WO2021197606A1

WO2021197606A1 - Receiver devices and methods for multicarrier modulation schemes

Info

Publication number: WO2021197606A1
Application number: PCT/EP2020/059426
Authority: WO
Inventors: Kamel TOURKI; Merouane Debbah; Rostom ZAKARIA
Original assignee: Huawei Technologies Co., Ltd.
Priority date: 2020-04-02
Filing date: 2020-04-02
Publication date: 2021-10-07
Also published as: EP4094411A1; CN115244902A

Abstract

A receiver device is disclosed that, in a current transmission slot, determines a plurality of signature roots, obtains predicted channel state information (CSI) of a communication channel for a next transmission slot, determines a radius of a circle, and provides a feedback message to a transmitter device. Moreover, a further receiver device is disclosed that, in a current transmission slot, determines a plurality of signature roots, obtains estimated CSI of a communication channel for the current transmission slot, determines a radius of a circle, performs a demodulation of a multicarrier modulated signal to obtain a demodulated signal, determines a signal-to-interference-plus-noise ratio for a subcarrier, performs a first equalization on a first set of subcarriers of the demodulated signal, performs a second equalization on a second set of subcarriers of the multicarrier modulated signal, and obtains an output signal.

Description

RECEIVER DEVICES AND METHODS FOR MULTICARRIER MODULATION

SCHEMES TECHNICAL FIELD

The present disclosure relates generally to the field of multicarrier systems, particularly to receiver devices of multicarrier systems. To this end, two receiver devices, a transceiver device, and methods are disclosed, e.g., for time-frequency domain Lagrange- Vandermonde Division Multiplexing (LVDM) or Vandermonde-Lagrange Division Multiplexing (VLDM) equalization in doubly selective (time and frequency selective) channels.

The disclosed receiver devices may perform a channel prediction (e.g., obtain channel state information (CSI) for a next transmission slot) and/or a channel estimation (e.g., obtain CSI for a current transmission slot). The predicted CSI may be used, e.g., to build the transceiver blocks for the next LVDM symbols transmission. The estimated CSI may be used for feeding a detector, in particular a detector of the receiver device, for performing an equalization.

BACKGROUND

An example of a conventional orthogonal frequency division multiplexing (OFDM)-based scheme is the Zero-Padding (ZP) OFDM scheme. In frequency selective channels, the ZP- OFDM scheme may enable an inter-symbol interference (ISI) cancellation. For example, assuming that K subcarriers have been used in the ZP-OFDM scheme, the frequency domain received signal (at the output of the demodulator) is given by Eq. (1):

ponse channel at the k^th subcarrier, and A is a Discrete Fourier Transform (DFT) K x K matrix given by Eq. However, it has an issue that the symbol ¾v transmitted on the k^th subcarrier cannot be recovered when it is hit by a channel zero (H_k — 0).

Moreover, some conventional devices perform a time-domain channel estimation procedure, e.g., the time-domain channel may be estimated for multicarrier signals in a fast and frequency- selective Rayleigh fading channel. However, an issue of such conventional devices is that, as a consequence of the time- varying channel, the orthogonality between subcarriers is destroyed, resulting in inter-carrier interference (ICI). The ICI may further increase an irreducible error floor in proportion to the normalized Doppler frequency. Moreover, some conventional devices and methods are based on a technique that exploits the time-selective channel as a provider of time diversity. However, such devices have an issue of complexity. For example, when K (the number of subcarriers) increases, such conventional devices demand a very high computation and may not be feasible in a practical system. Besides, some conventional devices may exploit the temporal diversity in the time-varying channel by using a Decision Feedback Equalization (DFE) technique. The DFE technique assumes that, in a time-varying channel, most of the symbol energy may be distributed over a few subcarriers and that the ICI power on a subcarrier may originate from several neighboring subcarriers. Moreover, the channel matrix may be approximated by the band matrix and by neglecting the ICI that is coming from faraway subcarriers.

However, such conventional devices have an issue that, for example, the bit error rate (BER) performance may be saturated (BER floor) for banded schemes at moderate signal-to-noise ratios (SNRs). Another issue of such conventional devices is the complexity, which increases with the number of sub carriers.

SUMMARY

In view of the above-mentioned problems and disadvantages, embodiments of the present disclosure aim to improve receiver devices, transceiver devices, and methods for multicarrier modulation schemes. An objective is to provide an advanced receiver for LVDM or VLDM that is able to deal with doubly selective channels.

The objective is achieved by the embodiments of the present disclosure as described in the enclosed independent claims. Advantageous implementations of the embodiments of the present disclosure are further defined in the dependent claims.

In particular, the devices (e.g., the receiver devices) and methods of the present disclosure may use a two-stage-based time-frequency domain equalization. For example, channel estimation and channel prediction are presented. The channel estimation part (e.g., obtaining CSI for a current transmission slot) may feed the detector of the receiver device for performing an equalization while the channel prediction output (e.g., obtaining a predicted CSI for a next transmission slot) may be used, e.g., to build the transceiver blocks for the next LVDM symbols transmission.

In the following, for the sake of simplicity, the discussion is primarily focused on the LVDM scheme, without limiting the present disclosure to the LVDM scheme. A corresponding discussion for the VLDM scheme can be derived by the skilled person.

A first improvement of the conventional devices and methods resulted in an exemplary transceiver device for multicarrier modulation scheme, the transceiver device comprising a receiver device and a transmitter device. This transceiver device is described in the following (FIG. 19 and FIG. 20), because it simplifies the understanding of the embodiments of the present disclosure and their advantages, which will be described below. Further, the exemplary transceiver device (including a transmitter device and a receiver device) lays a basis for the embodiments of the present disclosure, and shares some advantageous properties with these embodiments. FIG. 19 depicts an exemplary scheme of a transceiver device 1900 comprising a transmitter device 1910 using a Lagrange matrix for modulation and a receiver device 1920 using a Vandermonde matrix for demodulation.

Moreover, a new waveform generalizing the ZP-OFDM, referred to as LVDM, has been proposed, where the perfect recovery (PR) condition has been satisfied. The LVDM relies on a one-tap equalization leading to a low-complexity implementation of the transceiver device 1900.

In the block diagram of the LV modulator of FIG. 19, the transceiver device 1900 (i.e., being based on an LV modulator) is exemplarily shown for K signature roots, which will be defined below.

In the following, a discussion for the transceiver device 1900 is presented based on the LVDM in frequency selective channels. Generally, the LV modulator uses K distinct nonzero complex points {/¾}>= l , referred to as signature roots, which are chosen uniformly spread jmk over a circle of radius “a”, such that p_k = ae «

The transmitter device 1910 includes a precoder 1901, a modulator 1902, and a ZP block 1903.

The precoder 1901 may apply the tuning factors K_k, for example, for allocating the determined transmit power, which may be a KxK diagonal matrix W, as shown in FIG. 19.

Here, and without limiting the present disclosure, it is assumed that all transmit filters have a same energy, thus

Moreover, the modulator 1902 uses the Lagrange matrix R, which has a size of KxK (for example, it may construct a Lagrange matrix and may further generate a multicarrier modulated signal based on the Lagrange matrix). The Lagrange matrix R of size KxK may be as follows: Furthermore, the ZP block 1903 may be used for the zero-padding procedure, where every input block of K symbols may be trailed by L zeros. Therefore, it may provide and may further output block symbols with the length of P, where P =K + L.

Moreover, the communication channel of the transceiver device 1900 comprises the transmitter (Tx) filter 1904 and the receiver (Rx) filter 1906. For example, the transmitter filter 1904 and the receiver filter 1906 may be raised cosine filters. Moreover, the communication channel of the transceiver device 1900 comprises the parameter C 1905, which is a propagation channel of order L and may be obtained according to Eq. (4):

Eq. (4)

Furthermore, the convolution of the transmitter filter 1904, the parameter C 1905, and the receiver filter 1906 may be given by a channel matrix H (frequency selective channels).

The transceiver device 1900 further comprises the receiver device 1920, which includes the demodulator 1907, the one-tap Equalizer unit 1908, and the decision block 1909.

The demodulator 1907 performs a demodulation based on constructing a matrix E, which is a Vandermonde matrix having a size of KxP, as follows:

The one-tap equalizer 1908 uses a KxK diagonal matrix, and a convolution of the modulation, channel, and demodulation, is given by:

Therefore, the demodulated signal may be obtained according to Eq. (7) as follows:

and the one tap-equalization is given by:

Here, for example, a perfect recovery of s is satisfied.

Next, the decision block 1909 of the transceiver device 1900 and the signaling exchange of a modified, optimized radius of the circle ( a_opt ) will be discussed. Reference is made to FIG. 20, which is a schematic view for signaling exchange, the signaling indicating the modified radius a_opt of a circle. For example, the plurality of signature roots ( p_k ) may be uniformly distributed on the circumference of the circle, e.g., uniformly spread over a circle of radius a, such that p_k = jmk ae i< Moreover, the radius “a” may be modified (e.g., optimized) at the receiver device 1920, then the optimized radius ( a_opt ) may be fed back to the transmitter device 1910, for example, to build the precoder 1901 and the modulator 1902, as it is shown in FIG. 20. An optimization block 2002 is provided that needs channel state information, which can be obtained from the channel estimation unit 2001, to compute an optimization metric. Further, the optimization block 2002 may compute the modified radius a_opt. Moreover, a signalling 2003 may be sent to feedback the modified, optimized radius a_opt to the transmitter device 1910, which may be required for the modulator 1902 and the precoder 1901.

Furthermore, the receiver device 1920 may use the modified, optimized radius a_opt to compute the demodulation matrix.

Moreover, in time-selective channels, the orthogonality between subcarriers may be destroyed and the matrix D (see above in Eq. (8)) may not be diagonal anymore. Consequently, inter carrier interference (ICI) appears and the one-tap equalization techniques may become inadequate for detection. Furthermore, the signaling exchange of the signature roots’ radius a_opt becomes challenging in time-varying channels.

The receiver devices and methods of the present disclosure enable dealing with doubly (time and frequency) selective channels while maintaining the low complexity of the transceiver implementation.

A first aspect of the present disclosure provides a receiver device for a multicarrier modulation scheme, the receiver device being configured to, in a current transmission slot, determine a plurality of signature roots, wherein each signature root of the plurality of signature roots is a nonzero complex point; obtain predicted CSI of a communication channel between the receiver device and a transmitter device for a next transmission slot; determine a first radius of a circle based on the predicted CSI, wherein the determined plurality of signature roots are uniformly distributed on a circumference of the circle; and provide a feedback message to the transmitter device, the feedback message indicating the first radius of the circle. The receiver device may be a receiver for a transceiver device of the multicarrier modulation scheme. The receiver device is an advanced receiver for LVDM or VLDM, in that it is able to deal with doubly selective channels.

The receiver device may be an electronic device comprising circuitry. The circuitry may comprise hardware and software. The hardware may comprise analog or digital circuitry, or both analog and digital circuitry. In some embodiments, the circuitry comprises one or more processors and a non-volatile memory connected to the one or more processors. The non volatile memory may carry executable program code which, when executed by the one or more processors, causes the device to perform the operations or methods described herein.

According to some embodiments, a channel estimation and a channel prediction may be done. The channel estimation part may feed the detector (i.e., for the equalization), while the channel prediction may be used to build the transceiver blocks for the next LVDM symbols transmission (during a next transmission slot).

According to some embodiments, the receiver device may be adapted (e.g., it may perform two equalizations, comprising a first equalization and a second equalization, which may be different from each other) based on a performance-complexity trade-off that the multicarrier system should satisfy.

In an implementation form of the first aspect, the receiver device is further configured to obtain estimated CSI of the communication channel for the current transmission slot; determine a second radius of a further circle based on the estimated CSI, wherein the determined plurality of signature roots are uniformly distributed on a circumference of the further circle; construct a Lagrange matrix or a Vandermonde matrix based on the plurality of signature roots; and perform a demodulation of a multicarrier modulated signal received from the transmitter device, based on the Lagrange matrix or the Vandermonde matrix to obtain a demodulated signal.

In a further implementation form of the first aspect, the receiver device is further configured to determine a signal-to-interference-plus-noise ratio (SINR) for at least one subcarrier of the demodulated signal; perform a first equalization for a first set of subcarriers having a SINR value equal to or above a threshold value to obtain an equalized first set of subcarriers; perform a second equalization for a second set of subcarriers having a SINR value below the threshold value to obtain an equalized second set of subcarriers; and obtain an equalized demodulated signal based on a combination of the equalized first set of subcarriers and the equalized second set of sub carriers.

For example, the receiver device may determine the SINR at the k-th subcarrier according to Eq. (9):

and S₂ are the sub carrier sets given by

Eq. (10) where

For example, the receiver device may perform the first equalization for the first set of subcarriers (i.e. 5_C) and perform the second equalization for the second set of subcarriers (i.e., ¼)·

A second aspect of the present disclosure provides a receiver device for a multicarrier modulation scheme, the receiver device being configured to, in a current transmission slot, determine a plurality of signature roots, wherein each signature root of the plurality of signature roots is a nonzero complex point; obtain estimated C SI of a communication channel between the receiver device and a transmitter device for the current transmission slot; determine a first radius of a circle based on the estimated CSI, wherein the determined plurality of signature roots are uniformly distributed on a circumference of the circle; construct a Lagrange matrix or a Vandermonde matrix based on the plurality of signature roots; perform a demodulation of a multicarrier modulated signal received from the transmitter device, based on the Lagrange matrix or the Vandermonde matrix, to obtain a demodulated signal; determine a SINR for at least one subcarrier based on the demodulated signal and the determined first radius of the circle; perform a first equalization on a first set of subcarriers of the demodulated signal, the first set of subcarriers having a SINR value equal to or above a threshold value, to obtain an equalized demodulated signal; perform a second equalization on a second set of sub carriers of the multicarrier modulated signal received from the transmitter device, the second set of subcarriers having a SINR value below the threshold value, to obtain an equalized modulated signal; and obtain an output signal based on a combination of the equalized demodulated signal and the equalized modulated signal.

The receiver device of the second aspect may be similar or identical to the receiver device of the first aspect and may perform a similar or identical function. The receiver device is an advanced receiver device for LVDM or VLDM, in that it is able to deal with doubly selective channels.

The receiver device may determine the SINR. The SINR may be determined according to Eq. (9) to Eq. (11), as discussed above.

Moreover, the receiver device may perform the first equalization for the first set of subcarriers (i.e., 5_X) for obtaining equalized demodulated signal, and may perform the second equalization for the second set of subcarriers (i.e., S₂) for obtaining equalized modulated signal.

In an implementation form of the second aspect, the receiver device is further configured to obtain predicted CSI of the communication channel for a next transmission slot; determine a second radius of a further circle based on the predicted CSI, wherein the determined plurality of signature roots are uniformly distributed on a circumference of the further circle; and provide a feedback message to the transmitter device, the feedback message indicating the second radius of the further circle.

In a further implementation form of the second aspect, the receiver device is further configured to compute a metric for evaluating the first radius of the circle and/or the second radius of the further circle to obtain a modified first radius of the circle and/or a modified second radius of the further circle; and provide a feedback message to the transmitter device, the feedback message indicating the modified first radius of the circle and/or the modified second radius of the further circle. In a further implementation form of the first aspect or the second aspect, the first equalization is based on a zero-forcing (ZF) equalization, comprising an inversion of a diagonal matrix on the first set of subcarriers of the demodulated signal.

For example, the receiver device of the first aspect and/or the receiver device of the second aspect may perform the first equalization for the first set of subcarriers (e.g., 5_C)

For instance, the receiver device may apply the inversion of the diagonal matrix on the first set of subcarriers of the demodulated signal. The receiver device may comprise a decision block which may give s_x = P^), where: s, diag (1./z(S, !l y | S, )

Eq. (12) and z diag(Z) Eq. (13)

In a further implementation form of the first aspect or the second aspect, the second equalization comprises removing a contribution of the first set of subcarriers from the multicarrier modulated signal received from the transmitter device; and applying a minimum mean square error, (MMSE) criteria on the second set of subcarriers of a remainder of the multicarrier modulated signal received from the transmitter device.

For example, the receiver device of the first aspect and/or the receiver device of the second aspect may perform the second equalization for the second set of subcarriers (e.g., S₂).

For instance, the receiver device may remove the contribution of the decided symbols in s_x from the time domain received signal (r) such that: r₂ r - H_t2 R I_, : . S, ) s,

Eq. (14)

Moreover, the receiver device may apply MMSE to r₂, then decide s₂ I1(W r₂ ), as follows: Eq. (15) and

R₂ R ( : , ¾ ) Eq. (16)

Here, R₂ matrix may be formed from R by the columns of indices in S₂.

In a further implementation form of the first aspect or the second aspect, the first equalization is based on a ZF parallel interference cancellation (PIC) equalization, comprising estimating an ICI based on the first set of subcarriers; removing a contribution of the estimated ICI; and applying, after removing the contribution of the estimated ICI, an inversion of a diagonal matrix on a remainder of the demodulated signal.

For example, the receiver device of the first aspect and/or the receiver device of the second aspect may perform the first equalization for the first set of subcarriers (e.g., 5_X)

For instance, the receiver device may use the frequency domain one-tap equalization (1TE) and may estimate ICI such that u = Z^, where:

Eq. (17)

Moreover, the receiver device may remove the contribution of the estimated ICI, and, after removing the contribution of the estimated ICI, it may apply the inversion of the diagonal matrix on the remainder of the demodulated signal as follows:

Eq. (18)

In a further implementation form of the first aspect or the second aspect, the first equalization is based on a MMSE PIC equalization comprising estimating an ICI based on the first set of subcarriers; removing a contribution of the estimated ICI; and applying, after removing the contribution of the estimated ICI, an MMSE matrix on a remainder of the demodulated signal. For example, the receiver device of the first aspect and/or the receiver device of the second aspect may perform the first equalization for the first set of subcarriers (e.g., 5_X)

The receiver device may use the frequency domain MMSE such that: s_x = i sq) Further, the receiver device may obtain ^ according to Eq. (19):

and

Eq. (20)

Moreover, the receiver device may estimate ICI such that Q = ₁s_1, and

Z, = (Z - diag(z)) (:, S, ) Eq. (21)

Further, the receiver device may remove the contribution of the estimated ICI and apply the MMSE matrix according to Eq. (22) as follows:

Eq. (22)

In a further implementation form of the first aspect or the second aspect, the second equalization is based on a MMSE ordered successive interference cancellation (OSIC) equalization comprising removing a contribution of the first set of subcarriers from the multicarrier modulated signal received from the transmitter device; and applying a MMSE OSIC operation on the second set of subcarriers of a remainder of the multicarrier modulated signal received from the transmitter device.

The receiver device may remove the contribution of the decided symbols in s_x from the time domain received signal r such that: eq. (23)

Further, the receiver device may apply the MMSE-OSIC operation to r₂.

For example, let (z₁ z₂, ... , z_Kf) be the order of the indices of the detected symbols, and H_Zi = H = H_t2R₂. Further, the receiver device may obtain R₂ according to Eq. (24) as follows:

* R * R* V I · ». ^V SZ_o) / Eq. (24)

Furthermore,

1. at the n-th iteration, n = 1: K₂, and K₂ = card(S₂ ), the MMSE may be carried out using Eq. (25):

Eq. (25) where H_z is the matrix H obtained after removing the columns indexed by (z z₂, ... , z_n-1).

2. The index of the selected symbol to be detected during the n- th iteration may be obtained according to Eq. (26):

Eq. (26) where f₍ are given by Eq. (27):

and h₍ given by:

Eq. (28)

3. The receiver device may obtain s_Zn through a hard decision on Eq. (29)

where

and

Eq. (31)

In summary, the receiver device of the first aspect and the receiver device of the second aspect are designed to deal with doubly selective channels, such as doubly selective fading channels, without limiting the present disclosure to specific channels.

A third aspect of the present disclosure provides a transceiver device comprising a transmitter device configured to generate a multicarrier modulated signal based on constructing a Lagrange matrix or a Vandermonde matrix; and a receiver device according to according to the first aspect or any of its implementation forms or a receiver device according to the second aspect or any of its implementation forms.

A fourth aspect of the present disclosure provides a method for a receiver device for a multicarrier modulation scheme, wherein the method comprises, in a current transmission slot, determining a plurality of signature roots, wherein each signature root of the plurality of signature roots is a nonzero complex point; obtaining predicted CSI of a communication channel between the receiver device and a transmitter device for a next transmission slot; determining a first radius of a circle based on the predicted CSI, wherein the determined plurality of signature roots are uniformly distributed on a circumference of the circle; and providing a feedback message to the transmitter device, the feedback message indicating the first radius of the circle.

In an implementation form of the fourth aspect, the method further comprises obtaining estimated CSI of the communication channel for the current transmission slot; determining a second radius of a further circle based on the estimated CSI, wherein the determined plurality of signature roots are uniformly distributed on a circumference of the further circle; constructing a Lagrange matrix or a Vandermonde matrix based on the plurality of signature roots; and performing a demodulation of a multicarrier modulated signal received from the transmitter device, based on the Lagrange matrix or the Vandermonde matrix to obtain a demodulated signal. In a further implementation form of the fourth aspect, the method further comprises determining a SINR for at least one subcarrier of the demodulated signal; performing a first equalization for a first set of subcarriers having a SINR value equal to or above a threshold value to obtain an equalized first set of subcarriers; performing a second equalization for a second set of subcarriers having a SINR value below the threshold value to obtain an equalized second set of subcarriers; and obtaining an equalized demodulated signal based on a combination of the equalized first set of subcarriers and the equalized second set of subcarriers.

A fifth aspect of the present disclosure provides a method for a receiver device for a multicarrier modulation scheme, wherein the method comprises, in a current transmission slot, determining a plurality of signature roots, wherein each signature root of the plurality of signature roots is a nonzero complex point; obtaining estimated CSI of a communication channel between the receiver device and a transmitter device for the current transmission slot; determining a first radius of a circle based on the estimated CSI, wherein the determined plurality of signature roots are uniformly distributed on a circumference of the circle; constructing a Lagrange matrix or a Vandermonde matrix based on the plurality of signature roots; performing a demodulation of a multicarrier modulated signal received from the transmitter device, based on the Lagrange matrix or the Vandermonde matrix, to obtain a demodulated signal; determining a SINR for at least one subcarrier based on the demodulated signal and the determined first radius of the circle; performing a first equalization on a first set of subcarriers of the demodulated signal, the first set of subcarriers having a SINR value equal to or above a threshold value, to obtain an equalized demodulated signal performing a second equalization on a second set of subcarriers of the multicarrier modulated signal received from the transmitter device, the second set of subcarriers having a SINR value below the threshold value, to obtain an equalized modulated signal; and obtaining an output signal based on a combination of the equalized demodulated signal and the equalized modulated signal.

In an implementation form of the fifth aspect, the method further comprises obtaining predicted CSI of the communication channel for a next transmission slot; determining a second radius of a further circle based on the predicted CSI, wherein the determined plurality of signature roots are uniformly distributed on a circumference of the further circle; and providing a feedback message to the transmitter device, the feedback message indicating the second radius of the further circle. In a further implementation form of the fourth aspect or the fifth aspect, the method further comprises computing a metric for evaluating the first radius of the circle and/or the second radius of the further circle to obtain a modified first radius of the circle and/or a modified second radius of the further circle; and providing a feedback message to the transmitter device, the feedback message indicating the modified first radius of the circle and/or the modified second radius of the further circle.

In a further implementation form of the fourth aspect or the fifth aspect, the first equalization is based on a ZF equalization, comprising an inversion of a diagonal matrix on the first set of subcarriers of the demodulated signal.

In a further implementation form of the fourth aspect or the fifth aspect, the second equalization comprises, removing a contribution of the first set of subcarriers from the multicarrier modulated signal received from the transmitter device; and applying a MMSE criteria on the second set of subcarriers of a remainder of the multicarrier modulated signal received from the transmitter device.

In a further implementation form of the fourth aspect or the fifth aspect, the first equalization is based on a ZF PIC equalization, comprising estimating an ICI based on the first set of subcarriers; removing a contribution of the estimated ICI; and applying, after removing the contribution of the estimated ICI, an inversion of a diagonal matrix on a remainder of the demodulated signal.

In a further implementation form of the fourth aspect or the fifth aspect, the first equalization is based on a MMSE PIC equalization, comprising estimating an ICI based on the first set of subcarriers; removing a contribution of the estimated ICI; and applying, after removing the contribution of the estimated ICI, an MMSE matrix on a remainder of the demodulated signal.

In a further implementation form of the fourth aspect or the fifth aspect, the second equalization is based on a MMSE OSIC equalization comprising removing a contribution of the first set of subcarriers from the multicarrier modulated signal received from the transmitter device; applying a MMSE OSIC operation on the second set of subcarriers of a remainder of the multicarrier modulated signal received from the transmitter device. A sixth aspect of the present disclosure provides a computer program comprising a program code for performing the method according to the fourth aspect or any of its implementation forms or the method according to the fifth aspect or any of its implementation forms.

A seventh aspect of the present disclosure provides a non-transitory storage medium storing executable program code which, when executed by a processor, causes the method according to the fourth aspect or any of its implementation forms or the method according to the fifth aspect or any of its implementation forms to be performed.

It has to be noted that all devices, elements, units and means described in the present application could be implemented in the software or hardware elements or any kind of combination thereof. All steps which are performed by the various entities described in the present application as well as the functionalities described to be performed by the various entities are intended to mean that the respective entity is adapted to or configured to perform the respective steps and functionalities. Even if, in the following description of specific embodiments, a specific functionality or step to be performed by external entities is not reflected in the description of a specific detailed element of that entity which performs that specific step or functionality, it should be clear for a skilled person that these methods and functionalities can be implemented in respective software or hardware elements, or any kind of combination thereof.

BRIEF DESCRIPTION OF THE DRAWINGS

The above described aspects and implementation forms (embodiments of the present disclosure) will be explained in the following description of specific embodiments in relation to the enclosed drawings, in which

FIG. 1 depicts a schematic view of a receiver device for a multicarrier modulation scheme, according to an embodiment of the present disclosure;

FIG. 2 depicts a schematic view of another receiver device for a multicarrier modulation scheme, according to an embodiment of the present disclosure; FIG. 3 depicts a schematic view of a transceiver device for a multicarrier modulation scheme, according to an embodiment of the present disclosure;

FIG. 4 depicts a schematic view of a diagram illustrating a signaling exchange in the transceiver device for a doubly selective channel;

FIG. 5 depicts a diagram illustrating pilot patterns using dedicated LVDM symbols;

FIG. 6 depicts a diagram illustrating NP stacked pilot vectors, where ( NP — 1) are buffered pilot vectors with a new received one;

FIG. 7 depicts a diagram illustrating the receiver device performing a first equalization based on the one-tap equalization (ZF) and a second equalization based on the MMSE;

FIG. 8 depicts a diagram illustrating the receiver device performing a first equalization based on the one-tap equalization (ZF) and a second equalization based on the MMSE-OSIC;

FIG. 9 depicts a diagram illustrating the receiver device performing a first equalization based on the one-tap equalization-PIC and a second equalization based on the MMSE-OSIC;

FIG. 10 depicts a diagram illustrating the receiver device performing a first equalization based on the MMSE-PIC and a second equalization based on the MMSE-OSIC;

FIGS. 11A-11B depict diagrams illustrating performance results of scheme 1 discussed with respect to FIG. 7 and scheme 2 discussed with respect to FIG. 8;

FIGS. 12A-12B depict diagrams illustrating performance results of scheme 3 discussed with respect to FIG. 9 and scheme 4 discussed with respect to FIG. 10; FIGS. 13A-13B depict diagrams illustrating performance results of scheme 1 discussed with respect to FIG. 7 and scheme 3 discussed with respect to FIG. 9, in 3GPP ETU channels, using L = 11;

FIGS. 14A-14B depict diagrams illustrating performance results of scheme 1 discussed with respect to FIG. 7 and scheme 3 discussed with respect to FIG. 9, in 3GPP EVB channels, using L = 40;

FIGS. 15A-15B depict diagrams illustrating performance results of scheme 1 discussed with respect to FIG. 7 and scheme 3 discussed with respect to FIG. 9, in 3 GPP TDL-C channels, using L = 21;

FIG. 16A-16B depict diagrams illustrating a sensitivity to the channel and a_opt radius estimation errors in scheme 3 ;

FIG. 17 depicts a flowchart of a method for a receiver device for a multicarrier modulation scheme, according to an embodiment of the present disclosure;

FIG. 18 depicts a flowchart of a method for another receiver device for a multicarrier modulation scheme, according to an embodiment of the present disclosure;

FIG. 19 depicts an exemplary embodiment of a transceiver device comprising a transmitter device using a Lagrange matrix for modulation and a receiver device using a Vandermonde matrix for demodulation; and

FIG. 20 depicts a diagram illustrating an exemplary scheme for signaling exchange indicating a radius of a circle.

DETAILED DESCRIPTION OF EMBODIMENTS

FIG. 1 depicts a schematic view of a receiver device 100 for a multicarrier modulation scheme, according to an embodiment of the present disclosure. The receiver device 100 is configured to, in a current transmission slot, determine a plurality of signature roots 101, 102, wherein each signature root of the plurality of signature roots 101, 102 is a nonzero complex point.

The receiver device 100 is further configured to, in the current transmission slot, obtain predicted CSI 103 of a communication channel 111 between the receiver device 100 and a transmitter device 110 for a next transmission slot.

The receiver device 100 is further configured to, in the current transmission slot, determine a first radius 104 of a circle 105 based on the predicted CSI 103, wherein the determined plurality of signature roots 101, 102 are uniformly distributed on a circumference of the circle 105; and provide a feedback message 106 to the transmitter device 110, the feedback message 106 indicating the first radius 104 of the circle 105.

Hence, the receiver device 100 is able to, in the current transmission slot, obtain (e.g., estimate) a predicted CSI for the next transmission slot. Moreover, the device 100 is able to, in the current transmission slot, provide (e.g., send to the transmitter device) the feedback message 106 indicating the first radius 104 of the circle 105.

The receiver device 100 may comprise a processing circuitry (not shown in FIG. 1) configured to perform, conduct or initiate the various operations of the device 100 described herein. The processing circuitry may comprise hardware and software. The hardware may comprise analog circuitry or digital circuitry, or both analog and digital circuitry. The digital circuitry may comprise components such as application-specific integrated circuits (ASICs), field- programmable arrays (FPGAs), digital signal processors (DSPs), or multi-purpose processors. In one embodiment, the processing circuitry comprises one or more processors and a non- transitory memory connected to the one or more processors. The non-transitory memory may carry executable program code which, when executed by the one or more processors, causes the device 100 to perform, conduct or initiate the operations or methods described herein.

FIG. 2 depicts a schematic view of a receiver device 200 for a multicarrier modulation scheme, according to an embodiment of the present disclosure. The receiver device 200 of FIG. 2 may be similar or identical to the receiver device 100 of FIG. 1, and may perform a similar or an identical function.

The receiver device 200 is configured to, in a current transmission slot, determine a plurality of signature roots 101, 102, wherein each signature root of the plurality of signature roots 101, 102 is a nonzero complex point.

The receiver device 200 is further configured to, in the current transmission slot, obtain estimated CSI 203 of a communication channel 111 between the receiver device 200 and a transmitter device 110 for the current transmission slot.

The receiver device 200 is further configured to, in the current transmission slot, determine a first radius 204 of a circle 205 based on the estimated CSI 203 wherein the determined plurality of signature roots 101, 102 are uniformly distributed on a circumference of the circle 205.

The receiver device 200 is further configured to, in the current transmission slot, construct a Lagrange matrix 201-L or a Vandermonde matrix 201-V based on the plurality of signature roots 101, 102.

Furthermore, the receiver device 200 is further configured to, in the current transmission slot, perform a demodulation of a multicarrier modulated signal 120 received from the transmitter device 110, based on the Lagrange matrix 201-L or the Vandermonde matrix 201-V, to obtain a demodulated signal 202.

The receiver device 200 is further configured to, in the current transmission slot, determine a SINR for at least one subcarrier 121, 122 based on the demodulated signal 202 and the determined first radius 204 of the circle205; perform a first equalization on a first set of subcarriers 121 of the demodulated signal 202, the first set of subcarriers having a SINR value equal to or above a threshold value, to obtain an equalized demodulated signal 221; perform a second equalization on a second set of subcarriers 122 of the multicarrier modulated signal 120 received from the transmitter device 110, the second set of subcarriers 122 having a SINR value below the threshold value, to obtain an equalized modulated signal 222; and obtain an output signal 220 based on a combination of the equalized demodulated signal 221 and the equalized modulated signal 222. The receiver device 200 may comprise a processing circuitry (not shown in FIG. 2) configured to perform, conduct or initiate the various operations of the device 100 described herein. The processing circuitry may comprise hardware and software. The hardware may comprise analog circuitry or digital circuitry, or both analog and digital circuitry. The digital circuitry may comprise components such as application-specific integrated circuits (ASICs), field- programmable arrays (FPGAs), digital signal processors (DSPs), or multi-purpose processors. In one embodiment, the processing circuitry comprises one or more processors and a non- transitory memory connected to the one or more processors. The non-transitory memory may carry executable program code which, when executed by the one or more processors, causes the device 100 to perform, conduct or initiate the operations or methods described herein.

FIG. 3 depicts a schematic view of a transceiver device for a multicarrier modulation scheme, according to an embodiment of the present disclosure.

The transceiver device 300 for the multicarrier modulation scheme comprises a transmitter device 110 that is configured to generate a multicarrier modulated signal 120 based on constructing a Lagrange matrix or a Vandermonde matrix.

The transceiver device 300 further comprises a receiver device, which may be the receiver device 100 or the receiver device 200.

The transceiver device 300 may comprise a processing circuitry (not shown in FIG. 3) configured to perform, conduct or initiate the various operations of the device 100 described herein. The processing circuitry may comprise hardware and software. The hardware may comprise analog circuitry or digital circuitry, or both analog and digital circuitry. The digital circuitry may comprise components such as application-specific integrated circuits (ASICs), field-programmable arrays (FPGAs), digital signal processors (DSPs), or multi-purpose processors. In one embodiment, the processing circuitry comprises one or more processors and a non-transitory memory connected to the one or more processors. The non-transitory memory may carry executable program code which, when executed by the one or more processors, causes the device 100 to perform, conduct or initiate the operations or methods described herein.

FIG. 4 depicts a diagram illustrating the transceiver device 300 providing a feedback message. In FIG. 4, the transceiver device 300 (based on an LV modulator for a doubly selective channels) is shown as an example for K signature roots.

The transceiver device 300 comprises the transmitter device 110 that includes a precoder 401, a modulator 402, and a ZP block 403. Moreover, the communication channel 111 of the transceiver device 300 comprises the receiver filter 406. The transceiver device 300 further comprises the receiver device (e.g., it may be the receiver device 100 of FIG.1 or the receiver device 200 of FIG. 2), which includes the demodulator 407, the one-tap equalizer unit 408 (which may be a time-frequency domain equalizer), and the decision block 409.

In the following, the transmitter device 300 is discussed as an example for time-frequency domain equalizations for the Lagrange Vandermonde division multiplexing, without limiting the present disclosure.

At first, in order to deal with doubly selective channels, a joint channel estimation and prediction (CEP) has been proposed, to provide a timely signaling exchange between the receiver device 100 (or the receiver device 200) and the transmitter device 110. For example, the receiver device 100 or the receiver device 200 may estimate (e.g., based on the mean squared error (MSE)), the modified, optimized radius of the circle a_opt , and may further feed the modified radius of the circle back to the transmitter device 110, during the training phase, to build the precoder 401 and modulator 402 blocks.

Moreover, the transceiver device 300 (e.g., the receiver device 100 or the receiver device 200) may solve two issues of the time-varying channel, including:

1. Outdated feedback signaling that breaks the signature roots’ optimization.

2. Inter-carrier interference that makes the one-tap equalization inadequate, and the necessity of providing an advanced receiver device that keeps the low-complexity implementation of the transceiver device.

The above issues may be solved by a time-frequency domain equalization discussed in the following. Without limiting the present disclosure, it may be assumed that the signature roots are uniformly j2nk spread over a circle of radius a, such that p_k = ae « , and all transmit filters have a same energy, thus

The received (time domain) signal is given by Eq. (32) as follows:

Eq. (32) where H_t is the time-varying channel matrix, where h(n, l) = h_c(nT_s, IT_S) and h_c(t, t) is the time-varying impulse response of the channel that includes transmitter-receiver filters as well as the doubly selective propagation effects.

In the received signal expression, the channel impulse response may vary even within one LVDM symbol, which may result in issues in the signaling exchange for sending the feedback message or in the detection process.

The transceiver device 300 (e.g., the receiver device 100 or the receiver device 200) may solve the two issues subsequently, within two consecutive steps including:

1. A joint channel estimation and prediction algorithm, wherein some values of optimized radius a_opt should be predicted at the receiver device 100, 200 and sent to the transmitter device 110, to be used for the transmission of the next LVDM symbols. 2. The receiver device 100, 200 may use the channel estimation to detect the received LVDM symbols, and a processing (that will be discussed in below) may be used to overcome the ICI.

Moreover, the transceiver device 300 may perform a (joint) channel estimation and prediction. The channel estimation part may feed the detector (e.g., of the receiver device for performing an equalization) while the channel prediction output may be used to build the transceiver blocks for the next LVDM symbols transmission.

The transmitter device 300 further comprises the optimization block 412 that may compute the optimization metric (for instance, the MSE) based on the CSI, and then compute the modified, optimized radius a_opt values, for example, for the actual received symbols during the current transmission slot and for the next transmission slot.

The transmitter device may further, optionally, comprise a refinement block, for example, to refine the plurality of signature roots. For example, the plurality of signature roots may be individually refined based on a specific optimization method and using a metric such as MSE.

The transmitter device 300 may further provide a signal to feedback the modified, optimized radius a_opt (or the refined signature roots), derived from the prediction entity, to transmitter device 110 for the modulation 402 and precoding block 401.

The receiver device 100 or the receiver device 200 may use the modified, optimized radius a_opt to compute the demodulation matrix, determine the SINR, perform equalization, etc.

At step 1 above, a joint channel estimation and prediction may be performed. For example, by assuming that x_max and f_D are the delay spread and the Doppler spread, respectively, and T_s is the sampling period at the receiver device, both x_max and f_D may be measured. Moreover, the NT_S may be the channel coherence time.

Furthermore, a basis expansion channel model (BEM) may be used (generally known to the skilled person), in which h_c(t, x) may be obtained for t e [kNT_s, (k + T)NT_S) (in the k^th channel coherence time) by using: L/2 a. L + 1 coefficients {¾ —A/2 that remain invariant per block, but are allowed to change with k , and b. A + 1 Fourier bases j_e/²⁷⁷' ^/v}^'^ that may capture the time variation, but are common for all of the k channels.

Further, each time-varying delay tap of the channel impulse response may be approximated as follows:

Eq. (33) where L = [T_max/T_s\ and A = 2\f_DNT_s , and where L-J and [-1 are the integer floor and the integer ceiling, respectively.

FIG. 5 depicts a diagram illustrating the transmitted LVDM frames, wherein NP training sequence vectors are inserted every D transmitted symbol vectors (one pilot vector followed by

N

(D- 1) LVDM symbols), wherein — = NP X D, and wherein P = K + L is the size of the

IPJ transmitted LVDM symbols using K subcarriers.

In the diagram of FIG. 4, the dashed arrows represents a scenario when the modified, optimized radius a_opt is fed back to the transmitter device 110 and is further sent to the demodulation block 407 (e.g., of the receiver device 100 or the receiver device 200) to be used in the next transmission slots.

FIG. 5 depicts a diagram illustrating pilot patterns using dedicated LVDM symbols, where NP = 4, and wherein every pilot symbol vector is followed by ( D - 1) LVDM symbols (vectors).

In the following, an exemplary procedure is presented for estimating the (L + 1) X (L + 1) coefficients discussed above, which may lead to the channel estimation over the

coherence time period ( NT_S ), and using the BEM approximation, without limiting the present disclosure to this specific procedure.

SUBSTITUTE SHtET (RULE 26) 1. The transceiver device 300 (e.g., at block CEP 410 of the receiver device 100 or the receiver device 200) may stack the received NP pilot vectors in y_b (see FIG. 6). Moreover, y_b may have a size of ((JVP x P) x l) and may be obtained according to Eq. (34) as follows: y_b = f_ϋ1i + h_ύ, Eq. (34) where

Eq. (35) where

is the vector stacking the X^th coefficient of every I^th delay tap to be determined, and

Eq. (37) has a size ( NP X P) X ((A + 1) X (L + 1)) , where, in above Eq. (37),

is a Toeplitz matrix formed by the transmitted pilot vectors. For example, the Toeplitz matrix may be formed by a number of ( K + 1) modulated pilot symbols followed by a number of L- zeros padded symbols (i.e., L zeros that are added at the end of the modulated pilot symbols), as it is shown in FIG. 6), and D jF is a P x P diagonal matrix and can be obtained according to Eq. (39) as follows:

where t(b/> = ((/ - 1) P D : P - 1 + (/ - 1) P D) Eq. (40)

FIG. 6 depicts a diagram illustrating NP stacked pilot vectors, wherein ( NP — 1) are the buffered pilot vectors illustrated along with a newly received pilot vector.

At next, the transceiver device 300, particularly its CEP block 410, may apply the linear MMSE channel estimator and may further obtain the estimated channel according to Eq. (41) as follows:

Eq. (41) where

Eq. (42)

Furthermore, it may be assumed that R_h is known at the receiver device 100, 200. For example, since R_h depends only on the channel delay profile, it may be determined by the receiver device 100 or the receiver device 200.

The aforementioned details are summarized in the following algorithm, wherein the (estimated) channel matrices H _et and H_pred, which are the output of the algorithm, may be used to detect the actual (D-l) received LVDM symbols and to further predict the (I)- \ ) coming values of the optimized radius a_opt , respectively (see FIG. 6).

Therefore, the transceiver device 300 (i.e., its receiver device 100 or 200, and particularly at its optimization block 412, may use (perform) this algorithm to output and obtain the m-th ((L + 1) X K) channel matrix H_{a m} =

according to Eq. (43) as follows:

Moreover, the transceiver device 300 may modify (optimize) the radius a at the receiver device 100 or the receiver device 200 through the corresponding optimization block 412 and by using a metric (such as the MSE) and may further obtain, for example, the modified, optimized radius ^a _oPt , a vector of (D-l) values for the a_{opt m} according to Eq. (44) as follows:

Eq. (44) where

The above-mentioned algorithm (the algorithm for joint channel estimation and prediction (CEP algorithm)) may further be summarized according to Eq. (46).

The inputs of the algorithm are R_h and y_b , and the outputs of the algorithm are H _et and H _Pred. Moreover, the algorithm includes five computing steps, wherein each computing step of the algorithm is indicated with a bullet point as follows:

Inputs: R_h, y_b.

Out

• for / = 1 : NP, compute t,(1 + (/ — 1 )K : iK) = ((/ — 1 )P + 1 : (i — i)P + K) + (NP - 1)PD.

• Compute t₂ = t, + P D.

• Compute

H

l=-L/2 Eq_. (46)

The next step is the detection phase. During the detection phase, the receiver device 100 or the receiver device 200 may use the estimated channel for detecting the received LVDM symbols, and processing (that will be discussed below) may be used to overcome the ICI.

Here, a time-frequency domain equalization is disclosed to deal with the doubly selective channels. The equalization may be performed over two stages (including a first equalization and a second equalization) using both frequency and time-domain processing.

During the detection phase, the detector (of the receiver device) uses the m-th ((L + 1) x K) channel matrix H _rn = H _et(: , (1: K) + (m — 1)K) to detect the m-th LVDM received symbol that can be, for example, obtained in the frequency domain by Eq. (47), as follows: f W = EfiiiJ rfinj = Efro] H_{% (|7I)} R[mJ sfiiij + E{m} T? Z« Eq. (47)

Moreover, the SINR at the k-th subcarrier may be determined according to Eq. (9) to Eq. (11), as discussed above.

In the following, four different configurations of the receiver device are discussed with respect to FIG. 7 to FIG. 10, in which the equalization is performed over two stages (i.e., the first equalization and the second equalization) using both frequency- and time-domain processing, without limiting the present disclosure to a specific configuration or type of performed equalization. Moreover, in stage 1, the first equalization is performed for the first set of subcarriers (5_C), and in stage 2, the second equalization is performed for the second set of subcarriers (S₂). Also, for the sake of simplicity, the index m is dropped in the sequel.

For example, the receiver device 100 may perform the first equalization (indicated with stage

1 in FIGS 7 to 10) for the first set of sub carriers (5_X ) to obtain the equalized first set of subcarriers, and/or the receiver device 200 may perform the first equalization for the first set of subcarriers (5_X) to obtain the equalized demodulated signal 221.

Moreover, the receiver device 100 may perform the second equalization (indicated with stage

2 in FIGS 7 to 10) for the second set of sub carriers (S₂) to obtain the equalized second set of subcarriers, and/or the receiver device 200 may perform the second equalization for the second set of subcarriers (S₂) to obtain an equalized modulated signal 222.

FIG. 7 depicts a diagram illustrating the receiver device 100, 200 performing a first equalization based on the one-tap equalization 1TE (ZF) and a second equalization based on the MMSE.

In FIG. 7 (also hereinafter referred to as scheme 1), the receiver device 100 or the receiver device 200 may perform the first equalization being based on the ZF equalization (i.e., discussed above with respect to the Eq. (12) to Eq. (13)). The ZF equalization comprises applying the inversion of the diagonal matrix on the first set of subcarriers 121 of the demodulated signal 202.

Furthermore, the receiver device 100 or the receiver device 200 may perform the second equalization based on the MMSE equalization (i.e., discussed above with respect to the Eq. (14) to Eq. (16)). For example, the receiver device 100 or the receiver device 200 may remove the contribution of the first set of subcarriers 121 from the multicarrier modulated signal 120 received from the transmitter device 110, and may further apply the MMSE criteria on the second set of subcarriers 122 of the remainder of the multicarrier modulated signal 120 received from the transmitter device 110. FIG. 8 depicts a diagram illustrating the receiver device performing a first equalization based on the one-tap equalization 1TE (ZF) and a second equalization based on the MMSE-OSIC.

In FIG. 8 (also hereinafter referred to as scheme 2), the receiver device 100 or the receiver device 200 may perform the first equalization being based on the ZF equalization (i.e., discussed under the Eq. (12) to Eq. (13) above).

Furthermore, the receiver device 100 or the receiver device 200 may perform the second equalization being based on the MMSE-OSIC equalization (i.e., discussed above with respect to the Eq. (23) to Eq. (31)). For example, the receiver device 100 or the receiver device 200 may remove the contribution of the first set of subcarriers 121 from the multicarrier modulated signal 120 received from the transmitter device 110, and may further apply the MMSE OSIC operation on the second set of subcarriers 122 of the remainder of the multicarrier modulated signal 120 received from the transmitter device 110.

FIG. 9 depicts a diagram illustrating the receiver device performing a first equalization based on the one-tap equalization (lTE)-PIC and a second equalization based on the MMSE-OSIC.

In FIG. 9 (also hereinafter referred to as scheme 3), the receiver device 100 or the receiver device 200 may perform the first equalization based on the one-tap equalization (lTE)-PIC (ZF- PIC) equalization (i.e., discussed above with respect to the Eq. (17) to Eq. (18)). For instance, the receiver device 100 or the receiver device 200 may estimate the ICI based on the first set of subcarriers 121, removing the contribution of the estimated ICI, and may further apply, after removing the contribution of the estimated ICI, the MMSE matrix on the remainder of the demodulated signal 202.

Furthermore, the receiver device 100 or the receiver device 200 may perform the second equalization being based on the MMSE-OSIC equalization (i.e., discussed above with respect to the Eq. (23) to Eq. (31)).

FIG. 10 depicts a diagram illustrating the receiver device performing a first equalization based on the MMSE-PIC and a second equalization based on the MMSE-OSIC. In FIG. 10 (also hereinafter referred to as scheme 4), the receiver device 100 or the receiver device 200 may perform the first equalization based on the MMSE-PIC equalization (i.e., discussed above with respect to the Eq. (19) to Eq. (22)). For instance, the receiver device 100 or the receiver device 200 may estimate the ICI based on the first set of subcarriers 121, remove the contribution of the estimated ICI, and may further apply, after removing the contribution of the estimated ICI, the MMSE matrix on the remainder of the demodulated signal 202.

Furthermore, the receiver device 100 or the receiver device 200 may perform the second equalization based on the MMSE-OSIC equalization (i.e., discussed above with respect to the Eq. (23) to Eq. (31)).

Reference is made to FIG. 11 A, 11B, 12A, 12B, 13A, 13 B, 14A, 14B, 15A, 15B, 16A, and 16B, which depict respective diagrams illustrating performance results of the proposed schemes (i.e., scheme 1 discussed with respect to FIG. 7, scheme 2 discussed with respect to FIG. 8, scheme 3 discussed with respect to FIG. 9, and scheme 4 discussed above with respect to FIG. 10), in a general doubly selective channel. Furthermore, a comparison is carried out where the performance/complexity tradeoff is discussed.

Moreover, the sensitivity to the channel and the sensitivity of the optimized radius a_opt to the channel estimation errors are presented for Scheme 3, without limiting the present disclosure to a specific scheme or configuration.

Furthermore, it is considered that both LVDM and OFDM are using low-complex OSIC. Moreover, the complexities are generally known to the skilled person.

• Doubly Selective Fading Channels

For example, K = 64 and L = 16 may be set. Moreover, the maximum Doppler spread is set to f_D = 1 KHz while the subcarrier spacing is set to D/ = 30 KHz. Also, the quadratic phase- shift keying (QPSK) modulations is considered.

Reference is made to FIG. 11 A and 1 IB, which depict diagrams illustrating performance results of scheme 1 discussed with respect to FIG. 7 and scheme 2 discussed with respect to FIG. 8. In FIGS. 11 A and 1 IB, scheme 1 provides 5 dB of gain for LVDM over LVDM-OSIC, where the complexity is 0((m³ + 2 m²)K³) , where = ^Card(-^S^ Moreover, this performance gain increases to 7 dB when using scheme 2 with a complexity of 0 where

b is the average number of iterations in stage 2 (see FIGS. 11 A and 1 IB). Note that scheme 1 and scheme 2 have comparative complexity orders of 0

.

Furthermore, the performance results show that LVDM outperforms OFDM by 2.5 dB at BER = 1(T⁵.

Reference is made to FIG. 12A and 12B, which depict diagrams illustrating performance results of scheme 3 discussed with respect to FIG. 9 and scheme 4 discussed with respect to FIG. 10.

From FIGS. 12A and 12B, it can be derived that both scheme 3 and scheme 4 provide 8 dB of gain for LVDM over LVDM-OSIC. Moreover, they have the same complexity order too, scheme 4 performs more operations in the first equalization (stage 1), since it is using MMSE.

Next, the discussion is based on focusing in the sequel on schemes 1 and 3, and simulation results are provided in the third-generation partnership project (3GPP) channels.

• 3rd Generation Partnership Project (3 GPP) Channels

The parameters may be set such that K = 64, carrier frequency f_c = 3.5 GHz, the velocity is v = 200 Km/h, Doppler spread is f_D = 648 Hz, and subcarrier spacing D/ = 30 KHz. Further, the QPSK modulation is considered.

Reference is made to FIG. 13A and 13B, which depict diagrams illustrating performance results of scheme 1 discussed with respect to FIG. 7 and scheme 3 discussed with respect to FIG. 9, in 3 GPP ETU channels, using L = 11.

From FIG. 13 A and 13B, it can be derived that both schemes 1 and 3 provide 3dB of gains for LVDM using the advanced receiver over LVDM-OSIC at BER = 10^-5 in Extended Typical Urban (ETU) channels. However, scheme 3 brings 4 dB of SNR gain over Scheme 1 at BER = HG⁶.

Reference is made to FIG. 14A and 14B, which depict diagrams illustrating performance results of scheme 1 discussed with respect to FIG. 7 and scheme 3 discussed with respect to FIG. 9, in 3 GPP EVB channels, using L = 40.

From FIG. 14A and 14B, it can be derived that both schemes 1 and 3 perform well in Extended Vehicular B (EVB) channels, where the LVDM using the advanced receiver provides 7.5 dB and 8 dB of gain over LVDM-OSIC at BER = 10^-5, respectively. However, in Tapped Delay Line C channel model (TDL-C), scheme 3 provides 7 dB of SNR gain over LVDM-OSIC at BER = 10^-5, while the gain in scheme 1 is limited to 5 dB at the same BER, as it is shown in FIG. 15A and 15B.

Reference is made to FIG. 15 A and 15B, which depict diagrams illustrating performance results of the scheme 1 discussed with respect to FIG. 7 and scheme 3 discussed with respect to FIG. 9, in 3GPP TDL-C channels, using L = 21.

From FIG. 14A, 14B, 15A and 15B, it can be derived that scheme 3 provides 2 dB of additional SNR gain over scheme 1 at BER = 10^-6. Yet, note that scheme 3 outperforms scheme 1 while having the same complexity order of implementation.

It is worth mentioning that FIG. 11A, 11B, 12A, 12B, 13A, 13 B, 14A, 14B, 15A, and 15B have been depicted using perfect CSI at the receiver device. Next, the performance results are shown using the CEP algorithm (discussed above with respect to Eq. (46)), and it was proposed as step 1 above to be performed by the receiver device 100 or the receiver device 200.

Without limiting the present disclosure to a specific scheme, in FIG. 16A and 16B, the performance result is provided for the scheme 3 (discussed with respect to FIG. 9) in EVB channels. Reference is made to FIG. 16A and 16B, which depict diagrams illustrating the effect of CEP errors (FIG. 16A) and normalized MSE (NMSE) of the modified, optimized radius a_opt in CEP (FIG. 16B).

In FIG. 16A and 16B, the sensitivity to the channel and the sensitivity of modified, optimized radius a_opt to the estimation errors in scheme 3 are illustrated.

It is worth reminding that OFDM performance depends on the channel estimation quality while LVDM performance depends on both the channel estimation and prediction qualities. FIG. 16B shows that Normalized MSE (NMSE) of predicted (e.g., for next transmission slot) optimized radius a_opt is more accentuated than that of the estimated radius a_opt (e.g., estimated for the current transmission slot). However, despite these sensitivities, LVDM outperforms the OFDM in 3GPP EVB channels when using either perfect or imperfect CSI.

FIG. 17 shows a method 1700 according to an embodiment of the present disclosure for a multicarrier modulation scheme. The method 1700 may be carried out by the receiver device 100 or the receiver device 200, as they are described above. Without limiting the present disclosure, in the following, the method 1700 is exemplarily discussed as a method being performed by the receiver device 100.

The method 1700 comprises a step SI 701 of determining, in a current transmission slot, a plurality of signature roots 101, 102, wherein each signature root of the plurality of signature roots 101, 102 is a nonzero complex point.

The method 1700 further comprises a step SI 702 of obtaining, in the current transmission slot, predicted CSI 103 of a communication channel 111 between the receiver device 100 and a transmitter device 110 for a next transmission slot.

The method 1700 further comprises a step SI 703 of determining, in the current transmission slot, a first radius 104 of a circle 105 based on the predicted CSI 103, wherein the determined plurality of signature roots 101, 102 are uniformly distributed on a circumference of the circle 105. The method 1700 further comprises a step SI 704 of providing, in the current transmission slot, a feedback message 106 to the transmitter device 110, the feedback message 106 indicating the first radius 104 of the circle 105.

FIG. 18 shows a method 1800 according to an embodiment of the present disclosure for a multicarrier modulation scheme. The method 1800 may be carried out by the receiver device 100 or the receiver device 200, as they are described above. Without limiting the present disclosure, in the following, the method 1800 is exemplarily discussed as a method being performed by the receiver device 200.

The method 1800 comprises a step SI 801 of determining, in a current transmission slot, a plurality of signature roots 101, 102, wherein each signature root of the plurality of signature roots 101, 102 is a nonzero complex point.

The method 1800 further comprises a step SI 802 of obtaining, in the current transmission slot, estimated CSI 203 of a communication channel 111 between the receiver device 200 and a transmitter device 110 for the current transmission slot.

The method 1800 further comprises a step SI 803 of determining, in the current transmission slot, a first radius 204 of a circle 205 based on the estimated CSI 203 wherein the determined plurality of signature roots 101, 102 are uniformly distributed on a circumference of the circle.

The method 1800 further comprises a step SI 804 of constructing, in the current transmission slot, a Lagrange matrix 201-L or a Vandermonde matrix 201-V based on the plurality of signature roots 101, 102.

The method 1800 further comprises a step SI 805 of performing, in the current transmission slot, a demodulation of a multicarrier modulated signal 120 received from the transmitter device 110, based on the Lagrange matrix 201-L or the Vandermonde matrix 201-V, to obtain a demodulated signal 202.

The method 1800 further comprises a step SI 806 of determining, in the current transmission slot, a SINR for at least one subcarrier 121, 122 based on the demodulated signal 202 and the determined first radius 204 of the circle 205. The method 1800 further comprises a step SI 807 of performing, in the current transmission slot, a first equalization on a first set of subcarriers 121 of the demodulated signal 202, the first set of subcarriers having a SINR value equal to or above a threshold value, to obtain an equalized demodulated signal 221.

The method 1800 further comprises a step SI 808 of performing, in the current transmission slot, a second equalization on a second set of subcarriers 122 of the multicarrier modulated signal 120 received from the transmitter device 110, the second set of subcarriers 122 having a SINR value below the threshold value, to obtain an equalized modulated signal 222.

The method 1800 further comprises a step SI 809 of obtaining, in the current transmission slot, an output signal 220 based on a combination of the equalized demodulated signal 221 and the equalized modulated signal 222.

The present disclosure has been described in conjunction with various embodiments of the present disclosure as examples as well as implementations. However, other variations can be understood and effected by those persons skilled in the art and practicing the claimed embodiments of the present disclosure, from the studies of the drawings, this disclosure and the independent claims. In the claims as well as in the description the word “comprising” does not exclude other elements or steps and the indefinite article “a” or “an” does not exclude a plurality. A single element or other unit may fulfill the functions of several entities or items recited in the claims. The mere fact that certain measures are recited in the mutual different dependent claims does not indicate that a combination of these measures cannot be used in an advantageous implementation.

Claims

1. A receiver device (100) for a multicarrier modulation scheme, the receiver device (100) being configured to, in a current transmission slot: determine a plurality of signature roots (101, 102), wherein each signature root of the plurality of signature roots (101, 102) is a nonzero complex point; obtain predicted Channel State Information, CSI, (103) of a communication channel (111) between the receiver device (100) and a transmitter device (110) for a next transmission slot; determine a first radius (104) of a circle (105) based on the predicted CSI (103), wherein the determined plurality of signature roots (101, 102) are uniformly distributed on a circumference of the circle (105); and provide a feedback message (106) to the transmitter device (110), the feedback message (106) indicating the first radius (104) of the circle (105).

2. The receiver device (100) according to claim 1, further configured to: obtain estimated CSI (203) of the communication channel (111) for the current transmission slot; determine a second radius (204) of a further circle (205) based on the estimated CSI (204), wherein the determined plurality of signature roots (101, 102) are uniformly distributed on a circumference of the further circle (205); construct a Lagrange matrix (201-L) or a Vandermonde matrix (201-V) based on the plurality of signature roots (101, 102); and perform a demodulation of a multicarrier modulated signal (120) received from the transmitter device (110), based on the Lagrange matrix (201-L) or the Vandermonde matrix (201-V) to obtain a demodulated signal (202).

3. The receiver device (100) according to claim 2, further configured to: determine a signal-to-interference-plus-noise ratio, SINR, for at least one subcarrier (121, 122) of the demodulated signal (202); perform a first equalization for a first set of subcarriers (121) having a SINR value equal to or above a threshold value to obtain an equalized first set of subcarriers; perform a second equalization for a second set of subcarriers (122) having a SINR value below the threshold value to obtain an equalized second set of subcarriers; and obtain an equalized demodulated signal (220) based on a combination of the equalized first set of subcarriers and the equalized second set of subcarriers.

4. A receiver device (200) for a multicarrier modulation scheme, the receiver device (200) being configured to, in a current transmission slot: determine a plurality of signature roots (101, 102), wherein each signature root of the plurality of signature roots (101, 102) is a nonzero complex point; obtain estimated Channel State Information, CSI, (203) of a communication channel (111) between the receiver device (200) and a transmitter device (110) for the current transmission slot; determine a first radius (204) of a circle (205) based on the estimated CSI, (203) wherein the determined plurality of signature roots (101, 102) are uniformly distributed on a circumference of the circle; construct a Lagrange matrix (201-L) or a Vandermonde matrix (201-V) based on the plurality of signature roots (101, 102); perform a demodulation of a multicarrier modulated signal (120) received from the transmitter device (110), based on the Lagrange matrix (201-L) or the Vandermonde matrix (201-V), to obtain a demodulated signal (202); determine a signal-to-interference-plus-noise ratio, SINR, for at least one subcarrier (121, 122) based on the demodulated signal (202) and the determined first radius (204) of the circle (205); perform a first equalization on a first set of subcarriers (121) of the demodulated signal (202), the first set of subcarriers having a SINR value equal to or above a threshold value, to obtain an equalized demodulated signal (221); perform a second equalization on a second set of subcarriers (122) of the multicarrier modulated signal (120) received from the transmitter device (110), the second set of subcarriers (122) having a SINR value below the threshold value, to obtain an equalized modulated signal (222); and obtain an output signal (220) based on a combination of the equalized demodulated signal (221) and the equalized modulated signal (222).

5. The receiver device (200) according to claim 4, further configured to: obtain predicted CSI (103) of the communication channel (111) for a next transmission slot; determine a second radius (104) of a further circle (105) based on the predicted CSI (103), wherein the determined plurality of signature roots (101, 102) are uniformly distributed on a circumference of the further circle (105); and provide a feedback message (106) to the transmitter device, the feedback message (106) indicating the second radius (104) of the further circle (105).

6. The receiver device (100, 200) according to one of the claims 2, 3, or 5, further configured to: compute a metric for evaluating the first radius (204) of the circle (205) and/or the second radius (104) of the further circle (105) to obtain a modified first radius of the circle and/or a modified second radius of the further circle; and provide a feedback message (106) to the transmitter device (110), the feedback message (106) indicating the modified first radius of the circle (205) and/or the modified second radius of the further circle (105).

7. The receiver device (100, 200) according to one of the claims 3 to 6, wherein the first equalization is based on a zero-forcing, ZF, equalization, comprising applying an inversion of a diagonal matrix on the first set of subcarriers (121) of the demodulated signal (202).

8. The receiver device (100, 200) according to one of the claims 3 to 7, wherein the second equalization comprises: removing a contribution of the first set of subcarriers (121) from the multicarrier modulated signal (120) received from the transmitter device (110); and applying a minimum mean square error, MMSE, criteria on the second set of subcarriers (122) of a remainder of the multicarrier modulated signal (120) received from the transmitter device (110).

9. The receiver device (100, 200) according to one of the claims 3 to 6, wherein the first equalization is based on a zero-forcing, ZF, parallel interference cancellation, PIC, equalization, comprising: estimating an inter-carrier interference, ICI, based on the first set of subcarriers (121); removing a contribution of the estimated ICI; and applying, after removing the contribution of the estimated ICI, an inversion of a diagonal matrix on a remainder of the demodulated signal (202) .

10. The receiver device (100, 200) according to one of the claims 3 to 6, wherein the first equalization is based on a minimum mean square error parallel interference cancellation, MMSE PIC, equalization, comprising: estimating an inter-carrier interference, ICI, based on the first set of subcarriers (121); removing a contribution of the estimated ICI; and applying, after removing the contribution of the estimated ICI, an MMSE matrix on a remainder of the demodulated signal (202).

11. The receiver device (100, 200) according to claim 3 or according to one of the claims 4 to 7, 9, or 10, wherein the second equalization is based on a minimum mean square error, MMSE, ordered successive interference cancellation, OSIC, equalization, comprising: removing a contribution of the first set of subcarriers (121) from the multicarrier modulated signal (120) received from the transmitter device (110); and applying a MMSE OSIC operation on the second set of subcarriers (122) of a remainder of the multicarrier modulated signal (120) received from the transmitter device (110).

12. A transceiver device (300) for a multicarrier modulation scheme, the transceiver device (300) comprising: a transmitter device (110) configured to generate a multicarrier modulated signal (120) based on constructing a Lagrange matrix or a Vandermonde matrix; and a receiver device (100) according to one of the claims 1 to 3 or a receiver device (200) according to one of the claims 4 to 11.

13. A method (1700) for a receiver device (100) for a multicarrier modulation scheme, wherein the method (1700) comprises, in a current transmission slot: determining (S1701) a plurality of signature roots (101, 102), wherein each signature root of the plurality of signature roots (101, 102) is a nonzero complex point; obtaining (S1702) predicted Channel State Information, CSI, (103) of a communication channel (111) between the receiver device (100) and a transmitter device (110) for a next transmission slot; determining (S1703) a first radius (104) of a circle (105) based on the predicted CSI (103), wherein the determined plurality of signature roots (101, 102) are uniformly distributed on a circumference of the circle (105); and providing (S1704) a feedback message (106) to the transmitter device (110), the feedback message (106) indicating the first radius (104) of the circle (105).

14. A method (1800) for a receiver device (200) for a multicarrier modulation scheme, wherein the method (1800) comprises, in a current transmission slot: determining (SI 801) a plurality of signature roots (101, 102), wherein each signature root of the plurality of signature roots (101, 102) is a nonzero complex point; obtaining (SI 802) estimated Channel State Information, CSI, (203) of a communication channel (111) between the receiver device (200) and a transmitter device (110) for the current transmission slot; determining (SI 803) a first radius (204) of a circle (205) based on the estimated CSI,

(203) wherein the determined plurality of signature roots (101, 102) are uniformly distributed on a circumference of the circle; constructing (SI 804) a Lagrange matrix (201-L) or a Vandermonde matrix (201-V) based on the plurality of signature roots (101, 102); performing (SI 805) a demodulation of a multicarrier modulated signal (120) received from the transmitter device (110), based on the Lagrange matrix (201-L) or the Vandermonde matrix (201-V), to obtain a demodulated signal (202); determining (SI 806) a signal-to-interference-plus-noise ratio, SINR, for at least one subcarrier (121, 122) based on the demodulated signal (202) and the determined first radius

(204) of the circle (205); performing (SI 807) a first equalization on a first set of subcarriers (121) of the demodulated signal (202), the first set of subcarriers having a SINR value equal to or above a threshold value, to obtain an equalized demodulated signal (221); performing (SI 808) a second equalization on a second set of subcarriers (122) of the multicarrier modulated signal (120) received from the transmitter device (110), the second set of subcarriers (122) having a SINR value below the threshold value, to obtain an equalized modulated signal (222); and obtaining (SI 809) an output signal (220) based on a combination of the equalized demodulated signal (221) and the equalized modulated signal (222).

15. A computer program which, when executed by a computer, causes the method (1700) of claim 13 or the method (1800) of claim 14 to be performed.