Multiple access wireless communications using a non-gaussian manifold

A method and apparatus for multiple-access wireless transmission is disclosed. The method involves mapping a plurality of signals onto a multi-dimensional non-Gaussian source manifold, the plurality of signals including signals targeted for transmission to a plurality of receivers. The method also involves transforming the source manifold into a multi-dimensional target manifold using a polarization stream network. The method further involves generating a multiple-access transmission waveform for transmission to the plurality of receivers, the multiple-access transmission waveform being based on the target manifold.

BACKGROUND

This disclosure relates generally to wireless communications, and more specifically to multiple access wireless communications using a non-Gaussian manifold.

2. Description of Related Art

In wireless communications networks, multiple access techniques allow several independent data streams or signals to share the same transmission spectrum simultaneously to increase system efficiency. For example, a base station transmitter may combine and modulate signals intended for different receiving devices into a single downlink waveform. The same waveform is thus received by all of the receiving devices, each of which demodulates the received waveform and extracts its own signals from the waveform.

Linear modulation techniques are commonly used to modulate Gaussian signals for transmission. However, when using linear modulation techniques for modulating multiple access transmissions, it becomes difficult to implement different transmission parameters for different receiving devices. The use of linear modulation of Gaussian signals may result in inefficient use of spectral capacity in cases where the receiving devices experience differing channel conditions. Linear modulators also have difficulty in limiting a peak-to-average-ratio (PAPR) of the transmitted waveform, which results in equipment such as power amplifiers having to accommodate a higher maximum power. Attempts to limit the PAPR usually involve a tradeoff, such as a reduction of spectral efficiency associated with the transmission.

There is a desire in the art for improved modulation techniques.

SUMMARY

In accordance with one disclosed aspect there is provided a method for multiple-access wireless transmission. The method involves mapping a plurality of signals onto a multi-dimensional non-Gaussian source manifold, the plurality of signals including signals targeted for transmission to a plurality of receivers. The method also involves transforming the source manifold into a multi-dimensional target manifold using a polarization stream network. The method further involves generating a multiple-access transmission waveform for transmission to the plurality of receivers, the multiple-access transmission waveform being based on the target manifold.

The target manifold may include a multi-dimensional Gaussian manifold.

The method may involve transmitting configuration information defining the polarization stream network to the plurality of receivers.

The method may involve selecting the source manifold from a plurality of source manifolds in response to a channel condition determined for the transmission.

Some regions of the source manifold may be associated with increased signal attenuation and mapping the plurality of signals may involve mapping the plurality of signals onto regions of the source manifold not associated with increased signal attenuation.

The source manifold may include an N-dimensional manifold and transforming the signals may involve transforming the signals into an M-dimensional target manifold.

The dimension N associated with the source manifold may be equal to the dimension M associated with the target manifold.

The multiple-access transmission waveform may include an orthogonal frequency-division multiple access (OFDMA) transmission waveform including M sub-carriers.

The polarization stream network may be configured for transforming between an N-dimensional source manifold and M-dimensional target manifold, and the dimension N of the source manifold may exceed the dimension M of the target manifold, and excess dimensions of the target manifold may be held constant when transforming signals from the source manifold to the target manifold.

The method may further involve transmitting information to the plurality of receivers identifying the excess dimensions on the target manifold that are held constant.

The multiple-access transmission waveform may include a sparse code multiple access (SCMA) transmission waveform.

The polarization stream network may be configured for transforming between an N-dimensional source manifold and M-dimensional target manifold and the dimension M associated with the target manifold may exceed the dimension N associated with the source manifold by at least one excess dimension.

The method may involve transmitting information to the plurality of receivers identifying the at least one excess dimension.

The multiple-access transmission waveform may include a code-division multiple access (CDMA) transmission waveform and the at least one excess dimension may include a spreading code.

The polarization stream network may include at least one neural network and the method may further involve training the neural network to determine a set of weights for the at least one neural network that are operable to configure the polarization stream network to perform the transformation between the source manifold and the target manifold.

Training the at least one neural network may involve training the neural network to transform from the target manifold to the source manifold to determine the set of weights for the at least one neural network, the polarization stream network being reversible to provide parameters for a reversed polarization stream network operable to transform from the source manifold to the target manifold.

Training the at least one neural network may involve causing the transmitter to train the at least one neural network and the method may further involve transmitting information to the plurality of receivers defining a configuration of the polarization stream network and the set of weights for the least one neural network.

Training the neural network may involve causing one of the plurality of receivers to train the neural network and the method may further involve transmitting information to the plurality of receivers defining a configuration of the polarization stream network and the set of weights for the least one neural network.

The polarization stream network may include a cascade of one or more polarization stages, each polarization stage including at least a shuffle function that shuffles signal data in accordance with a shuffle order, and the method may further involve transmitting information identifying the shuffle order to the plurality of receivers.

The method may involve receiving the multiple-access transmission waveform at one of the plurality of receivers and using the polarization stream network to transform the multiple-access transmission waveform from the target manifold to the source manifold to facilitate recovery of signals targeted for transmission to the one of the plurality of receivers.

In accordance with another disclosed aspect there is provided an apparatus for multiple-access wireless transmission. The apparatus includes a transmitter operably configured to map a plurality of signals onto a multi-dimensional non-Gaussian source manifold, the plurality of signals including signals targeted for transmission to a plurality of receivers. The transmitter is also operably configured to transform the source manifold into a multi-dimensional target manifold using a polarization stream network, and to generate a multiple-access transmission waveform for transmission to the plurality of receivers, the multiple-access transmission waveform being based on the target manifold.

Other aspects and features will become apparent to those ordinarily skilled in the art upon review of the following description of specific disclosed embodiments in conjunction with the accompanying figures.

DETAILED DESCRIPTION

FIG. 1Aillustrates an example communication system100in which embodiments of the present disclosure could be implemented. In general, the system100enables multiple wireless or wired elements to communicate data and other content. The purpose of the system100may be to provide content (voice, data, video, text) via broadcast, narrowcast, user device to user device, etc. The system100may operate efficiently by sharing resources such as bandwidth.

In this example, the communication system100includes a wireless communications network102including electronic devices (ED)110-114and radio access networks (RANs)120,122. The system100also includes a core network130, a public switched telephone network (PSTN)132, the Internet134, and other networks136. Although certain numbers of these components or elements are shown inFIG. 1, any reasonable number of these components or elements may be included in the system100.

The EDs110-114are configured to operate, communicate, or both, in the system100. For example, the EDs110-114are configured to transmit, receive, or both via wireless communication channels. Each ED110-114represents any suitable end user device for wireless operation and may include such devices (or may be referred to) as a user equipment/device (UE), wireless transmit/receive unit (WTRU), mobile station, mobile subscriber unit, cellular telephone, station (STA), machine type communication device (MTC), personal digital assistant (PDA), smartphone, laptop, computer, touchpad, wireless sensor, or consumer electronics device.

InFIG. 1A, the RANs120and122include base stations140and142, respectively. Each base station140,142is configured to wirelessly interface with one or more of the EDs110-114to enable access to any other base station, the core network130, the PSTN132, the Internet134, and/or the other networks136. For example, the base stations140-142may include (or be) one or more of several well-known devices, such as a base transceiver station (BTS), a Node-B (NodeB), an evolved NodeB (eNodeB), a Home eNodeB, a gNodeB (sometimes called a “gigabit” NodeB), a transmission point (TP), a transmit/receive point (TRP), a site controller, an access point (AP), or a wireless router. Any ED110-114may be alternatively or jointly configured to interface, access, or communicate with any other base station140-142, the internet134, the core network130, the PSTN132, the other networks136, or any combination of the preceding. Optionally, the system may include RANs, such as RAN120, wherein the corresponding base station140accesses the core network130via the internet134.

The EDs110-114and base stations140-142are examples of communication equipment that can be configured to implement some, or all of the functionality and/or embodiments described herein. In the embodiment shown inFIG. 1A, the base station140forms part of the RAN120, which may include other base stations, base station controller(s) (BSC), radio network controller(s) (RNC), relay nodes, elements, and/or devices. Any base station140or142may be a single element, as shown, or multiple elements, distributed in the corresponding RAN, or otherwise. Also, the base station140forms part of the RAN120, which may include other base stations, elements, and/or devices. Each base station140-142may be configured to operate to transmit and/or receive wireless signals within a particular geographic region or area, sometimes referred to as a coverage area. A cell may be further divided into cell sectors, and a base station140-142may, for example, employ multiple transceivers to provide service to multiple sectors. In some embodiments a base station140-142may be implemented as pico or femto nodes where the radio access technology supports such. In some embodiments, multiple-input multiple-output (MIMO) technology may be employed having multiple transceivers for each coverage area. The number of RAN120,122shown inFIG. 1Ais exemplary only. Any number of RAN may be contemplated when devising the system100.

The base stations140-142communicate with one or more of the EDs110-114over one or more air interfaces150and152using wireless communication links e.g. RF, μWave, IR, etc. The air interfaces150and152may utilize any suitable radio access technology. For example, the system100may implement one or more channel access methods, such as code division multiple access (CDMA), time division multiple access (TDMA), frequency division multiple access (FDMA), orthogonal FDMA (OFDMA), or single-carrier FDMA (SC-FDMA) in the air interfaces150and152.

A base station140-142may implement Universal Mobile Telecommunication System (UMTS) Terrestrial Radio Access (UTRA) to establish an air interface150using wideband CDMA (WCDMA). In doing so, the base station140-142may implement protocols such as HSPA, HSPA+ optionally including HSDPA, HSUPA or both. Alternatively, a base station140-142may establish an air interface150with Evolved UTMS Terrestrial Radio Access (E-UTRA) using LTE, LTE-A, and/or LTE-B. It is contemplated that the system100may use multiple channel access functionality, including such schemes as described above. Other radio technologies for implementing air interfaces include IEEE 802.11, 802.15, 802.16, CDMA1800, CDMA1800 1X, CDMA1800 EV-DO, IS-1800, IS-95, IS-856, GSM, EDGE, and GERAN. Of course, other multiple access schemes and wireless protocols may be utilized.

The RANs120and122are in communication with the core network130to provide the EDs110-114with various services such as voice, data, and other services. Understandably, the RANs120and122and/or the core network130may be in direct or indirect communication with one or more other RANs (not shown), which may or may not be directly served by core network130, and may or may not employ the same radio access technology as RAN120, RAN122or both. The core network130may also serve as a gateway access between (i) the RANs120and122or EDs110-114or both, and (ii) other networks (such as the PSTN132, the Internet134, and the other networks136). In addition, some, or all of the EDs110-114may include functionality for communicating with different wireless networks over different wireless links using different wireless technologies and/or protocols. PSTN132may include circuit switched telephone networks for providing plain old telephone service (POTS). Internet134may include a network of computers and subnets (intranets) or both, and incorporate protocols, such as IP, TCP, UDP. EDs110-114may be multimode devices capable of operation according to multiple radio access technologies, and incorporate multiple transceivers necessary to support such.

The RANs120,122, base stations140,142, and the core network130together may be referred to as “network equipment”. The network equipment elements may be physically distributed within a coverage area. The core network130generally includes computer processor hardware that interfaces between the PSTN132, Internet134, and other networks136and the RANs120,122to provide services to the EDs110-114.

FIGS. 1B and 1Cillustrate example devices that may be used in implementing the network102shown inFIG. 1A. In particular,FIG. 1Billustrates an example of an ED160, andFIG. 1Cillustrates an example base station180. These components could be used in the communication system100or in any other suitable system.

As shown inFIG. 1B, the ED160includes at least one processing unit162. The processing unit162implements various processing operations of the ED160. For example, the processing unit162could perform signal coding, data processing, power control, input/output processing, or any other functionality enabling the ED160to operate in the communication system100. The processing unit162may also be configured to implement some or all of the functionality and/or embodiments described in more detail elsewhere herein. Each processing unit162includes any suitable processing or computing device configured to perform one or more operations. Each processing unit162could, for example, include a microprocessor, microcontroller, digital signal processor, field programmable gate array, or application specific integrated circuit.

The ED160also includes at least one transceiver164. The transceiver164is configured to modulate data or other content for transmission by at least one antenna or Network Interface Controller (NIC)166. The transceiver164is also configured to demodulate data or other content received by the at least one antenna166. Each transceiver164includes any suitable structure for generating signals for wireless or wired transmission and/or processing signals received wirelessly or by wire at the antenna166. Each antenna166includes any suitable structure for transmitting and/or receiving wireless or wired signals172. One or multiple transceivers164could be used in the ED160. One or multiple antennas166could be used in the ED160. Although shown as a single functional unit, a transceiver164could also be implemented using at least one transmitter and at least one separate receiver.

The ED160further includes one or more input/output devices168or interfaces (such as a wired interface to the internet134inFIG. 1A). The input/output devices168permit interaction with a user or other devices in the network. Each input/output device168includes any suitable structure for providing information to or receiving information from a user, such as a speaker, microphone, keypad, keyboard, display, or touch screen, including network interface communications.

In addition, the ED160includes at least one memory170. The memory170stores instructions and data used, generated, or collected by the ED160. For example, the memory170could store software instructions or modules configured to implement some or all of the functionality and/or embodiments described herein and that are executed by the processing unit(s)162. Each memory170includes any suitable volatile and/or non-volatile storage and retrieval device(s). Any suitable type of memory may be used, such as random access memory (RAM), read only memory (ROM), hard disk, optical disc, subscriber identity module (SIM) card, memory stick, secure digital (SD) memory card, and the like.

As shown inFIG. 1C, the base station180includes at least one processing unit182, at least one transmitter184, at least one receiver186, one or more antennas188, at least one memory190, and one or more input/output devices or interfaces192. A transceiver, not shown, may be used instead of the transmitter184and receiver186. A scheduler194may be coupled to the processing unit182. The scheduler194may be included within or operated separately from the base station180. The processing unit182implements various processing operations of the base station180, such as signal coding, data processing, power control, input/output processing, or any other functionality. The processing unit182can also be configured to implement some or all of the functionality and/or embodiments described in more detail herein. Each processing unit182includes any suitable processing or computing device configured to perform one or more operations. Each processing unit182could, for example, include a microprocessor, microcontroller, digital signal processor, field programmable gate array, or application specific integrated circuit.

Each transmitter184includes any suitable structure for generating signals for wireless or wired transmission to one or more EDs or other devices. Each receiver186includes any suitable structure for processing signals received wirelessly or by wire from one or more EDs or other devices. Although shown as separate components, at least one transmitter184and at least one receiver186could be combined into a transceiver. Each antenna188includes any suitable structure for transmitting and/or receiving wireless or wired signals172. Although a common antenna188is shown here as being coupled to both the transmitter184and the receiver186, one or more antennas188could be coupled to the transmitter(s)184, and one or more separate antennas188could be coupled to the receiver(s)186. Each memory190includes any suitable volatile and/or non-volatile storage and retrieval device(s) such as those described above in connection to the ED160inFIG. 1B. The memory190stores instructions and data used, generated, or collected by the base station180. For example, the memory190could store software instructions or modules configured to implement some or all of the functionality and/or embodiments described herein and that are executed by the processing unit(s)182.

Each input/output device192permits interaction with a user or other devices in the network. Each input/output device192includes any suitable structure for providing information to or receiving/providing information from a user, including network interface communications.

It should be appreciated that one or more steps of the embodiment methods provided herein may be performed by corresponding units or modules, according toFIGS. 1A-1C. For example, a signal may be transmitted by a transmitting unit or a transmitting module. A signal may be received by a receiving unit or a receiving module. A signal may be processed by a processing unit or a processing module. Other steps may be performed by a machine learning (ML) module in both transmitting and receiving modules. The respective units/modules may be implemented using hardware, one or more components or devices that execute software, or a combination thereof. For instance, one or more of the units/modules may be an integrated circuit, such as field programmable gate arrays (FPGAs) or application-specific integrated circuits (ASICs). It will be appreciated that where the modules are implemented using software for execution by a processor unit for example, they may be retrieved by a processor, in whole or part as needed, individually or together for processing, in single or multiple instances, and that the modules themselves may include instructions for further deployment and instantiation. Additional details regarding the EDs such as the ED160and the base stations such as180are known to those of skill in the art. As such, these details are omitted here.

A physical layout of a portion of a wireless communications network in which a multiple access wireless transmission is taking place is shown schematically at200inFIG. 2A. Referring toFIG. 2A, the wireless communications network200includes a base station202, and a plurality of receivers204(respectively identified as A, B, and C inFIG. 2). The base station202is configured to transmit a multiple access transmission waveform210within a geographic region212generally as described above in connection with the base stations140,142. Each of the plurality of receivers204are capable of receiving the multiple access transmission waveform210and processing the waveform to extract signals targeted for transmission to the receiver. The multiple access transmission waveform thus combines signals targeted to each one of the plurality of receivers204, which are modulated to generate the multiple access transmission waveform. The multiple access transmission waveform210facilitates more efficient use of the available spectrum in the region212than would be the case if individual waveforms were to be generated and transmitted to each of the plurality of receivers204.

InFIG. 2A, the multiple access transmission waveform210is transmitted in a downlink communication from the base station202to the plurality of receivers204. Referring toFIG. 2B, in some embodiments, each of the plurality of receivers204may be configured to generate and transmit respective waveforms220,222, and224to the base station202in an uplink communication. The waveforms220,222, and224may be generated such that in combination, the waveforms when received at the base station202may be processed to extract signals transmitted by each of the receivers A, B and C. The waveforms220,222, and224may thus make use of generally the same available spectrum in the region212as used for the multiple access transmission waveform210.

Various multiple access modulation techniques such as orthogonal frequency-division multiple access (OFDMA), sparse code multiple access (SCMA), and code-division multiple access (CDMA), may be used to generate the multiple access transmission waveform210. Linear multiple access modulators may be inherently less flexible in the amount of shaping that can be performed in the frequency domain. For example, in the case of a linear OFDMA modulator, the same processing is generally applied to each of the signals targeted to each of the receivers A, B, and C in the plurality of receivers204, to reduce interference between transmitted sub-carriers of the OFDMA waveform. However, transmissions of the waveform210to one or more of the plurality of receivers204may be more or less impacted by noise. For example, the receiver B inFIG. 2is shown located further away from the base station202within the region212and the transmission waveform210may be attenuated due to the additional distance or transmission obstacles between the transmitter and the receiver. Linear multiple access modulators are not generally able to perform different processing of signals targeted to one or more of the plurality of receivers204to compensate for channel conditions that only affect certain receivers. The linear OFDMA modulator is thus unable to perform separate processing, for example, implementing more robust modulation scheme, for the receiver B.

The spectral capacity of a communications channel in the wireless communications network200is important for efficient multiple access transmissions. The efficiency of use of available spectrum depends on how information intended for receipt by any of the plurality of receivers204is modulated onto the transmission waveform210. An example of a symbol constellation is shown inFIG. 3Aat300, in which four two-bit quadrature phase shift keying (QPSK) symbols are represented at coordinate locations a complex I-Q plane. The separation between each symbol in the constellation may be expressed in terms of a Euclidian distances between the constellation points in the in the I-Q plane (indicated by the arrows inFIG. 3). The closer together the points are the more susceptible or vulnerable the resulting modulated waveform will be to noise and data errors. As the level of noise on the channel between the base station transmitter202and the receivers204increases, the receiver may be unable to unambiguously determine which position on the constellation a received signal is supposed to occupy, resulting in errors.

The multiple access transmission waveform210may be generated by modulating a waveform based on the constellation300. Gaussian waveforms may be represented as a manifold or probability distribution. Referring toFIG. 3B, a simplified three-dimensional Gaussian manifold for generating the multiple access transmission waveform210may be represented as a three-dimensional sphere302, having a radius corresponding to the transmitted signal power S. The sphere302provides a geometric representation of the spectral capacity of a communications channel for the example of a three-dimensional signal. In practice, typical signals transmitted in the wireless communications network200will have more than three dimensions. The capacity of the channel or bandwidth B is determined by the number of non-overlapping circles304can be arranged on a surface306of the sphere302. The size of the circles304correspond to the Euclidian distance between constellation points inFIG. 3A, and thus a minimum size of the circles will be lower bounded by the noise N on the channel. The capacity of the channel C is given by the Shannon-Hartley theorem:
C=B·log2(1+S/N).  Eqn 1

From equation 1, it can be seen that the capacity C for a given transmission power S may be increased by increasing B (i.e. the number of overlapping circles304). By increasing the number of circles304, more circles can be accommodated on the surface306. However, as the number of circles on the surface306increases, the size of the circles304decreases, and eventually the circle size would reach a lower bound of the channel noise N. Alternatively, for a given number of circles304(i.e. fixed B), the transmission power S may be reduced until the size of the circles reaches the lower bound of the noise N. In either case, there is an assumption in applying the Shannon-Hartley theorem that the circles304should be non-overlapping, which leaves unused area308between adjacent circles, because the Shannon capacity limit is based on Euclidean distance. The unused area308on the surface306of the sphere302represents a potentially unused portion of the spectral capacity of the channel.

A block diagram of a modulator implemented at the base station202is shown generally at400inFIG. 4. Referring toFIG. 3, the modulator400is configured to receive signals402targeted for transmission to each of the plurality of receivers A, B and C in the plurality of receivers204. The signals402for the receivers A, B and C are mapped by respective constellation mapping blocks404,406, and408onto a source manifold410, such as a non-Gaussian manifold. The source manifold410is transformed by a polarization stream network412into a target manifold414, which may be a Gaussian manifold. The target manifold414is used as the basis for generation of the multiple-access transmission waveform416by a transmitter of the base station202. The multiple access transmission waveform416is transmitted to the plurality of receivers204.

In existing wireless communications networks, it may be expected that transmissions over a communication channel between base station202and the plurality of receivers204involve linear processes. The selection of a Gaussian target manifold414facilitates operation of the modulator400with existing linear network equipment. However, in other embodiments the target manifold414may be a non-Gaussian manifold.

An example of a constellation500on a simplified and generic representation of a non-Gaussian source manifold502is shown inFIG. 5A. As an example, the manifold502may be a multi-dimensional non-orthonormal manifold such as a Riemannian manifold, or other non-Gaussian manifold. Four two-bit symbols are represented on the manifold502. In this case the separation between each symbol in the constellation500is based on Geodesic Distance rather than Euclidian distance, as in the case of the constellation300shown inFIG. 3. The Geodesic Distances between adjacent constellation points on the manifold502are indicated by arrows inFIG. 5A. The separation between constellation points in the constellation500is thus greater than the separation provided by the constellation300ofFIG. 3and should thus provide improved noise performance. The manifold capacity assumptions, related to a Gaussian manifold such as shown inFIG. 3B, of uniform non-overlapping circles no longer apply, and the capacity of the manifold is not limited by the Shannon-Hartley theorem.

A portion of a non-Gaussian manifold510is shown inFIG. 5Bas a three-dimensional surface512. Because the Gaussian constraint of non-overlapping circles no longer applies, a greater number of signal constellations can be mapped onto the non-Gaussian manifold510, thus reducing the amount of unused spectral capacity on the non-Gaussian manifold510. InFIG. 5B, the signal constellations are represented as areas outlined by broken lines514. Some regions of the non-Gaussian manifold510may be associated with increased signal attenuation. To improve performance, signals constellations may be mapped onto regions of the manifold that are not associated with increased signal attenuation.

An example of a non-Gaussian manifold for implementing the source manifold410is shown inFIG. 6at600. The source manifold600is represented by a cloud of samples or points distributed over the frequency range ƒ. The manifold600incorporates a tolerable white noise level602by generating thicker manifold rather than a simple multi-dimensional surface. The source manifold600accommodates different channel conditions for the receivers A, B, and C in the plurality of receivers204by including a less frequency selective portion604for receiver B and more frequency selective portions606and608for receivers A and C. The manifold600represents just one example that may be selected for use as the source manifold410. In practice, the selection of a manifold may be made from a plurality of source manifolds in response to channel conditions determined for the transmissions to the plurality of receivers204.

In one embodiment, the polarization stream network412may be implemented using a neural network. Referring toFIG. 7, a polarization stream neural network700may be trained in a training exercise to transform between the non-Gaussian source manifold600and a multi-dimensional Gaussian target manifold702. The polarization stream neural network700includes a cascade of homomorphism transformations for shaping between the non-Gaussian source manifold600and the target manifold702, which are configured in a training exercise. The training exercise is performed to transform from the multi-dimensional Gaussian target manifold702to the non-Gaussian source manifold600, which has been found to be a convenient training strategy. However, in other embodiments the training exercise may be performed for transformation from the non-Gaussian source manifold600to the multi-dimensional Gaussian target manifold702. In this embodiment the source manifold600and the target manifold702have the same number of signal dimensions, which facilitates inversion to generate a reverse polarization stream network for performing the reverse transformation.

Configurations of a forward polarization stream network800and a reverse polarization stream network820are shown schematically in generalized form inFIG. 8. The forward and reverse polarization stream networks800and820each include a cascade of n stages that transform between an input signal X and an output signal Y having the same number of dimensions. The input signal X may include a plurality of bits of information representing a complex value signal. Each stage in the cascade of stages is similarly configured and includes a shuffle block802, a split block804, a scaling function806, and an offset function808. The shuffle block802implements a shuffle or permutation function that receives the set of input bits X and outputs a set of shuffled or permuted bits. The shuffle or permutation may be performed in accordance with a permutation table, for example. The split block804implements a split function, which splits the shuffled bits into a first shuffled bit group X1(1)and a second shuffled bit group X2(1). With the inclusion of the scaling function806and offset function808, each stage in the cascade may be written as follows:
(n)=(n)×v((n))+u((n))
(n)=(n)
(n)=shufflen((n−1)),  Eqn 2
where the × operator is a dot-wise (or more generally element-wise) multiplication and the + operator represents element-wise addition operation between two operand vectors. Thus, each stage shuffles the input signals, and splits the shuffled information into a first group,and a second group,. The scaling function v(·)806is applied to the second groupto generate a scaling vector (v()), and the offset function u(·)808is applied to the second groupto generate an offset vector (u()). Both the scaling vector and the offset vector have dimension size equal to the first group. The output of each stagenis obtained by element-wise multiplying the first information group with the scaling vector, then element-wise adding the offset vector. The outputnis a copy of the second information group.

The reverse polarization stream network820operates on an input signal Y and produces an output signal X. The × operator is replaced by a dot-wise (or more generally element-wise) division and the + operator is replaced by an element-wise subtraction operation between two operand vectors. The scaling function v(·)812and offset function u(·)814are unchanged from the forward polarization stream network800. Thus, each stage in the reverse polarization stream network820shuffles the input signal and splits the shuffled information into a first groupand a second group. The scaling function v(·)812is applied to the second groupto generate a scaling vector (v()), and the offset function u(·)814is applied to the second groupto generate an offset vector (u()). Both the scaling vector and the offset vector have dimension size equal to the first information group. The outputs for each stage are thus given by:
(n)=((n))−U(((n)))/v((n))
(n)=(n)
(n)=Shufflen((n+1))  Eqn 3

The second outputis a copy of the group. The first output information group is obtained by element-wise subtracting the offset vector from the first information group, then element-wise dividing by the scaling vector.

Due to common elements appearing in both the forward and reverse polarization stream networks800and820, it is only necessary to perform the training for either the forward or the reverse network. For example, if the forward network800were to be trained, the reverse network820may be easily obtained by exchanging the multiplication and division operators, and the addition and subtraction operators, and reversing the input and output. The addition of the scaling function to the polarization stream networks800and820depresses the reliability of some points or dimensions and boosts the reliability of other points or dimensions. Together, the scaling function v(·) and the offset function u(·) provide flexibility to polarize the reliabilities over the signal space for shaping of the input X to the output Y.

In one embodiment, the scaling and offset functions v(·) and u(·) may be implemented as neural networks within the forward and reverse polarization stream networks800and820. An example of a neural network portion for implementing the scaling and offset functions v(·) and u(·) is shown inFIG. 9at900. The neural network900includes sets of fully connected nodes902in multiple layers including an input layer904, an output layer906, and multiple hidden layers908. The input layer904includes nodes that receive the second group vectorn. The output layer906includes output nodes that provide the scaling and offset functions v(·) and u(·) for each stage in the cascade of stages for the forward and reverse polarization stream networks800and820. Each arrow connecting between the nodes may have an associated weighting factor wi, which is determined in the training exercise shown inFIG. 7. The training exercise shown inFIG. 7results in a set of weights wibeing determined for the network820to perform the transformation between an input Y (i.e. the target manifold702) and the output X (i.e. the source manifold600).

Additional details and configurations and training of forward and reverse polarization stream neural networks are described in commonly owned patent application U.S. Ser. No. 16/562,045 filed on Sep. 5, 2019 and entitled “A METHOD AND APPARATUS FOR WIRELESS COMMUNICATION USING POLARIZATION-BASED SIGNAL SPACE MAPPING”, which is incorporated herein by reference in its entirety.

Referring toFIG. 10, a modulation and transmission process implemented by the base station transmitter202for transmissions to the plurality of receivers204is illustrated schematically at1000. The base station transmitter202performs constellation mapping404-406(FIG. 4) to map signals intended for transmission to each receiver A, B or C as symbols on the source manifold600. Each symbol represents one or more bits of information for transmission, and inFIG. 10these symbols are indicated by squares “□”, circles“∘”, or diamonds “⋄”. The symbols indicated as squares “□” are intended for transmission to receiver A and are mapped onto a first portion of the source manifold600. The symbols indicated as circles “∘” are intended for transmission to receiver B and are mapped onto a second portion of the source manifold600. The symbols indicated as diamonds“⋄” are intended for transmission to receiver C and are mapped onto a third portion of the source manifold600. As shown inFIG. 10, it is not necessary for each dimension of the source manifold600to carry the same number of constellation symbols. Some of the dimensions of the source manifold600may accommodate more constellation symbols than other dimensions. For example, a central portion of the manifold accommodates four “∘” symbols, whereas adjacent portions may only accommodate two “∘” symbols. Other dimensions of the source manifold600may accommodate only a single symbol.

The base station202configures a reverse polarization stream neural network ƒ−1(·)1002using weights wi, determined during the training exercise. The network1002thus transforms the symbols mapped onto the source manifold600into a source manifold1004. In this embodiment the source manifold1004has a multi-dimensional Gaussian distribution, which represents the transmitted symbols from each of the plurality of receivers204. The source manifold600is an N-dimensional manifold and the target manifold1004is an M-dimensional manifold including M sub-carriers. The number of dimensions of the source manifold600thus corresponds with the number of dimensions in the source manifold1004such that M=N.

A transmitter1006then generates a multiple-access transmission waveform1010based on the multi-dimensional Gaussian distribution of the source manifold1004. The waveform1010is then transmitted by the base station202to each of the plurality of receivers204.

Referring toFIG. 11, a process implemented by the receiver B of the plurality of receivers204for receiving and demodulating the multiple-access transmission waveform1010is illustrated schematically at1100. Each one of plurality of receivers204receives the same multiple-access transmission waveform1010at a receiver block1102and must extract a portion of the waveform that includes the signal targeted to the receiver. As an example, the receiver B needs to extract specific symbols intended for receiver B, while discarding symbols intended for reception by the receivers A and C. The receiver block1102receives the waveform1010and produces a multi-dimensional Gaussian distribution1104, which generally corresponds to the multi-dimensional Gaussian distribution of the source manifold1004produced by the polarization stream neural network1002. During propagation of the waveform1010between the base station202and the receiver block1102, noise, propagation losses, and/or multi-path propagation effects may cause some degradation. This may cause the received waveform to differ from the multi-dimensional Gaussian distribution of the source manifold1004.

The multi-dimensional Gaussian distribution of the source manifold1004is then processed through a polarization stream neural network ƒ(·)1106. The polarization stream neural network1106may be configured using configuration information, including weights wiand biases bi, which are transmitted to the receiver by the base station202, as described in more detail below. The polarization stream neural network1106thus performs a transformation from the received multi-dimensional Gaussian distribution1104into symbols on the manifold1108. The circle symbols “∘” intended for receipt by the receiver B are processed by a de-mapper1110, which extracts the signal. The square “□” and diamond symbols “⋄” are discarded by the receiver B. The other receivers A and C in plurality of receivers204similarly process the waveform1010and extract their respective symbols.

For a linear modulation technique such as orthogonal frequency-division multiplexing (OFDM), both input and output are orthonormal manifolds over which the distance between constellation symbols is a Euclidean distance. An advantage of using the non-Gaussian source manifold600is that the effective distance between two constellation symbols is no longer based on Euclidean distance, but is rather based on geodesic distance. This is illustrated inFIG. 12, where Euclidian and geodesic distances between a pair of constellation symbols are indicated. The geodesic distance represents a shortest path between the two symbols along the surface of the source manifold600. The geodesic distance thus represents a greater effective separation distance between constellation symbols for the non-Gaussian manifold than would be the case based on Euclidian distance for a linear manifold. The use of the non-Gaussian manifold provides for enhanced noise immunity between symbols and thus has the potential of reducing symbol confusion when demodulated at the receiver.

In one embodiment the training of the polarization stream neural network ƒ(·) or ƒ−1(·) is performed either by the base station202or other network equipment. The neural networks ƒ(·) or ƒ−1(·) may be defined by configuration information such as a set of weights wiand biases bifor the scaling and offset functions v(·) and u(·), the number and configuration of the polarization stages, and details of the implemented shuffle functions. The configuration information may be transmitted to the plurality of receivers204via an existing communications channel between the base station202and each of the receivers. The configuration information is used by each receiver A, B and C of the plurality of receivers204to configure their respective polarization stream neural networks1106. Each receiver A, B and C of the plurality of receivers204will also need to receive constellation information identifying specific constellation points on dimensions of the manifold1108to facilitate extraction by the de-mapper1110of symbols intended for reception by the receiver. The manifold1108can output either Euclidean or geodesic distance to the de-mapper1110, based on a de-mapping algorithm implemented by the de-mapper.

In some embodiments, the training of the polarization stream neural network ƒ(·) or ƒ−1(·) may be performed by one of the receivers204. The receiver would then transmit the configuration information to the base station202for configuring transmissions to the plurality of receivers204, using control channels or data channels.

Multiple-access transmissions in which the waveform1010is modulated using a non-linear polarization stream neural network have several advantages over multiple-access transmissions generated using linear modulators. As an example of a linear modulation, an OFDMA source manifold1300is shown inFIG. 13and includes a plurality of sinc(·) functions in the frequency domain. The zero points of each sinc(·) function overlap poles of other sinc(·) functions. For example, the pole1302associated with a sinc(·) function1304overlaps a zero1306associated with sinc(·) functions1308and1310. The overlapping of the poles and zeros allows adjacent sinc(·) functions or sub-carriers to be closely juxtaposed in the OFDMA source manifold1300and thus the sub-carrier spacing Δƒ is less than for conventional FDMA.

However, in an OFDMA transmission, all the sub-carriers must share the same sinc(·) profile and it is not possible to only adjust some sub-carriers based on differences in channel conditions for some receivers. OFDMA transmissions are thus limited in their ability to compensate for channel conditions. The non-Gaussian source manifold600shown inFIG. 6has the advantage of facilitating shaping of the manifold to include different portions604,606, and608for different receivers. Additionally, for the OFDMA transmission shown inFIG. 13, a transmission power PTXis equally shared by the sub-carriers. As much as 50% of PTXmay be wasted in secondary poles associated with each sinc(·) function (some of the secondary poles1312are shown inFIG. 13for the sinc(·) functions1304inFIG. 13).

The OFDMA source manifold1300, when transformed into a time domain manifold by an FFT (Fast Fourier Transformation) manifold transformer1314, results in a time domain manifold having relatively high peak-to-average power ratio (PAPR). Higher PAPR for a modulation scheme is associated with poor power efficiency. Higher PAPR may also be associated with possible signal degradation, if the transmitter power amplifier is driven into a non-linear region. Non-linear amplification may lead to in-band distortion, increased Bit Error Rate (BER), and adjacent channel interference and other negative impacts. Attempts to filter the time domain signal generally result in some of the outlying sub-carriers on the OFDMA source manifold1300being distorted and unusable. For example, in OFDMA having 1024 complex carriers (i.e. 2048 carriers in total) it is not unusual to disable 900 or more of the sub-carriers, thus significantly reducing spectral efficiency.

The non-Gaussian source manifold600used in the process1000may however be shaped and selected to reduce the PAPR without incurring any significant loss in spectral efficiency. For example, the Gaussian source manifold600may be shaped to effectively reduce energy wastage on secondary poles.

One of the advantages of using a polarization stream architecture to generate the multiple access waveform is that the waveform may be generated based on an actual signal transmission environment. In practice, different systems may be differently optimized. For example, in some embodiments, the polarization stream network may be optimized to generate a waveform that avoids highly attenuated sub-carriers. In other embodiments, the polarization stream network may be optimized to generate a waveform that tolerates greater Doppler frequency offsets with larger sub-carrier spacing. For a multiple-access waveform, the polarization stream network may be optimized for multiple receivers that have different optimization targets. In general, Gaussian manifolds have a low PAPR, due to maximum entropy theory, and in practice a Gaussian signal has a at least a probability of resulting in a high PAPR. The polarization stream network may thus be used to control the possible variance in PAPR when configuring a waveform for transmission using a Gaussian manifold.

As disclosed above, configuration information may be transmitted to the plurality of receivers204via an existing communications channel between the base station202and each of the receivers and used by each receiver to configure their respective demodulators. The configuration information would include the shuffle functions shuffle(1) to shuffle(n+1), that would permit the receivers204to each configure the corresponding polarization stream networks800or820at the respective receivers. In one embodiment, the shuffle functions may be shared with the plurality of receivers204on a secure basis. In this embodiment, the multiple-access transmission waveform1010could only be demodulated by a receiver that has the necessary configuration information to implement the shuffle functions.

In the modulation and transmission process1000shown inFIG. 10and the receive process1100shown inFIG. 11, the source manifold600and target manifold702have the same number of signal dimensions. This has the advantage of making the polarization stream neural network700easily invertible to configure the reverse polarization stream network820once the forward polarization stream network800has been configured. One difficulty in employing other types of non-linear transformers is that it is usually computationally difficult and/or computationally inefficient to invert a non-linear transformer. As disclosed above in connection with the polarization stream networks shown inFIG. 8, after the forward network800has been trained, the reverse network820may be easily obtained by exchanging the multiplication and division operators, the addition and subtraction operators, and reversing the input and output. The ability to generate the reverse polarization stream network820through a simple reconfiguration of the forward polarization stream network800avoids further computational steps. However, in order to make this simple inversion feasible the inputs X and outputs Y of the forward polarization stream network800should have the same number of signal dimensions.

In other modulation schemes, information to be transmitted may be compressed from a higher dimensional signal space to lower dimensional space. An example of such a modulation scheme is Sparse Code Multiple Access (SCMA) transmission, in which coded non-orthogonal transmissions of multiple signals are used to improve spectral efficiency for a transmission. Referring toFIG. 14A, an example of a modulation and transmission process for a dimension-reduced transmission is shown generally at1400. In this example, a source manifold1402of six signal dimensions is transformed into a target manifold1404having four dimensions. The transformation is performed using an inverse polarization stream network ƒ−1(·)1406, configured generally as shown inFIG. 8at820. The polarization stream network1406must therefore be configured to transform between an N-dimensional source manifold and M-dimensional target manifold, where the dimension N exceeds the dimension M.

In the embodiment shown, the inverse polarization stream network1406receives three input signal dimensions1408. The three input signal dimensions1408are based on a first circular constellation on the source manifold1402that maps information intended to be received by a first receiver. The inverse polarization stream network1406also receives three input signal dimensions1410. The three input signal dimensions1410are based on a second circular constellation on the source manifold1402that maps information intended to be received by a second receiver.

The inverse polarization stream network1406processes the six input signal dimensions1408and1410and generates two sets of three signal dimensions1414and1416at an output1412of the inverse polarization stream network1406. However, one of the signal dimensions in each of the sets of three signal dimensions1414and1416is collapsed to a zero value (or some other constant value). A transmitter1418then generates a multiple-access transmission waveform1420based on the remaining four signal dimensions of the target manifold1404that have not been collapsed by the inverse polarization stream network1406. In one embodiment, the inverse polarization stream network1406may be configured using neural network portions, as described above.

Referring toFIG. 14B, a forward polarization stream neural network1430may be trained using a pair of Gaussian distributions1432, in which the first and third dimensions are collapsed to zero. The forward polarization stream neural network1430may be implemented generally as shown at800inFIG. 8. A target manifold1434(x0, x1, x2, x3, x4, x5) simulates a logistic function represented by cloud of samples:

The forward polarization stream neural network1430will thus be trained based on the pair of Gaussian distributions1432with the first and third dimensions collapsed to zero. The forward polarization stream neural network1430remains invertible due to the input and output having the same number of signal dimensions. Accordingly, once the forward polarization stream neural network1430has been trained, the inverse polarization stream network ƒ−1(·) (1406) is readily configured for use in the dimension-reduced transmission shown generally at1400inFIG. 14A.

Referring toFIG. 14C, an example of a process for reception and demodulation of a dimension-reduced transmission is shown generally at1450. The multiple-access transmission waveform1420having four signal dimensions is received by a receiver1452and provided to a forward polarization stream neural network ƒ(·)1454, such as shown at800inFIG. 8. The receiver1452also receives configuration information defining the neural network ƒ(·), such as a set of weights wifor the scaling and offset functions v(·) and u(·), the number and configuration of the polarization stages, and details of the implemented shuffle functions. In this embodiment the configuration information further includes an identification of which of the signal dimensions are to be collapsed at an input1456of the forward polarization stream neural network1454. In this embodiment, the first and third dimensions1458and1460are collapsed to zero to correspond to the training conditions shown inFIG. 14B. The forward polarization stream neural network1454transforms the input signals and collapsed dimensions to recreate the original six signal dimensions1462corresponding to the source manifold1402, which provide output constellations1464and1466. In this embodiment, information intended for receipt by the first receiver is carried on the output constellation1464. For receipt of the multiple-access transmission waveform1420by the first receiver, a de-mapper1468extracts the signal intended for receipt by this receiver from the output constellation1464. The information intended for receipt by the second receiver that is carried on the output constellation1466is discarded by the first receiver.

The dimension-reduced transmission1400has the advantage of increasing spectral efficiency by reducing the number of signal dimensions transmitted over the channel. However, because the reduction in signal dimension causes loss in performance for the transmission, it may be necessary to take this loss into account in configuring transmissions. For example, aspects such as constellation design, codebook design, or power control may be specifically selected to ensure that adjacent constellation points are as distant as possible over the source manifold1402. Additionally, or alternatively, advanced non-linear receiving algorithms such as message passing algorithm, successive cancellation, and/or interference cancellation may be implemented at the receiver to improve reception reliability.

In some embodiments a transmission from the base station202may extend a signal dimension such that a modulated transmission waveform has a greater number of signal dimensions than the source manifold. As an example, Code-division multiple access (CDMA) modulation extends the signal dimension by using a spreading code C to spread each information bit over F bits, where F is known as the spreading factor. Data intended for multiple receivers may be encoded using different spreading codes CA, CB, etc. The spreading codes may be carefully selected to be mutually orthogonal to each other using an orthogonal variable spreading factor (OVSF).

Referring toFIG. 15, a block diagram of a modulator implemented at the base station202for performing a dimension-extended modulation is shown generally at1500. The modulator1500is described in the context of transmitting signals1502targeted for transmission to each of a pair of receivers A and B. The modulator1500includes a bit interleaver1504that multiplexes the signals1502from the receivers A and B into one or more bit streams. The bit interleaver1504may implement an interleaving scheme such as block interleaving, convolutional interleaving, matrix interleaving, random interleaving, or any other scheme for combining streams of data bits. The one or more interleaved bit streams produced by the bit interleaver1504are then processed by a constellation mapping and spreading block1506. The constellation mapping and spreading block1506maps the bit streams onto a non-Gaussian source manifold1508. The constellation mapping and spreading block1506also implements a spreading function C that spreads the constellation points on the source manifold1508using a spreading factor F. The spreading function F increases the signal dimension from N to a signal dimension M on the source manifold1508, where M=N×F.

The modulator1500includes a polarization stream network1510that performs a transformation of the non-Gaussian source manifold1508into a target manifold1512. The target manifold1512may be a Gaussian manifold and is used as the basis for generation of a multiple-access transmission waveform1514by a transmitter of the base station202.

Referring toFIG. 16A, an example of a transmission process is shown inFIG. 16at1600. Signal bits intended for transmission to one of the receivers A and B are interleaved into a bit stream1602and mapped onto each of three constellations1604as shown by the arrows. In this embodiment, the bit stream1602includes a single bit for each of the users A and B, and the spreading factor is F=6 for each device. The constellations1604spread the signals for the receivers A and B over a non-Gaussian source manifold1606, which has 6 signal dimensions. The source manifold1606is transformed by an inverse polarization stream neural network ƒ−1(·)1608to produce a target Gaussian manifold1610. The target Gaussian manifold1610also has 6 signal dimensions and may be used as a basis for generating a multiple-access transmission waveform1616. Because the source manifold1606and target manifold1610have the same number of signal dimensions, the polarization stream neural network1608is easily invertible as described above. The transmission process1600thus implements a dimension-extended transmission by transforming the bit stream1602including 2 bits into a target manifold having 6 dimensions. The circle1612of the target Gaussian manifold1610generally represents a capacity associated with the manifold and the arrow1614indicates the distance between adjacent constellation points on the manifold.

Referring toFIG. 16B, a simplified training example1620involves training a forward polarization stream neural network1622to transform a Gaussian distribution1624into a sine wave manifold1626, where:

Although the target manifold1626in the training example is selected as a sine-wave manifold for purposes of this description, a suitable non-Gaussian manifold may be selected based on channel conditions between the base station202and the plurality of receivers204. Because the polarization stream neural network1620has the same input and output dimensions, the forward network ƒ(·) may be inverted to generate the reverse network ƒ−1(·) The reverse network ƒ−1(·) may be used as the reverse polarization stream neural network1608inFIG. 16A. The training may be performed at the base station202or other network equipment associated with the communications network. Configuration information defining the neural networks ƒ(·) or ƒ−1(·) may be transmitted to the plurality receivers A and B via an existing communications channel between the base station202and each of the receivers. Additionally, in this embodiment the spreading code C, constellation mapping information, and bit interleaving scheme information would also be transmitted to each receiver A and B.

Referring toFIG. 16C, an example of a reception and demodulation process implemented on the receiver B for receiving the multiple-access transmission waveform1616is shown at1630. The multiple-access transmission waveform1616is received and demodulated by a forward polarization stream neural network ƒ(·)1632to recreate the manifold1606at the receiver as a received manifold1634. The receiver B is then able to de-map the constellation point by performing an autocorrelation based on the spreading code C, to recover the stream 1 0. The received bit interleaving configuration information may then be used to extract the bit 0 intended for receipt by the receiver B. The bit 1 intended for receipt by the receiver A is discarded at the receiver B.

In some embodiments the shuffling functions for the polarization stream neural networks1608and1632may be shared on a secure basis between base station and receivers A and B. Receivers other than the receivers A and B would not be able to demodulate the multiple-access transmission waveform1616, thus providing an additional layer of security for the transmission. Similarly, sharing the spreading code C on a secure basis would add a further level of security, because receivers not included in the multiple access transmission would also not be able to de-map constellation points on the received manifold1634.