub.m(t.sub.N)=maximum(C.sub.i(t.sub.N)), for each i=1, . . . ,64 Equation 15 where (m) is the value of (i) where the cumulative score at the end node (N) is the largest. This node (m) is used to backtrack through the trellis to determine an optimal path. The sequence of (+1,1,+2) along each optimal backward path defines an optimal sequence of symbols through the trellis. To get the second optimal path through the trellis, one must first expurgate the trellis (i.e. delete the nodes of the optimal sequence of symbols from the previous backtracking step), so that these nodes are not duplicated when searching through the trellis in the forward direction to determine path-2 through the trellis. There is no need to re-compute the node metrics d.sub.i(t.sub.k) for the second forward pass through the trellis since the scores have already been computed. However new cumulative scores C.sub.i(t.sub.N) are computed based on this new trellis that doesn't include the nodes from the previous forward processing step. After forward processing is complete then Equation 5 is performed to find the largest cumulative score at the end node (N) from which the backtracking step is repeated with new set of optimal nodes. By using this 2-pass process, the 2 optimal nodes are determined for each time epoch (t.sub.i), since there are 2-nodes at each time epoch for each path. There is only NO thresholding step at the LAST set of nodes in the trellis to determine top 2 paths.
(170) The backward path processing when the paths have trellis path nodes in common is essentially the same 2-pass processing as for the case when there are separate paths through the trellis, with the exception that any node with a hypothesis score (+2) is NOT expurgated from the trellis for the after the backtracking is complete from the first-path. Now the same steps are performed for the second forward pass and Equation 5 determines the end node for the second backtracking step.
(171) After backward path processing is complete, the 2 paths provide hard decisions for the sequence of sparse symbols. The jointly decoded sparse signals may be re-ordered in time Step 2720, Permutation group mapped Step 2730, using for example, a permutation group element mapper, in similar manner as described with respect to Steps 2310 and 2320 respectively. These sparse signals are converted to compressive sensing samples with D/A converter as shown in (Step 2620) for further processing by Compressive sensing recovery algorithms, by for example, sparse reconstruction unit 1920.
(172) It should be appreciated by one skilled in the art, that the foregoing description has been directed to specific and exemplary embodiments of this invention. It will be apparent; however, that other variations and modifications may be made to the described embodiments, with the attainment of some or all their advantages. Therefore, it is the object of the appended claims to cover all such variations and modifications as come within the true spirit and scope of the invention.