Patent Description:
Data transmission in a communication system involves efficient handling of the detrimental effects of multipath interference and Additive white Gaussian noise (AWGN). This poses unique challenges in systems where the problem evolves into a high-dimensional search in a large search space, such as in MIMO (multiple-input and multiple-output) OFDM (Orthogonal frequency-division multiplexing) systems. To this end, receivers typically perform multiple tasks in series to decode the signal. Custom Hardware (HW) blocks may be designed to perform these tasks with individual optimization metrics that allow a reasonable performance-complexity tradeoff. Typically, channel estimation is based on minimizing mean-squared error (MSE) criterion leading to an MMSE channel estimator, while symbol demodulation is based on a Sphere Decoder that achieves near Maximum Likelihood (ML) performance. Often, HW complexity limits the design choices of these algorithms, especially since each module is optimized in isolation, and implementing near-ML solutions HW for even moderately sized antenna configurations still remains a challenge.

An ever-growing demand for high data rates and service capabilities provides a need for highly efficient system design. Multimedia capabilities with different quality-of-service (QoS), latency and performance requirements must be supported for a wide range of devices and networks. Multiple Input Multiple Output (MIMO) and Orthogonal Frequency Division Multiplexing (OFDM) are example communication technologies that enable bandwidth efficient communication. While MIMO and OFDM are stable technologies to use bandwidth efficiently, there is a desire for optimizing system architecture to reduce the area, power consumption and other system resources.

In the document <NPL>, a blind receiver for coded orthogonal frequency-division multiplexing communication systems in the presence of frequency offset and frequency-selective fading is described. The proposed blind receiver iterates between a Bayesian demodulation stage and a maximum a posteriori channel decoding stage. The extrinsic a posteriori probabilities of data symbols are iteratively exchanged between these two stages to achieve successively improved performance. The Bayesian demodulator computes the a posteriori data symbol probabilities, based on the received signals, by using Markov chain Monte Carlo techniques.

In the document<NPL>, a Gibbs sampler is employed to calculate the Bayesian estimates.

In the document<NPL>, a joint iterative data detection and channel decoding under imperfect channel state information is described.

Aspects of the disclosure leverage Markov-Chain Monte-Carlo (MCMC) algorithms to provide systems (e.g. receiver) and methods that advantageously reduce or eliminate implementation of dedicated signal processing blocks in the physical layer, which becomes even more advantageous with advances in fifth generation (<NUM>) wireless communications. Aspects further incorporating probabilistic methods to process a received signal, which allows for machine learning algorithms to be leveraged in both data and control planes of the wireless receiver when compared to the traditional implementations of the baseband.

The object to be solved is to ensure receiver performance in an efficient manner. The object is achieved by a receiver having the features of the independent claim. Additional features for advantageous embodiments are provided in the dependent claims.

The accompanying drawings, which are incorporated herein and form a part of the specification, illustrate the aspects of the present disclosure and, together with the description, further serve to explain the principles of the aspects and to enable a person skilled in the pertinent art to make and use the aspects.

The exemplary aspects of the present disclosure will be described with reference to the accompanying drawings. The drawing in which an element first appears is typically indicated by the leftmost digit(s) in the corresponding reference number.

In the following description, numerous specific details are set forth in order to provide a thorough understanding of the aspects of the present disclosure. However, it will be apparent to those skilled in the art that the aspects, including structures, systems, and methods, may be practiced without these specific details. The description and representation herein are the common means used by those experienced or skilled in the art to most effectively convey the substance of their work to others skilled in the art. In other instances, well-known methods, procedures, components, and circuitry have not been described in detail to avoid unnecessarily obscuring aspects of the disclosure.

Receivers in wireless communication devices may perform multiple tasks in series to decode the received signal, including channel estimation, symbol demodulation and channel decoding. Receiver performance may be increased when aforementioned receiver tasks are optimized jointly with Maximum a posteriori Probability (MAP) criterion, since they maximize both likelihood and prior information of all the parameters being estimated (output as well as latent). Although aspects are described with reference to wireless communications, the present disclosure is not limited to wireless communication technologies and the aspects can advantageously be implemented in any signal processing and signal estimation technologies, such as image, video, audio, or other data processing operations.

Aspects of the present disclosure include Probabilistic Computing and use Bayesian Inference to get optimal Maximum a posteriori Probability (MAP) estimates. One or more aspects use Markov-Chain Monte-Carlo (MCMC) sampling (e.g. Gibbs and Metropolis Hastings sampling). In exemplary aspects, the systems and methods include performing both channel estimation and symbol demodulation, which may be optimize individually or jointly.

Aspects of the disclosure employ MCMC using improved Gibbs sampling and Metropolis Hastings sampling techniques to achieve MAP performance while enabling reusable, scalable, area efficient HW designs as well as provide improved trade-off of performance and complexity. In one or more exemplary aspects, channel estimation and symbol demodulation may use the same hardware logic that performs MCMC sampling to obtain optimal MAP estimates of the channel or symbol, respectively. Supporting these two broad categories of MCMC sampling techniques also enable aspects of the present disclosure to be applied to other signal estimation operations, such as image, video, audio processing operations.

Aspects of the present disclosure advantageously provide: reduced system resources (e.g. low area and power consumption for handling multiple functionalities) while providing optimal MAP performance, improved performance-complexity-latency trade-off (e.g. a configurable number of samples drawn and number of parallel samplers for the MCMC probabilistic sampler can provide better trade-off opportunities and design choices), scalable configurations supporting large number of antennas and modulation orders, especially Massive and Multiuser MIMO scenarios, and joint processing configurations for communication and computing (e.g. using a same hardware module).

<FIG> illustrates a wireless communication device according to an exemplary aspect of the present disclosure.

The communication device <NUM> is configured to transmit and/or receive wireless communications via one or more wireless technologies. The communication device <NUM> can be configured for wireless communications to fifth generation (<NUM>) wireless technologies and related spectrums, or other wireless technologies and spectrums as would be understood by one of ordinary skill in the relevant arts. The other wireless communication technologies may include, but are not limited to Institute of Electrical and Electronics Engineers (IEEE) <NUM> standards, Long Term Evolution (LTE), and/or one or more other communication protocols as would be understood by one of ordinary skill in the relevant arts, such as Radio Frequency (RF), Infra-Red (IR), Frequency-Division Multiplexing (FDM), Orthogonal FDM (OFDM), Time-Division Multiplexing (TDM), Time-Division Multiple Access (TDMA), Extended TDMA (E-TDMA), General Packet Radio Service (GPRS), Extended GPRS, Code-Division Multiple Access (CDMA), Wideband CDMA (WCDMA), CDMA <NUM>, Multi-Carrier Modulation (MDM), Discrete Multi-Tone (DMT), Bluetooth, ZigBee, or the like.

The communication device <NUM> can be configured to communicate with one or more other communication devices, including, for example, one or more base stations, one or more access points, one or more other communication devices, one or more network components, and/or one or more other devices as would be understood by one of ordinary skill in the relevant arts.

In an exemplary aspect, the communication device <NUM> includes a controller <NUM> communicatively coupled to one or more transceivers <NUM>. In an exemplary aspect, the controller <NUM> includes processor circuity <NUM> that is configured to control the overall operation of the communication device <NUM>, such as the operation of the transceiver(s) <NUM>. The processor circuitry <NUM> may be configured to control the transmitting and/or receiving of wireless communications via the transceiver(s) <NUM>.

In an exemplary aspect, the processor circuitry <NUM> is configured to perform one or more baseband processing functions (e.g., media access control (MAC), encoding/decoding, modulation/demodulation, data symbol mapping; error correction, etc.) in cooperation with the transceiver <NUM> or instead of such operations/functions being performed by the transceiver <NUM>. The processor circuitry <NUM> is configured to run one or more applications and/or operating systems; power management (e.g., battery control and monitoring); display settings; volume control; and/or user interactions via one or more user interfaces (e.g., keyboard, touchscreen display, microphone, speaker, etc.) in one or more aspects.

In an exemplary aspect, the controller <NUM> further includes a memory <NUM> that stores data and/or instructions, where when the instructions are executed by the processor circuitry <NUM>, controls the processor circuitry <NUM> to perform the functions described herein.

The memory <NUM> may be any well-known volatile and/or non-volatile memory.

Examples of the communication device <NUM> include (but are not limited to) Access Points (APs), base stations, eNodeBs (E-UTRAN Node B), New Radio (NR) or next generation Node Bs (gNodeB or gNB - note that this term is typically used in the context of 3GPP fifth generation (<NUM>) communication systems). In other aspects, some or all features defined for network equipment may be implemented by a User Equipment (UE), and the communication device <NUM> may include a mobile computing device (mobile device)-such as a laptop computer, a tablet computer, a mobile telephone or smartphone, a "phablet," a personal digital assistant (PDA), and mobile media player; a wearable computing device-such as a computerized wrist watch or "smart" watch, and computerized eyeglasses; and/or internet-of-things (IoT) device. In some aspects of the present disclosure, the communication device <NUM> may be a stationary communication device, including, for example, a stationary computing device-such as a personal computer (PC), a desktop computer, television, smart-home device, security device (e.g., electronic/smart lock), automated teller machine, a computerized kiosk, and/or an automotive/aeronautical/maritime in-dash computer terminal. The communication device <NUM> may also be remotely controllable device, such as a drone or other controllable device.

In one or more aspects, the communication device <NUM> or one or more components of the communication device <NUM> is additionally or alternatively configured to perform digital signal processing (e.g., using a digital signal processor (DSP)), modulation and/or demodulation (using a modulator/demodulator), a digital-to-analog conversion (DAC) and/or an analog-to-digital conversion (ADC) (using a respective DA and AD converter), an encoding/decoding (e.g., using encoders/decoders having convolution, tail-biting convolution, turbo, Viterbi, and/or Low Density Parity Check (LDPC) encoder/decoder functionality), frequency conversion (using, for example, mixers, local oscillators, and filters), Fast-Fourier Transform (FFT), precoding, and/or constellation mapping/de-mapping to transmit and/or receive wireless communications conforming to one or more wireless protocols and/or facilitate the beamforming scanning operations and/or beamforming communication operations.

The transceiver(s) <NUM> is configured to transmit and/or receive wireless communications via one or more wireless technologies. In an exemplary aspect, the transceiver <NUM> includes processor circuitry that is configured for transmitting and/or receiving wireless communications conforming to one or more wireless protocols.

In an exemplary aspect, the transceiver <NUM> includes a transmitter <NUM> and a receiver <NUM> configured for transmitting and receiving wireless communications, respectively, via one or more antennas <NUM>. In aspects having two or more transceivers <NUM>, the two or more transceivers <NUM> can have their own antenna <NUM> or can share a common antenna via, for example, a duplexer and/or diplexer in one or more aspects. In an exemplary aspect, the transceiver <NUM> (including the transmitter <NUM> and/or receiver <NUM>) is configured to perform one or more baseband processing functions (e.g., media access control (MAC), encoding/decoding, modulation/demodulation, data symbol mapping; error correction, etc.).

The antenna <NUM> can include one or more antenna/radiating elements <NUM> forming an integer array of antenna elements. In an exemplary aspect, the antenna <NUM> is a phased array antenna that includes multiple radiating elements (antenna elements) each having a corresponding phase shifter. The antenna <NUM> configured as a phased array antenna can be configured to perform one or more beamforming operations that include generating beams formed by shifting the phase of the signal emitted from each radiating element to provide constructive/destructive interference so as to steer the beams in the desired direction. In some aspects, the antenna elements <NUM> of the antenna <NUM> may be activated individually rather than as being part of a phased array.

<FIG> illustrates an exemplary aspect of receiver <NUM>. In an exemplary aspect, the receiver <NUM> includes a channel estimator <NUM>, a symbol demodulator <NUM>, and a decoder <NUM>.

The channel estimator <NUM> is configured to estimate the multipath channel. In an exemplary aspect, the channel estimator <NUM> is configured to receive, at its input, the received signals, Y (via the antenna <NUM>) and to estimate or otherwise determine channel state information corresponding to channel properties of the communication link (communication channel H). The channel state information may describe how the signal propagates from a transmitting device to the receiver <NUM>. The information may represent the combined effect of, for example, scattering, fading, and power decay with distance. The received signals Y can then be passed to the symbol demodulator <NUM>. In one or more aspects, the channel state information is also provided to the symbol demodulator <NUM>, and/or one or more other components of the receive <NUM>.

The symbol demodulator <NUM> is configured to perform symbol demodulation to identify the transmitted symbol according to a specified modulation scheme. In an exemplary aspect, the symbol demodulator <NUM> is configured to receive the received signals Y and to demodulate the received signals Y to generate demodulated signals. The demodulated signals are then provided to the decoder <NUM>. The demodulated signals can include the original information-bearing signal that are extracted from a carrier wave during demodulation. That is, the demodulator <NUM> can recover the information content from a modulated carrier wave. The demodulator <NUM> may also generate one or more demodulated symbols X, and provide the demodulated symbols X to the decoder <NUM> and/or one or more other components of the receiver <NUM> (e.g. the channel estimator <NUM>).

The decoder <NUM> is configured to performing channel decoding to decode the data bits according to a coding scheme. In an exemplary aspect, the decoder <NUM> is configured to decode the demodulated signals to generate an output bit sequence. In an exemplary aspect, the decoder <NUM> is configured to determine the log-likelihood ratio (LLR) for the bits of the output bit sequence. In an exemplary aspect, the decoder <NUM> can provide the LLR to one or more other components of the receiver <NUM> (e.g. the demodulator <NUM>). In an exemplary aspect, the decode <NUM> is a Low-density parity-check code (LDPC) decoder but is not limited thereto.

One or more aspects of the disclosure may involve the following linear system of equations, where received signal Y can be represented as transmitted bits / symbols X undergoing intersymbol interference due to the multipath channel H, and is further corrupted by Additive White Gaussian Noise (AWGN) - W. For example, in a MIMO system, Y and W are Nr dimensional vectors, H is Nr x Nt matrix and X is a Nt dimensional vector wherein Nt, Nr are the number of transmit and receive antennas, respectively. Note that Y, H, X, W are all complex Gaussian. Further in a MIMO-OFDM system, this input-output relationship is typically defined for each sub-carrier 'k'. This is illustrated in Equation (<NUM>) below: <MAT>.

From Bayes Theorem, a posterior distribution can be identified for symbol demodulation (Equation <NUM>) and channel estimation (Equation <NUM>) as follows:.

In one or more aspects, the optimization functions may disregard the denominator P(Y) as the functions do not depend on the estimated parameters.

Typically, for symbol demodulation, priors P(X) are from a uniform distribution since all symbols are equally likely. Hence, maximizing the a posteriori probability leads to Maximum Likelihood (ML) solution. However, for channel estimation, priori P(H) also to be maximized, which is a complex Gaussian function of the signal statistics, e.g., channel covariance.

It can be noted that the likelihood distribution is the same for both channel estimation and symbol demodulation: <MAT>.

For Symbol demodulation, the optimal Maximum Likelihood (ML) solution is set forth in Equation <NUM>: <MAT>.

For Channel estimation, the optimal Maximum a posteriori (MAP) solution is set forth in Equation <NUM>: <MAT>.

The receiver <NUM> may be configured to use the minimization of mean squared error (MMSE) methods for both symbol demodulation and channel estimation. While it is computationally less complex (apart from matrix inverse), MMSE often provides sub-optimal performance for both functions and serve mainly as a baseline for comparison or as an initializer. For symbol demodulation, ML methods may be more preferable while some exhaustive search methods may be less preferable due to prohibitive complexity. Although Sphere decoding for symbol demodulation provides near-ML performance with reasonable complexity in many cases, the complexity becomes more prohibitive with the dimensionality of the search space, especially higher order modulation schemes like <NUM>-QAM (Quadrature amplitude modulation) or <NUM>-QAM. Further, the degree of parallelism possible with sphere decoders is restrictive depending upon the neighborhood QAM symbols search definition (K-closest factor).

In exemplary aspects, the receiver <NUM> is configured to utilize Probabilistic Computing and/or Machine Learning. For example, communication is a probabilistic inference problem where information bits are estimated from coded data bits in the presence of unknown latent parameters. Since, communication involves the estimation of unobserved transmitted bits (X) from observed signals (Y), maximizing the a posteriori probability P(X|Y) yields the optimal estimate. Bayesian inference offers a solution methodology to this estimation problem, through the formulation of Maximization of a posteriori Probability (MAP) using Likelihood and a priori probabilities.

In an exemplary aspect, the receiver <NUM> is configured to use one or more Bayesian inference methodologies, including Markov Chain Monte Carlo (MCMC), which is a stochastic approximation, and Variational Inference, which is a deterministic approximation. With MCMC, the receiver <NUM> is configured such that samples are iteratively drawn from a probability distribution by constructing multiple Markov chains, which eventually converge to an equilibrium distribution proportional to the desired distribution. While MCMC seeks a numerical approximation by sampling the exact posterior, Variational inference provides an analytical solution using the approximate posterior, by using graphical models of observed data, unknown parameters, and latent variables.

In an exemplary aspect, the receiver <NUM> is configured to use a Metropolis-Hastings (MH) algorithm in the MCMC process. Using MH, candidate samples are generated according to a proposal distribution and are subsequently accepted or rejected according to certain acceptance probabilities. Exploring high dimensional space can be performed effectively through the careful choices of proposal and acceptance distributions. In an exemplary aspect, the receiver <NUM> can employ Gibbs sampling, which is a special case of the MH algorithm where the exact conditional distribution is used and all samples generated are accepted. In an exemplary aspect, the Gibbs Sampling is used when conditional distributions evaluated for the problem are tractable and simple to compute. When Gibbs sampling is not feasible, the receiver <NUM> can use a Random walk Metropolis in which the proposal distribution is chosen to be a normal distribution with manually tuned mean and variance. In other cases, the receiver <NUM> can use one or more gradient methods for the proposal distribution which converge quickly to the equilibrium distribution.

In an exemplary aspect, with reference to <FIG> and <FIG>, the receiver <NUM> may include a sampler <NUM>. In an exemplary aspect, the sampler <NUM> is a MCMC sampler. The sampler <NUM> is configured to perform various receiver functionalities efficiently: channel estimation, symbol demodulation and bit decoding. The sampler could operate both in the form of discrete functional modules specific to each functionality (<FIG>) and also jointly (<FIG>).

In an exemplary aspect, the sampler <NUM> is configured to only maximize terms arising from the likelihood function P(Y|H,X) when configured to perform symbol demodulation. When performing channel estimation, the sampler <NUM> is configured to consider both likelihood terms and a priori information of the channel deduced from the signal statistics such as the long term channel covariance matrix. In an exemplary aspect, the sampler <NUM> leverages the probabilistic computing view point of Bayesian inference with appropriate likelihoods and priors to perform multiple functionalities. Although the optimized parameter (X or H) is different for these two modules, Gaussian parameters of the distribution sampled by the sampler <NUM>--mean and variance--are identical in structure. The sampler <NUM> performs joint sampling to advantageously simplify the processing of latent channel coefficients. An example MCMC sampling dataflow is illustrated in <FIG>.

There are few differences in the likelihood evaluation for channel estimation and symbol demodulation. In an exemplary aspect, symbol demodulation performs an optimization over a Nt dimension vector X, whereas channel estimation optimizes over a Nr × Nt linear transformation H. As a result, the sampling structure would be different, which is ultimately dependent on the degree of parallelism in sampling. Also, symbol demodulation is an integer optimization problem since the symbols are from discrete alphabets, whereas channel estimation involves a search over continuous random variables. In an exemplary aspect, despite these two differences, the sampling mean and variance expressions in the likelihood distributions may be performed by the sampler <NUM> configured with a uniform structure for MCMC sampling.

<FIG> illustrates an exemplary aspect of the receiver <NUM> that includes sampler <NUM>. The sampler <NUM> includes a likelihood calculator <NUM> having a channel estimation (CE) likelihood calculator <NUM> and a symbol demodulation (SD) likelihood calculator <NUM>. In an exemplary aspect, likelihood calculator <NUM> is configured to calculate or otherwise determine likelihood information based on information received from the channel estimator <NUM>, the symbol demodulator <NUM>, and/or the decoder <NUM>. In an exemplary aspect, the CE likelihood calculator <NUM> is configured to determine likelihood information for channel estimation based on information received from the channel estimator <NUM>, and the SD likelihood calculator <NUM> is configured to determine likelihood information for symbol demodulation based on information received from the symbol demodulator <NUM>.

In an exemplary aspect, the sampler <NUM> may also include an a priori calculator <NUM> (e.g. as needed for channel estimation (CE)) configured to calculate or otherwise determine a priori information based on signal statistics such as the long term channel characteristics (e.g. channel covariance matrix). In an exemplary aspect, sampler <NUM> may also include an a posteriori calculator <NUM> configured to calculate or otherwise determine a posteriori information based on (e.g. a combination of) the likelihood information and the a priori information. In an exemplary aspect, the a posteriori calculator <NUM> is configured to calculate the a posteriori information based on a product or a sum of the likelihood information and the a priori information, but is not limited thereto.

Similarly, likelihood and a priori modules could be designed for decoding bits in a LDPC or polar decoder. As indicated above, the sampler <NUM> may be configured in an individual configuration that includes individual functional modules for both channel estimation and symbol demodulation, and a joint configuration that includes joint sampling for channel estimation and symbol demodulation, where the channel is treated as latent variable and only detected symbols are fed as output. In an exemplary aspect, the sampler <NUM> (or one or more components therein) includes processor circuitry that is configured to perform one or more functions of the sampler <NUM> (or respective functions of the components).

In an exemplary aspect, the sampler <NUM> may be configured to perform Gibbs sampling, where the sampler <NUM> is configured to generate posterior samples by sweeping through each variable to sample from its conditional distribution, by fixing all other variables to their current values. In aspects where random initializers are used, the initial samples generated may not be from the actual posterior distribution and are therefore discarded (called burn-in period, Nb). After substantial iterations, MCMC converges and starts generating samples for each variable from the stationary distribution as desired. In order to perform Gibbs sampling, knowledge of joint or at least the conditional distribution of the variables is necessary. However, manual parameter tuning as applied for other Metropolis-Hastings variants is not needed. In an exemplary aspect, the sampler <NUM> can use Gibbs sampling to leverage the Gaussian distributions defined using mean and variance, which can be derived for the likelihood and prior distributions. Hence, sampling from the joint posterior distributions is possible.

In an exemplary aspect, the sampler <NUM>, using Gibbs sampling, can break a complex high dimensional symbol search into multiple simple Gaussian sampling of conditionals with tractable mean and variance. As more samples are drawn, conditional distributions are modified accordingly which eventually converge to the stationary distribution. MCMC methods also allow a high degree of parallelism through the construction of multiple independent Markov chains, making them highly amenable to efficient HW implementation. This can also be facilitated in SW implementation by parallelizing MCMC over multiple CPU cores using several threads or using vectorization techniques.

In an exemplary aspect, the sampler <NUM> is configured to perform MCMC-based channel estimation utilizes the channel covariance to account for channel a priori. In an exemplary aspect, the sampler <NUM> is configured to model a priori distribution using appropriate channel covariance matrices and may use a shared hardware configuration as with symbol demodulation based on sampling from similar likelihood distributions.

In an exemplary aspect, channel coefficients h in Equation <NUM> are assumed to complex Gaussian with zero mean and covariance Σ across all the subcarriers. In an exemplary aspect, the full covariance is considered for obtaining optimal performance. In another aspect, a block-based local covariance (e.g. <NUM> or <NUM> subcarriers) is used to reduce computations. Considering <NUM> subcarriers, referred as one Resource Block - RB, Σ is a 12x12 complex valued matrix. <MAT> where CN denotes complex Gaussian distribution.

A MAP solution for MIMO channel estimation as defined in Equation (<NUM>) involves the product of <NUM> complex Gaussian distributions with (mean, variance) defined as ( <MAT>) for the likelihood distribution and ( <MAT>) for the a priori distribution, which can be calculated as follows. <MAT> where hj,i(k) refers to the channel coefficient between transmit antenna i and receive antenna j.

A MCMC-Gibbs Sampling method for Channel Estimation according to an exemplary aspect is illustrated by the following flow structure:
<IMG>.

In the structured flow, Np is the number of parallel MCMC samplers, Ns is the number of sample draws and Nb is the number of initial burn-in samples discarded. Superscript sc denoting subcarrier index is omitted from all channel variables above for ease of exposition. In an exemplary aspect, for each MCMC sampler, MMSE initialization is used due to the performance and quicker convergence to optimal solution.

<FIG> illustrates two flowcharts <NUM> and <NUM>. Flowchart <NUM> illustrates a MCMC-Gibbs Sampling method for Channel Estimation according to an exemplary aspect. Flowchart <NUM> illustrates a MCMC-Gibbs Sampling method for Symbol demodulation according to an exemplary aspect. In the flowchart <NUM>, both operations 610A and 610B are performed for channel estimation, and the flowchart <NUM> illustrates an exemplary sample draw procedure for the above Gibbs algorithm for Channel Estimation flow structure.

The flowchart <NUM> starts at operation <NUM> and transitions to operation <NUM> (both 610A and 610B in this aspect). Both operations 610A and 610B are performed in the MCMC-Gibbs Sampling method for Channel Estimation flow structure (algorithm). In operation 610A, the Likelihood Mean µ<NUM> and Variance σ<NUM><NUM> in the Conditional PDF (probability density function) is calculated.

In an exemplary aspect, the likelihood distribution for channel estimation is identified by optimizing for H using Equations (<NUM>) and (<NUM>) with mean and variance defined as follows in Equation (<NUM>).

Advantageously, given the similarity in structure with symbol demodulation Gibbs sampling as shown in Equation (<NUM>) and (<NUM>), the aspects of the present disclosure may utilize a shared HW or SW configuration. For example, the only differences are the Nr dimensional vector multiplications in Equation (<NUM>) replaced with a scalar symbol. Advantageously, the sampler <NUM> may be configured to adapt to these differences with minimal overhead.

In an exemplary aspect, mean and variance calculation logic (HW or SW) for likelihood distribution is shared between channel estimation and symbol demodulation, as shown above.

In another exemplary aspect, the sampler <NUM> makes use of results on partitioned Gaussians in order to calculate mean and variance of the a priori distribution of H using channel covariance matrix Σ, which is illustrated below in Equation set (<NUM>).

Note than "n" signifies consideration of only row or column corresponding to subcarrier "n", whereas "≠ n" signifies consideration of rows or columns corresponding to all subcarriers except subcarrier "n".

After operation <NUM> (610A and 610B), the flowchart <NUM> transitions to operation <NUM>, where Mean and Variance for Conditional PDF (Product of Gaussians) is calculated. In an exemplary aspect, the mean µ and variance σ<NUM> calculated based on the following equations: <MAT>.

After operation <NUM>, the flowchart <NUM> transitions to operation <NUM>, where two Gaussian random numbers with mean = <NUM>, variance = <NUM> are drawn, denoted as ϕ and ψ.

After operation <NUM>, the flowchart <NUM> transitions to operation <NUM>, where the drawn samples are mapped to the desired Gaussian PDF with mean µ and variance σ<NUM>. In an exemplary aspect, the mapping is based on the following equation: <MAT> Where <IMG>(µ), <IMG>(µ) refer to real and imaginary parts of mean µ respectively, ϕ and ψ are zero-mean unit-variance Gaussian random numbers and i denotes the complex imaginary number.

After operation <NUM>, the flowchart <NUM> returns to operation <NUM> to sample the next variable.

Advantageously, in an exemplary aspect, the arithmetic computation may be simplified in Equation <NUM> because variance term <MAT> can be precomputed for all subcarriers. Also product of vector and matrix <MAT> present in both mean and variance expressions can be precomputed once for all subcarriers. Further matrix inverse <MAT> unique for each subcarrier does not involve multiple matrix inverse computations. Instead, inverse of the covariance matrix Σ (or block covariance considered) is calculated once and rank-one updates are used to calculate other inverses of submatrices constructed with specific row and column removed. Due to these optimizations, MCMC based Gibbs Sampling for channel estimation by the sampler <NUM> is highly optimal and is amenable to parallel hardware or software implementation with high efficiency and reusability.

In an exemplary aspect, the sampler <NUM> is configured to perform MCMC-Gibbs sampling for MIMO symbol demodulation.

A MCMC-Gibbs Sampling method for Symbol Demodulation according to an exemplary aspect is illustrated by the following flow structure:
<IMG>
<IMG>.

In above algorithm, Ns denotes the number of MCMC sample draws, Nb denotes the burn-in period, and Np denote the number of MCMC samplers operating in parallel. In an exemplary aspect, for each MCMC sampler, MMSE initialization is used due to the performance and quicker convergence to optimal solution.

Again with reference to <FIG>, flowchart <NUM> of a MCMC-Gibbs Sampling method according to an exemplary aspect is illustrated. In flowchart <NUM>, operation 610A is selected for Symbol demodulation, and the flowchart <NUM> illustrates an exemplary draw procedure for the above Gibbs algorithm for Symbol demodulation structure flow. In this aspect, operation 610B is not performed, and the flow skips operation <NUM>.

Again, the flowchart <NUM> starts at operation <NUM> and transitions to operation <NUM> (Only 610A in this aspect). Only operation 610A is performed in the MCMC-Gibbs Sampling method for Symbol demodulation flow structure (algorithm). In Operation 610A, the Likelihood Mean µ = µ<NUM> and Variance σ<NUM> = σ <NUM><NUM> in Conditional PDF are calculated based on Equation (<NUM>), as follows <MAT>.

After operation 610A, the flowchart <NUM> transitions to operation <NUM>, where two Gaussian random numbers with mean = <NUM>, variance = <NUM> are drawn, denoted as ϕ and ψ. That is, unlike in the channel estimation method, operation <NUM> is omitted.

After operation <NUM>, the flowchart <NUM> transitions to operation <NUM>, where the drawn samples are mapped to the desired Gaussian PDF with mean µ and variance σ<NUM>. Note that the mean and variance expressions are similar in structure to those for Channel estimation in Equation (<NUM>). This advantageously enables a re-usable hardware design in various respects. After calculating the mean and variance that defines the conditional Gaussians, samplers are generated from the distribution according to Equation (<NUM>): <MAT> where <IMG>(µ), <IMG>(µ) refer to real and imaginary parts of mean µ respectively, ϕ and ψ are zero-mean unit-variance Gaussian random numbers and i denotes the complex imaginary number.

In an exemplary aspect, for symbol demodulation, samples drawn from the conditionals are then mapped onto the closest QAM constellation point according to Equation (<NUM>) as below. This advantageously is a simple slicing operation in hardware.

Where Q refers to the set of possible discrete QAM modulated symbols. MCMC Gibbs Sampling algorithm continues to iterate for Ns sample draws across Np parallel samplers, so as to converge to the stationary distribution.

In another exemplary aspect, variance calculated in Equation <NUM> is amended to improve performance at high SNR and avoid stalling. To be specific, variance is updated to be the maximum of the variance calculated in Equation <NUM> and half of the minimum distance between QAM symbols. This enables a wider search radius at high SNR scenarios, thus avoiding the sampler from getting stuck at local optima.

In an exemplary aspect, for symbol demodulation, the sampler <NUM>, configured as a Gibbs sampler, is configured with, for example, <NUM> or <NUM> sample draws for each of the, for example, <NUM> or <NUM> parallel samplers (although optimal ML solution could be obtained with much less sampling). Advantageously, the MCMC-Gibbs provides near-ML performance like sphere decoder, but increases the parallelism factor (thereby reducing latency) while having negligible or no complexity increase when the order of modulation schemes is increased.

In an exemplary aspect, the MCMC sampler <NUM> is configured to perform joint sampling for Channel Estimation and Symbol demodulation, where both channel coefficients and symbols are drawn using corresponding conditional distributions. Channel coefficients are treated as latent variables and are discarded at the end, while symbols detected are fed as the final output. A MCMC-Gibbs Sampling process flow (e.g. algorithm) for joint sampling according to an exemplary aspect is provided below:
<IMG>.

Sample draw for channel estimate H entails performing operations <NUM>-<NUM> according to flowchart <NUM> as described above while sample draw for symbol demodulation X entails performing operations <NUM>-<NUM> according to flowchart <NUM> as described above.

Advantageously, by ignoring the latent channel variables, post processing for channel estimation may be avoided, and better performance can be obtained since this approach optimizes the joint distribution considering both types of conditional distributions.

In many Bayesian inference problems, the exact posterior conditional may be intractable or difficult to compute, which may make Gibbs based sampling infeasible. In an exemplary aspect, in such cases, Metropolis-Hastings sampling may be used to sample from the target distribution. An outline of the Metropolis-Hastings process flow (algorithm) for symbol demodulation according to an exemplary aspect is provided below:
<IMG>.

In the Metropolis-Hastings sampling method, <MAT> denotes the proposal density and <MAT> is the target posterior density.

In an exemplary aspect, in Metropolis-Hastings, samples are iteratively generated from a proposal distribution, which could be a normal distribution with manually tuned mean and variance. Samples are accepted or rejected depending upon certain acceptance ratio, which indicates how likely the new sample is probable as compared to the previous accepted sample. Metropolis-Hastings algorithm constructs a Markov chain, which asymptotically reaches a unique stationary distribution. When the proposal density is symmetric, acceptance ratio further simplifies to just check if new sample is more likely than the old sample for acceptance.

Proposal distribution choice effects the performance of MH algorithm. For example, small jumps or low variance cause the algorithm to mix slowly since successive samples move around the search space too slowly. Large jumps or high variance causes samples to be chosen from the low probability region often leading to slow convergence. In an exemplary aspect, optimal convergence requires a careful choice of proposal distribution considering the nature of problem at hand. Random-walk metropolis suffers from the need to manually tune mean and variance, due to which algorithm designs are not scalable. Therefore, in an exemplary aspect, gradient based methods are preferable for choosing proposal distribution where tractable gradients can be computed with less complexity.

In an exemplary aspect, the sampler <NUM> is configured as a gradient-descent based Metropolis-Hastings sampler for both communication tasks of channel estimation and symbol demodulation. In an exemplary aspect, the first derivative (Gradient) of an error function, such as the Negative of Log Posterior (NLP, deduced from Equation (<NUM>)), or of a loss function, is used as the mean of proposal move, and its second derivative (Hessian) as the variance of the proposal move. Advantageously, the MH-GD sampler enables MCMC sampling with faster convergence compared to Gibbs sampling.

In MH-GD channel estimation, the gradient descent direction is first identified using the NLP function for Channel estimation, from two Gaussian distributions corresponding to likelihood and a priori.

In an exemplary aspect, to define the proposal distribution q(h(s)|h(s-<NUM>)) , the proposal walk (h(s) - h(s-<NUM>)) is calculated by generating Gaussian random numbers and making a move in the direction of the gradient and variance is defined using maximum of the inverse of Hessian and half of minimum distance between QAM symbols. NLP provides a cost function that helps define the target distribution <MAT>, which is used to calculate the acceptance probability. The proposed channel sample is then accepted or rejected.

The Gradient-descent based Metropolis-Hastings sampling algorithm for channel estimation according to an exemplary aspect is provided in the process flow below.

A corresponding flowchart <NUM> that illustrates a MCMC MH-GD channel estimation method is discussed below with reference to <FIG> illustrates two flowcharts <NUM> and <NUM>. Flowchart <NUM> illustrates a MCMC MH-GD Sampling method for Channel Estimation according to an exemplary aspect. Flowchart <NUM> illustrates a MCMC MH-GD Sampling method for Symbol demodulation according to an exemplary aspect.

First with reference to <FIG> for a MCMC MH-GD channel estimation method, the flowchart <NUM> is described for Channel Estimation (both operations 710A and 710B). That is, when operations 710A and 710B are selected, and the flowchart <NUM> is applied to channel estimation, and the flowchart <NUM> illustrates an exemplary sample draw procedure for the above MH-GD algorithm for Channel Estimation structure flow discussed above.

The flowchart <NUM> starts at operation <NUM> and transitions to operation <NUM> (both 710A and 710B in this aspect). Both operations 710A and 710B are performed in the MCMC MH-GD Sampling method for Channel Estimation flow structure (algorithm).

In operation 710A and 710B, the Likelihood Mean µ<NUM> and Variance σ<NUM><NUM> and a priori Mean µ<NUM> and Variance σ<NUM><NUM> in Proposal PDF are calculated using the Gradient and the Hessian of cost function used in Gibbs sampling. In an exemplary aspect, the mean value of the update is obtained from the Gradient, identified as <MAT> where ( <MAT> ) and ( <MAT> ) are the Gaussian (mean, variance) of likelihood and a priori distributions, respectively, as identified for Gibbs sampling in Equations (<NUM>) and (<NUM>) for Gibbs-based channel estimation. While the gradient is used for mean, variance may be deduced from the inverse of Hessian (second derivative of NLP), i.e., inverse of <MAT>.

After operation <NUM> (710A and 710B), the flowchart <NUM> transitions to operation <NUM>, where Mean and Variance for Proposal PDF (Product of Gaussians) is calculated. In an exemplary aspect, the mean µ and variance σ<NUM> calculated based on the following equations: <MAT>.

After operation <NUM>, the flowchart <NUM> transitions to operation <NUM>, where the drawn samples are mapped to the desired Gaussian PDF with mean µ and variance σ<NUM>. In an exemplary aspect, the mapping is based on the following equation: <MAT> <IMG>(µ), <IMG>(µ) refer to real and imaginary parts of mean µ respectively, ϕ and ψ are zero-mean unit-variance Gaussian random numbers and i denotes the complex imaginary number.

After operation <NUM>, the flowchart <NUM> transitions to operation <NUM>, where the acceptance probability is calculated using the ratio of likelihoods of proposal and the previous sample.

In an exemplary aspect, the acceptance probability is calculated according to the following equation: <MAT>.

Hcand denotes the candidate channel estimate calculated in operation <NUM> and Hi-<NUM> denotes the channel estimate in previous sample draw / iteration for same variable index. Y refers to the received signal and X denotes the transmitted symbol, typically a pilot sequence.

After operation <NUM>, the flowchart <NUM> transitions to operation <NUM>, where the sample is drawn from Uniform PDF. For example, the operation includes drawing a uniform random variable u. In an exemplary aspect, the sample draw corresponds to the equation below: <MAT>.

After operation <NUM>, the flowchart <NUM> transitions to operation <NUM>, where it is determined if a > u. This determination can include a comparison of a with u.

If u is less than α, the flowchart <NUM> transitions to operation <NUM>, where the proposal is accepted (Hi = Hcand).

If u is greater than or equal to α, the flowchart <NUM> transitions to operation <NUM>, where the proposal is rejected (Hi = Hi-<NUM>).

After operations <NUM> and <NUM>, the flowchart <NUM> returns to operation <NUM> to sample the next variable.

Advantageously, as compared to Gibbs sampling or Random-walk Metropolis, the Gradient-descent based MH algorithm, according to exemplary aspects, converges rather quickly to the stationary distribution. As a result, with the MH-GD algorithm, fewer sample draws and parallel samplers are sufficient to get superior performance. Further, with the MH-GD algorithm, using the direction of the gradient improves the generation of samples to increase the number of samples in the high probability region than the tails, which leads to better understanding of the target distribution. Further, since sample variance adapts to the Hessian (curvature of the cost function), large incorrect jumps are avoided and only the right moves get accepted. The MH-GD algorithm is also highly parallelizable with minimal computations per sample draw, making it highly amenable to hardware implementation. Therefore, this Bayesian receiver according to exemplary aspects is configured to support the multiple MCMC sampling configurations to enable better trade-off of performance and complexity.

For symbol demodulation, we have identified the mean of the update as the gradient given by H'(Y - HX). Here, vector-level random walk is adopted by stacking Nt transmit symbols as a vector X. Also, a positive-definite preconditioner matrix similar to the one used for MMSE <MAT> is used to steer the walk along the right gradient. Note that <MAT> denotes the measured noise variance in specific receiver antenna. After using gradient as the mean for proposal change, variance can be deduced as inverse of the Hessian (<NUM>nd derivative) as G = inv(H'H). Further, columns of this inverse matrix G are normalized to <NUM>. In an exemplary aspect, proposals for samples are generated using Gaussian random numbers as shown in Equation (<NUM>): <MAT>.

R denotes a Nt dimensional vector of complex Gaussian random numbers and k is a constant.

Similar to the MH-GD algorithm for channel estimation, acceptance probability is calculated using NLP of target posterior distribution, which is same as likelihood function, given as norm of |Y - HX|. Proposed symbols are either accepted or rejected according to (see <FIG>). Detailed MH-GD algorithm for Symbol demodulation is outlined below. <IMG>
<IMG>.

Similar to MH-GD channel estimation, usage of gradient and hessian helps the MH-GD symbol demodulation algorithm to converge faster as well. Hence, BER results show remarkable improvement with MH-GD even with small number of sample draws and parallel samplers.

Again with reference to <FIG>, flowchart <NUM> illustrates a MCMC MH-GD sampling method for Symbol Demodulation according to an exemplary aspect. In flowchart <NUM>, operation 710A is selected for Symbol demodulation, and the flowchart <NUM> illustrates an exemplary draw procedure for the above MH-GD algorithm for Symbol demodulation structure flow. In this aspect, operation 710B is not performed, and the flow skips operation <NUM>.

Again, the flowchart <NUM> starts at operation <NUM> and transitions to operation <NUM> (only 710A in this aspect). Only operation 710A is performed in the MCMC MH-GD Sampling method for Symbol demodulation flow structure (algorithm). That is, operation 710B is omitted.

In Operation 710A, Mean and Variance for Proposal PDF is calculated. In an exemplary aspect, the vector mean µ and variance σ<NUM> are deduced from the Gradient and the Hessian as follows: <MAT> wherein G = inv(H'H), inverse of the Hessian matrix column- normalized to <NUM> and k = max(|Y - HXi-<NUM>|, Q_d) is a vector of constants that factors in previous error residual and also avoids high SNR stalling by accounting for minimum distance between QAM symbols, Q_d.

After operation 710A, the flowchart <NUM> transitions to operation <NUM>, where two Gaussian random vectors (Nt dimensional) with mean = <NUM>, variance = <NUM> are drawn, denoted as ϕ and ψ. That is, unlike in the channel estimation method, operation <NUM> is omitted.

After operation <NUM>, the flowchart <NUM> transitions to operation <NUM>, where the drawn samples are mapped to the desired Gaussian PDF with mean µ and variance σ<NUM>. In an exemplary aspect, the mapping is based on the following equation: <MAT> <IMG>(µ), <IMG>(µ) refer to real and imaginary parts of mean µ = Xi-<NUM> + (H'H + σ<NUM>I)-<NUM> H'(Y - HX) respectively, ϕ and ψ are zero-mean unit-variance Gaussian random vectors (denoted as R in Equation (<NUM>)) and i denotes the complex imaginary number.

In an exemplary aspect, for symbol demodulation, samples drawn from the conditionals are then mapped onto the closest QAM constellation point according to Equation below. This advantageously is a simple slicing operation in hardware.

Where Q refers to the set of possible discrete QAM modulated symbols.

In an exemplary aspect, the acceptance probability is calculated according to the following equation: <MAT> Xcand denotes the candidate transmitted symbol calculated in operation <NUM> and Xi-<NUM> denotes the transmitted symbol estimated in previous sample draw / iteration for same variable index. Y refers to the received signal and H denotes the estimate of channel coefficients.

If u is less than α, the flowchart <NUM> transitions to operation <NUM>, where the proposal is accepted (Xi = Xcand).

If u is greater than or equal to α, the flowchart <NUM> transitions to operation <NUM>, where the proposal is rejected (Xi = Xi-<NUM>).

In an exemplary aspect, the MCMC sampler <NUM> may be configured to perform joint sampling for Channel Estimation and Symbol demodulation, where both channel coefficients and symbols are drawn using the MH-GD method using respective proposal and acceptance distributions. As can be appreciated, the algorithm for such joint sampling would be formed from the merging of the MH-GD algorithm for channel estimation and the MH-GD algorithm for Symbol demodulation. As will be appreciated, the process flow for joint sampling for Channel Estimation and Symbol demodulation would include the combination of the process flows for MH-GD Sampling based Channel Estimation and MH-GD Sampling based Symbol demodulation. Further, obtaining channel estimate H entails performing operations <NUM>-<NUM> according to flowchart <NUM> as described above while symbol demodulation X entails performing operations <NUM>-<NUM> according to flowchart <NUM> as described above.

In exemplary aspects, the receiver <NUM> is configured such that probability priors can be iteratively passed between the symbol demodulator <NUM> and the decoder <NUM>. Advantageously, the receiver <NUM> according to exemplary aspects is configured such that the computing of LLRs by the receiver <NUM> (e.g. by the decoder <NUM>) is not longer for the decoding operations by the decoder <NUM>. This advantageously reduces the computation time by the receiver <NUM> as the calculation of LLRs generally require extension computation. In these examples, the MCMC-based structure according to exemplary aspects allows for a single, unified hardware.

In an exemplary aspect, the demodulator <NUM> is configured to perform a Gibbs-based Markov Chain Monte Carlo (MCMC) methods, which has near optimal performance at low signal-to-noise-ratio (SNR) and to have efficient hardware implementations. In exemplary aspect, the method includes a random walk through the permutations of the transmitted bit sequence to estimate the posterior probability distribution and accordingly generate soft-output information.

In an exemplary aspect, for a system with NR receive antennas, NT transmit antennas, a transmitted symbol vector <MAT>, a received symbol vector <MAT>, a channel response matrix <MAT>, with additive gaussian noise power <MAT>, the Gibbs-MCMC MIMO demodulation algorithm satisfies the following pseudo-code:
<IMG>.

MCMC detectors may experience a performance degradation at higher SNR values. This issue is caused by stalling at high SNR. In an exemplary aspect, to reduce or avoid degrading performance, receiver <NUM> can include a sampler <NUM> that is configured to determine the variance based on the quantization noise power <MAT> to reduce or eliminate stalling at high SNR. In an exemplary aspect, to determine the variance based on the quantization noise power, the sampler <NUM> can replace the Gaussian noise power <MAT> in the calculation of the variance <MAT> with <MAT>, where: <MAT>.

This substitution results in the variance <MAT> being calculated based on the following Equation (<NUM>): <MAT>.

With the modified variance calculation, the Gibbs-MCMC MIMO demodulation algorithm is updated as shown below in pseudo-code Listing <NUM>:
<IMG>.

In an exemplary aspect, the decoder <NUM> is configured as a Metropolis-Hastings MCMC (MH-MCMC) LDPC decoder. In this example, the decoder <NUM> is configured to receive, as inputs: a parity check matrix (H ∈ RK×N), and <NUM>) an Initial log-likelihood ratio (LLR ∈ RN×<NUM>) for each bit in the received code word.

In an exemplary aspect, the decoder <NUM> is configured to precompute, before iterating:.

With the initial starting point, the decoder <NUM> can iterate through the MH-MCMC algorithm as shown below. In an exemplary aspect, it is assumed a maximum of <NUM>-bit flip per iteration, which can be generalized to multiple bits as would be understood by one of ordinary skill in the art. In an exemplary aspect, the MH-MCMC algorithm includes the following operations:.

In the above algorithm, Operation <NUM> uses the syndrome to compute the number of failing parity check equations each bit belongs to and weights them by a measure of confidence (the probability that the bit is in error; i.e. if the bit is currently assumed to be a "<NUM>", what is the probability it is actually a "<NUM>", and vice versa).

Operations <NUM> and <NUM> normalize these probabilities and uses a uniform random number to select a candidate bit B to flip.

Operations <NUM> and <NUM> compute the updated codeword and syndrome.

Operations <NUM> and <NUM> perform the Metropolis-Hastings step by computing an acceptance ratio based upon the number of failing parity check equations in the syndrome. If accepted, operation <NUM> also updates our confidence measure of the flipped bit.

Operation <NUM>: at the end of N iterations, the sampled code words are averaged to derive the posterior bit distributions.

Advantageously, the result is several orders of magnitude reduction in the number of iterations compared to Gibbs-MCMC algorithm, while matching or exceeding the performance of a general belief propagation (BP) decoder.

In an exemplary aspect, the decoder <NUM> is a MH-MCMC FEC decoder (e.g. LDPC decoder), and is configured to decode the bits based on the raw probability that the bit is "<NUM>", which is calculated by averaging the demodulated symbols samples (e.g. see operation <NUM> in Listing <NUM>). In this aspect, the raw probability is used instead of a calculated bit log-likelihood ratios (LLRs) (see operation <NUM> of Listing <NUM> where LLR are calculated). In an exemplary aspect, after a round of iterations from the MH-MCMC FEC decoder <NUM>, information is passed back information to the MCMC MIMO demodulator <NUM>. In an exemplary aspect, to pass back information, <MAT> is updated as <MAT> (Equation <NUM>) and µj is updated as µJOINT (Equation <NUM>), as follows: <MAT> <MAT> where µFEC and <MAT> are the straightforward calculation of the mean and variance of the transmitted symbols based upon the bit-probabilities derived at the end of the MH-MCMC FEC decoder <NUM>.

Listing <NUM> shows the updated pseudo-code for the MCMC MIMO demodulator <NUM> according to an exemplary aspect. It should be noted that µFEC and <MAT> are initialized to <NUM> and ∞ at the start of the first iteration before feedback information from the MH-MCMC LDPC decoder <NUM> is available. Under those conditions, the calculations in Listing <NUM> simplify to Listing <NUM>.

The aforementioned description of the specific aspects will so fully reveal the general nature of the disclosure that others can, by applying knowledge within the skill of the art, readily modify and/or adapt for various applications such specific aspects, without undue experimentation, and without departing from the general concept of the present disclosure. Therefore, such adaptations and modifications are intended to be within the meaning of the disclosed aspects, based on the teaching and guidance presented herein. It is to be understood that the phraseology or terminology herein is for the purpose of description and not of limitation, such that the terminology or phraseology of the present specification is to be interpreted by the skilled artisan in light of the teachings and guidance.

References in the specification to "one aspect," "an aspect," "an exemplary aspect," etc., indicate that the aspect described may include a particular feature, structure, or characteristic, but every aspect may not necessarily include the particular feature, structure, or characteristic. Moreover, such phrases are not necessarily referring to the same aspect. Further, when a particular feature, structure, or characteristic is described in connection with an aspect, it is submitted that it is within the knowledge of one skilled in the art to affect such feature, structure, or characteristic in connection with other aspects whether or not explicitly described.

The exemplary aspects described herein are provided for illustrative purposes, and are not limiting. Other exemplary aspects are possible, and modifications may be made to the exemplary aspects. Therefore, the specification is not meant to limit the disclosure. Rather, the scope of the disclosure is defined only in accordance with the following claims.

Aspects may be implemented in hardware (e.g., circuits), firmware, software, or any combination thereof. Aspects may also be implemented as instructions stored on a machine-readable medium, which may be read and executed by one or more processors. A machine-readable medium may include any mechanism for storing or transmitting information in a form readable by a machine (e.g., a computing device). For example, a machine-readable medium may include read only memory (ROM); random access memory (RAM); magnetic disk storage media; optical storage media; flash memory devices; electrical, optical, acoustical or other forms of propagated signals (e.g., carrier waves, infrared signals, digital signals, etc.), and others. Further, firmware, software, routines, instructions may be described herein as performing certain actions. However, it should be appreciated that such descriptions are merely for convenience and that such actions in fact results from computing devices, processors, controllers, or other devices executing the firmware, software, routines, instructions, etc. Further, any of the implementation variations may be carried out by a general purpose computer.

For the purposes of this discussion, the term "processor circuitry" shall be understood to be circuit(s), processor(s), logic, or a combination thereof. For example, a circuit includes an analog circuit, a digital circuit, state machine logic, other structural electronic hardware, or a combination thereof. A processor includes a microprocessor, a digital signal processor (DSP), central processing unit (CPU), application-specific instruction set processor (ASIP), graphics and/or image processor, multi-core processor, or other hardware processor. The processor can be "hard-coded" with instructions to perform corresponding function(s) according to aspects described herein. Alternatively, the processor can access an internal and/or external memory to retrieve instructions stored in the memory, which when executed by the processor, perform the corresponding function(s) associated with the processor, and/or one or more functions and/or operations related to the operation of a component having the processor included therein.

In one or more of the exemplary aspects described herein, processor circuitry can include memory that stores data and/or instructions. The memory can be any well-known volatile and/or non-volatile memory, including, for example, read-only memory (ROM), random access memory (RAM), flash memory, a magnetic storage media, an optical disc, erasable programmable read only memory (EPROM), register, and programmable read only memory (PROM). The memory can be non-removable, removable, or a combination of both.

Various aspects herein may utilize one or more machine learning models to perform corresponding functions of the communication device, such as the receiver (or other functions described herein). The term "model" as, for example, used herein may be understood as any kind of algorithm, which provides output data from input data (e.g., any kind of algorithm generating or calculating output data from input data). A machine learning model may be executed by a computing system to progressively improve performance of a specific task. In some aspects, parameters of a machine learning model may be adjusted during a training phase based on training data. A trained machine learning model may then be used during an inference phase to make predictions or decisions based on input data.

The machine learning models described herein may take any suitable form or utilize any suitable techniques. For example, any of the machine learning models may utilize supervised learning, semi-supervised learning, unsupervised learning, or reinforcement learning techniques.

In supervised learning, the model may be built using a training set of data that contains both the inputs and corresponding desired outputs. Each training instance may include one or more inputs and a desired output. Training may include iterating through training instances and using an objective function to teach the model to predict the output for new inputs. In semi-supervised learning, a portion of the inputs in the training set may be missing the desired outputs.

In unsupervised learning, the model may be built from a set of data which contains only inputs and no desired outputs. The unsupervised model may be used to find structure in the data (e.g., grouping or clustering of data points) by discovering patterns in the data. Techniques that may be implemented in an unsupervised learning model include, e.g., self-organizing maps, nearest-neighbor mapping, k-means clustering, and singular value decomposition.

A machine learning model described herein may be or may include a neural network. The neural network may be any kind of neural network, such as a Bayesian neural network. Such a neural network may include any number of layers. The training of the neural network (e.g., adapting the layers of the neural network) may use or may be based on any kind of training principle, such as backpropagation (e.g., using the backpropagation algorithm).

Aspects of the present disclosure and any of the radio links described herein may operate according to any one or more of the following radio communication technologies and/or standards including but not limited to: a Global System for Mobile Communications (GSM) radio communication technology, a General Packet Radio Service (GPRS) radio communication technology, an Enhanced Data Rates for GSM Evolution (EDGE) radio communication technology, and/or a Third Generation Partnership Project (3GPP) radio communication technology, for example Universal Mobile Telecommunications System (UMTS), Freedom of Multimedia Access (FOMA), 3GPP Long Term Evolution (LTE), 3GPP Long Term Evolution Advanced (LTE Advanced), Code division multiple access <NUM> (CDMA2000), Cellular Digital Packet Data (CDPD), Mobitex, Third Generation (<NUM>), Circuit Switched Data (CSD), High-Speed Circuit-Switched Data (HSCSD), Universal Mobile Telecommunications System (Third Generation) (UMTS (<NUM>)), Wideband Code Division Multiple Access (Universal Mobile Telecommunications System) (W-CDMA (UMTS)), High Speed Packet Access (HSPA), High-Speed Downlink Packet Access (HSDPA), High-Speed Uplink Packet Access (HSUPA), High Speed Packet Access Plus (HSPA+), Universal Mobile Telecommunications System-Time-Division Duplex (UMTS-TDD), Time Division-Code Division Multiple Access (TD-CDMA), Time Division-Synchronous Code Division Multiple Access (TD-CDMA), 3rd Generation Partnership Project Release <NUM> (Pre-4th Generation) (3GPP Rel. <NUM> (Pre-<NUM>)), 3GPP Rel. <NUM> (3rd Generation Partnership Project Release <NUM>), 3GPP Rel. <NUM> (3rd Generation Partnership Project Release <NUM>) , 3GPP Rel. <NUM> (3rd Generation Partnership Project Release <NUM>), 3GPP Rel. <NUM> (3rd Generation Partnership Project Release <NUM>), 3GPP Rel. <NUM> (3rd Generation Partnership Project Release <NUM>), 3GPP Rel. <NUM> (3rd Generation Partnership Project Release <NUM>), 3GPP Rel. <NUM> (3rd Generation Partnership Project Release <NUM>), 3GPP Rel. <NUM> (3rd Generation Partnership Project Release <NUM>), 3GPP Rel. <NUM> (3rd Generation Partnership Project Release <NUM>) and subsequent Releases (such as Rel. <NUM>, Rel. <NUM>, etc.), 3GPP <NUM>, <NUM>, <NUM> New Radio (<NUM> NR), 3GPP <NUM> New Radio, 3GPP LTE Extra, LTE-Advanced Pro, LTE Licensed-Assisted Access (LAA), MuLTEfire, UMTS Terrestrial Radio Access (UTRA), Evolved UMTS Terrestrial Radio Access (E-UTRA), Long Term Evolution Advanced (4th Generation) (LTE Advanced (<NUM>)), cdmaOne (<NUM>), Code division multiple access <NUM> (Third generation) (CDMA2000 (<NUM>)), Evolution-Data Optimized or Evolution-Data Only (EV-DO), Advanced Mobile Phone System (1st Generation) (AMPS (<NUM>)), Total Access Communication System/Extended Total Access Communication System (TACS/ETACS), Digital AMPS (2nd Generation) (D-AMPS (<NUM>)), Push-to-talk (PTT), Mobile Telephone System (MTS), Improved Mobile Telephone System (IMTS), Advanced Mobile Telephone System (AMTS), OLT (Norwegian for Offentlig Landmobil Telefoni, Public Land Mobile Telephony), MTD (Swedish abbreviation for Mobiltelefonisystem D, or Mobile telephony system D), Public Automated Land Mobile (Autotel/PALM), ARP (Finnish for Autoradiopuhelin, "car radio phone"), NMT (Nordic Mobile Telephony), High capacity version of NTT (Nippon Telegraph and Telephone) (Hicap), Cellular Digital Packet Data (CDPD), Mobitex, DataTAC, Integrated Digital Enhanced Network (iDEN), Personal Digital Cellular (PDC), Circuit Switched Data (CSD), Personal Handy-phone System (PHS), Wideband Integrated Digital Enhanced Network (WiDEN), iBurst, Unlicensed Mobile Access (UMA), also referred to as also referred to as 3GPP Generic Access Network, or GAN standard), Zigbee, Bluetooth(r), Wireless Gigabit Alliance (WiGig) standard, mmWave standards in general (wireless systems operating at <NUM>-<NUM> and above such as WiGig, IEEE <NUM>. 11ad, IEEE <NUM>. 11ay, etc.), technologies operating above <NUM> and THz bands, (3GPP/LTE based or IEEE <NUM>. 11p and other) Vehicle-to-Vehicle (V2V) and Vehicle-to-X (V2X) and Vehicle-to-Infrastructure (V2I) and Infrastructure-to-Vehicle (I2V) communication technologies, 3GPP cellular V2X, DSRC (Dedicated Short Range Communications) communication systems such as Intelligent-Transport-Systems and others (typically operating in <NUM> to <NUM> or above (typically up to <NUM> following change proposals in CEPT Report <NUM>)), the European ITS-G5 system (i.e. the European flavor of IEEE <NUM>. 11p based DSRC, including ITS-G5A (i.e., Operation of ITS-G5 in European ITS frequency bands dedicated to ITS for safety related applications in the frequency range <NUM>,<NUM> to <NUM>,<NUM>), ITS-G5B (i.e., Operation in European ITS frequency bands dedicated to ITS non- safety applications in the frequency range <NUM>,<NUM> to <NUM>,<NUM>), ITS-G5C (i.e., Operation of ITS applications in the frequency range <NUM>,<NUM> to <NUM>,<NUM>)), DSRC in Japan in the <NUM> band (including <NUM> to <NUM>) etc..

Besides cellular applications, specific applications for vertical markets may be addressed such as PMSE (Program Making and Special Events), medical, health, surgery, automotive, low-latency, drones, etc. applications.

Aspects described herein can also implement a hierarchical application of the scheme is possible, e.g. by introducing a hierarchical prioritization of usage for different types of users (e.g., low/medium/high priority, etc.), based on a prioritized access to the spectrum e.g. with highest priority to tier-<NUM> users, followed by tier-<NUM>, then tier-<NUM>, etc. users, etc..

Aspects described herein can also be applied to different Single Carrier or OFDM flavors (CP-OFDM, SC-FDMA, SC-OFDM, filter bank-based multicarrier (FBMC), OFDMA, etc.) and in particular 3GPP NR (New Radio) by allocating the OFDM carrier data bit vectors to the corresponding symbol resources.

Claim 1:
A receiver (<NUM>) of a communication device (<NUM>), comprising:
channel estimating means (<NUM>) for receiving a signal and estimating channel coefficients;
symbol demodulating means (<NUM>) for demodulating the received signal and estimate transmitted symbols based on the channel coefficients;
decoding means (<NUM>) for decoding the estimated transmitted symbols to generate an output bit sequence; and
sampling means (<NUM>) for generating samples based on the channel coefficients, the transmitted symbols, or the output bit sequence, using Markov-Chain Monte-Carlo, MCMC, sampling, the generated samples being used in one or more of: the channel estimation, the demodulation, and the decoding,
the receiver being characterized in that the sampling means (<NUM>) is reconfigurable for determining likelihood information and a priori information, in order to perform the channel estimation, the demodulation, and the decoding,
and in that the sampling means (<NUM>) comprises a mean and variance calculation logic (<NUM>) for likelihood distribution that is shared between channel estimation and symbol demodulation.