Method for reducing the peak-to-average power ratio of an ofdm-type signal, computer program products and corresponding devices
Patent Information
- Application Number
- EP2023742356
- Authority / Receiving Office
- EP · EP
- Patent Type
- Applications
- Current Assignee / Owner
- Priority Date
- 2022-06-27
- Filing Date
- 2023-06-27
- Publication Date
- 2025-04-30
Smart Images
Figure 1.1
Abstract
Description
[0001]DESCRIPTION TITLE: Method for reducing the crest factor of an OFDM type signal, computer program products and corresponding devices. Field of the invention The field of the invention is that of data transmission via the use of an OFDM (Orthogonal Frequency Division Multiplexing) type radiofrequency signal transmitted via a plurality of antennas of a radiofrequency transmitter to a plurality of receivers. The invention relates more particularly to a method for reducing the crest factor of such a signal. Such a waveform is used in numerous fields related to the transmission of data via radiofrequency links. The invention thus has applications, in particular, but not exclusively, in the field of mobile telephony (eg4G, 5G or beyond (6G) networks as defined by the 3GPP (for "3rd Generation Partnership Project" in English)) or WLAN (for "Wireless Local Area Network" in English, e.g. using WiFi), high-speed wireless internet access (WiMAX), asymmetric digital links (xDSL), point-to-multipoint wireless links, etc. Prior art and its disadvantages In the remainder of this document, we will focus more particularly on describing an existing problem in the technological field of cell-free massive MIMO (for "Multiple-Input Multiple-Output" in the English literature), or CF-mMIMO (for "cell-free massive MIMO" in the English literature), and more particularly in the technological field of scalable CF-mMIMO.The invention is of course not limited to this particular field of application, but is of interest for the generation of any OFDM type communications signal transmitted via a plurality of antennas of a radiofrequency transmitter to a plurality of receivers (e.g. receivers of user terminals). In recent decades, the exponential growth of mobile data traffic has been made possible by the densification of the network infrastructure, which can be ensured: (i) by increasing the cell density. Such an approach is known as ultra-dense network; and / or (ii) by adopting a large number of active antennas per access point, or AP (for "Access Point" in the English literature). Such an approach is known as massive MIMO, or mMIMO. Nevertheless, cell densification and mMIMO technology have fundamental limitations.In particular, inter-cell interference and large variations in quality of service make such technologies unable to cope with the challenges of next-generation networks (e.g. 6G) regarding increased data throughput for user terminals and low power consumption. To this end, a new wireless technology has recently attracted increasing attention, CF-mMIMO technology. The main property of CF-mMIMO technology is that there are many APs geographically distributed, but the coverage area is not divided into disjoint cells. Indeed, as illustrated in [Fig. 1a], according to CF-mMIMO technology a single system 120 centrally groups the necessary means (e.g. regarding computing power, data storage, etc.) for the operation of the different APs 110.In this way, CF-mMIMO technology presents two main characteristics which are: (i) the operating regime with more 110 APs than 100 user terminals as well as the physical layer operation inspired by recent advances in mMIMO; and (ii) each 100 terminal is served by all surrounding APs for a “cell-free” operation. However, the original version of CF-mMIMO technology was not scalable, i.e., the front-end capacity and computational complexity grow exponentially with the number of 100 terminals. This is due to the fact that all 110 APs are connected to a central processing unit, within the system 120, which is responsible for coordinating and processing the signals of all 100 terminals. Very recently, a new scalable version of CF-mMIMO (or scalable CF-mMIMO), has been introduced, in the article by E. Bjornson and L.Sanguinetti, “Scalable cell-free massive MIMO systems,” IEEE Transactions on Communications, vol.68, no.7, pp.4247–4261, 2020, where fully distributed processing is adopted as illustrated in [Fig.1b]. Notably, new scalable spatial precoding and combining schemes as well as channel estimation, power allocation, AP clustering methods can be introduced, obtaining very good advantages for the CF-mMIMO technique. Furthermore, the use of OFDM-like signals allows managing frequency-selective channels in a simple and robust way. In this way, a CF-mMIMO technology using such OFDM signals for data transmission seems to be a very promising combination to meet the ever-increasing demands regarding data rate.However, CF-mMIMO systems based on OFDM signal transmission have a high peak-to-average power ratio (PAPR) for the transmitted signals. However, to be commercially viable, an OFDM-based CF-mMIMO system requires that APs 110 be deployed using energy-efficient and low-cost hardware. Therefore, it is essential to reduce the PAPR of such CF-mMIMO systems to enable cost-effective and energy-efficient deployments of APs 110. The problem of PAPR reduction has been studied for a long time, with the first method proposed for OFDM dating back to 1999.Then, some methods have been introduced to improve energy efficiency, such as Tone Reservation (TR), Selective Mapping (SLM), Partial Transmit Sequence (PTS), Active Constellation Extension (ACE), and iterative coding and clipping with filtering. These methods, which were initially proposed for SISO (Single-Input Single-Output) and conventional MIMO-OFDM implementations, can unfortunately provide moderate PAPR reduction that does not meet the high energy efficiency requirements for massive MIMO-based 6G networks.Moreover, the bottlenecks of these methods are related to their respective drawbacks such as the increase in average power, the loss of spectral efficiency due to the reservation of some subcarriers, a high computational load and a high latency. Therefore, they are not suitable for massive MIMO systems. In this regard, more efficient techniques have been proposed for collocated massive MIMO-OFDM systems, such as the Fast Truncation Algorithm (FITRA) or the perturbation-assisted Alternative Direction Method of Multipliers (ADMM). More recently, joint multi-user precoding and PAPR reduction schemes have been studied. However, all these techniques are limited to traditional and / or collocated massive MIMO systems.Indeed, in the case of massive systems, many degrees of freedom can be exploited to effectively reduce the PAPR by equipping the AP 110 with a large number of antennas relative to the number of served user terminals. For example, the article by Rafik Zayani and Daniel Roviras: “Low-complexity linear precoding for low-PAPR massive MU-MIMO-OFDM downlink systems”, International Journal of Communication Systems, Wiley, 2021, 34 (12), uses the degrees of freedom related to the large number of antennas in order to transmit the distortion signal related to a clipping of the OFDM signal transmitted by the AP 110 in a direction in which no terminal 100 is present. However, in the perspective of a cost-effective implementation as envisaged for scalable CF-mMIMO, a reduced number of antennas, relative to a massive MIMO technique, must be considered.In such a configuration, the number of terminals 100 connected to a given AP 110 may be greater than the number of transmit antennas of the AP 110 in question. In such a configuration, there are no more free degrees of freedom to exploit and the approach set out in the aforementioned article cannot be applied. There is thus a need for a technique for reducing the crest factor of an OFDM type signal having improved performance compared to known techniques. Such a technique must in particular be adapted to the evolving CF-mMIMO context in which the number of UEs 100 connected to the same AP 110 may be greater than the number of transmit antennas of the AP 110 in question. Presentation of the invention In one embodiment of the invention, a method for reducing the crest factor of an OFDM type signal comprising N subcarriers is proposed.The signal results from the superposition of M spatial components each emitted by a respective antenna of a radiofrequency transmitter to a plurality of receivers. According to such a method, an electronic device executes: - obtaining M clipped OFDM symbols each intended to be a temporal portion of a spatial component transmitted by a respective antenna of the transmitter. The obtaining comprises, for at least one antenna of the transmitter: - generating an OFDM symbol by implementing an inverse Fourier transformation applied to an input vector that is a function of modulation symbols, each component of the input vector being intended to be carried by a corresponding subcarrier of a spatial component of the OFDM type signal; and - clipping the OFDM symbol delivering a clipped OFDM symbol intended to be a temporal portion of the spatial component transmitted by the antenna.The generation and clipping are repeated for each antenna of the transmitter delivering the M clipped OFDM symbols. According to the method, the electronic device executes, for at least one given antenna of the transmitter: - a Fourier transformation of an error vector depending on a difference between the clipped OFDM symbol and the OFDM symbol associated with the given antenna, delivering a transformed error vector of N error signals. The repeated Fourier transformation for each antenna of the transmitter delivers M transformed error vectors of N error signals. According to the method, the electronic device executes, for at least one given subcarrier: - a concatenation of the error signals associated with the given subcarrier in each of the M transformed error vectors delivering an error vector, called subcarrier error vector, of M error signals.Each error signal in the subcarrier error vector is associated with a respective antenna; and - a projection of the subcarrier error vector delivering a vector of M crest factor reduction signals associated with the given subcarrier. Each crest factor reduction signal in said vector of M reduction signals is associated with a respective antenna. According to the method, the electronic device performs a new implementation of said obtaining M clipped OFDM symbols to generate M updated clipped OFDM symbols, wherein the generation, for at least one antenna of the transmitter, of an OFDM symbol implements the inverse Fourier transformation applied to an updated input vector.The updated input vector is a function of N new modulation symbols, the crest factor reduction signal of the vector of M reduction signals corresponding to said antenna and associated with the given subcarrier being added to the new modulation symbol intended to be carried by the given subcarrier in the updated input vector. According to the method, the projection implements a spatial coding of the M error signals of the subcarrier error vector on the basis of an estimated propagation channel between the receivers and the transmitter so that the distortion signal linked to the difference between the clipped OFDM symbols and the OFDM symbols is transmitted by the transmitter in at least one direction of a receiver, called a weak receiver, for which the estimated propagation channel corresponds to a propagation loss greater than a predetermined threshold. The projection implements an operator ^. ^,^of spatial coding expressed as the identity operator from which a normalized modified spatial coding operator is subtracted. The normalized modified spatial coding operator is a function of a composition between a modified spatial precoding operator and an operator modeling the estimated propagation channel between the transmitter and the receivers. The modified spatial precoding operator is a function of an operator, called the receivers operator, from which a regularization operator is subtracted. The receivers operator is a function of a composition between an operator modeling the estimated propagation channel between the receivers and the transmitter and the operator modeling an estimated propagation channel between the transmitter and the receivers. Each diagonal element of the receivers operator is representative of a power received by the corresponding receiver.The regularization operator is of the diagonal type, each diagonal element of the regularization operator is associated with a corresponding receiver, an amplitude of each diagonal element of the regularization operator makes it possible to control the level of distortion linked to the difference between the OFDM symbols and the clipped OFDM symbols transmitted in the direction of the corresponding receiver. Thus, the invention proposes a new and inventive solution for reducing the crest factor of an OFDM type signal, e.g. in a CF-mMIMO context. More particularly, it is proposed to use a spatial coding of the distortion signal linked to the clipping so as to transmit the signal in question in priority to the receivers furthest from the AP incorporating the transmitter considered, i.e. the weak receivers. Indeed, it is likely that in an AP-dense system, as in a scalable CF-mMIMO type system, such weak receivers are located near another AP.It can thus be assumed that weak receivers from the point of view of a given AP are "strong" from the point of view of another AP. It is thus likely that the emission of the distortion linked to clipping towards weak receivers will not penalize the overall performances for weak receivers, the latter also receiving their data via another AP. Furthermore, the transmission of the distortion signal towards receivers connected to the AP considered rather than in a direction in which no receiver is present makes it possible to overcome the problem of the absence of degrees of freedom available when the number of receivers connected to the AP incorporating the transmitter considered is greater than the number of transmitting antennas of this AP. The present technique is thus particularly adapted to a system of the scalable CF-mMIMO type.In some embodiments, said at least one predetermined direction does not include at least one direction of a receiver, called a strong receiver, for which the estimated propagation channel corresponds to a propagation loss lower than the predetermined threshold. Thus, the spatial coding of the distortion signal linked to the clipping means that the distortion signal in question is not transmitted in the direction of the receivers closest to the AP incorporating the transmitter considered, i.e. the strong receivers. In some embodiments, obtaining M clipped OFDM symbols includes a spatial precoding of N vectors of ^. ^modulation symbols delivering M vectors of N precoded symbols. Each component of a given vector of N precoded symbols is intended to be carried by a corresponding subcarrier of a spatial component of the OFDM signal. The generation of an OFDM symbol implements, for each antenna of the transmitter, an inverse Fourier transformation applied to an input vector which is a function of a respective vector of N precoded symbols. The precoding implements a spatial precoding of the M spatial components on the basis of the estimated propagation channel between the receivers and the transmitter to compensate for the propagation channel during the propagation of the OFDM signal to the receivers. Thus, the useful data are transmitted towards the receivers concerned, the propagation channel being compensated during the propagation of the OFDM signal from the transmitter in question to the receivers concerned.In some embodiments, the modified spatial precoding operator is expressed as:. with, ^ being an index of said given subcarrier and ^ an identifier of the transmitter: - ^ ^ ^,^ the operator modeling the estimated propagation channel between the receivers and the transmitter; - ^ ^ ^ ^,^ the operator modeling the estimated propagation channel between the transmitter and the receivers; - ^ ^ ^ ^ ,^ ^ ^ ^,^the receivers operator; and - the diagonal type regularization operator. Thus, the spatial coding operator implemented during the projection is based on a spatial precoding operator obtained from a zero-forcing type propagation channel equalization technique. In some embodiments, at least one amplitude of a diagonal element of the regularization operator for controlling the level of distortion transmitted in the direction of a given weak receiver is inversely proportional to the power allocated to the given weak receiver. The allocated power is calculated as a function of the propagation loss corresponding to the estimated propagation channel between the given weak receiver and the transmitter.In some embodiments wherein said at least one predetermined direction does not include at least one direction of a strong receiver, at least one amplitude of a diagonal element of the regularization operator for controlling the level of distortion transmitted in the direction of a given strong receiver is zero. In some embodiments wherein obtaining M clipped OFDM symbols includes said spatial precoding, the modified spatial precoding operator reduces, when the regularization operator reduces to the zero operator, to an operator implemented during said precoding step. In some embodiments, said at least one given subcarrier corresponds to a modulated subcarrier of the OFDM type signal. In some embodiments, the concatenation and the projection are implemented for a plurality of modulated subcarriers of the OFDM type signal.In some embodiments, clipping implements a threshold ^ beyond which an amplitude of the OFDM symbol is made constant equal to ^. The threshold is given by:. with: - ^ ^ a variance of the spatial components transmitted by the transmitter antennas; - ^ ^ a maximum number of different pilot signals present in an uplink frame implemented between the receivers and the transmitter; and - ^ ^a low number of receivers. In some embodiments, the method is implemented iteratively. The updated OFDM symbol and the updated clipped OFDM symbol obtained during a given rank iteration correspond respectively to the OFDM symbol and the clipped OFDM symbol of a following rank iteration. In some embodiments, the projection comprises a normalization of the vector of M reduction signals to make the vector of M reduction signals and the subcarrier error vector similar. In some embodiments, the normalization implements a weighting of the vector of M reduction signals by a weighting factor ^ ^ given by: with, ^ being an index of said given subcarrier, ^ an identifier of the transmitter and m an index indexing the transmitter antennas: - ^ ^ the subcarrier error vector; and - ^ ^,^ ^ ^the vector of M reduction signals. The invention also relates to a computer program comprising program code instructions for implementing the method for reducing the crest factor as described above, according to any one of its various embodiments, when executed on a computer. In one embodiment of the invention, a device is provided for reducing the crest factor of an OFDM type signal comprising N subcarriers. The signal results from the superposition of M spatial components each emitted by a respective antenna of a radiofrequency transmitter to a plurality of receivers. Such a device comprises a reprogrammable computing machine or a dedicated computing machine configured to implement the steps of the method for reducing the crest factor described above (according to any one of the various embodiments mentioned above).Thus, the characteristics and advantages of this device are the same as those of the corresponding steps of the crest factor reduction method described above. Consequently, they are not detailed further. In one embodiment of the invention, a radiofrequency transmitter is provided comprising a crest factor reduction device described above (according to any one of the various embodiments mentioned above). List of figures Other aims, characteristics and advantages of the invention will appear more clearly on reading the following description, given by way of simple illustrative, and non-limiting, example, in relation to the figures, among which: [Fig. 1a], described above in relation to the prior art, illustrates a radiocommunications network implementing APs according to a technology of the CF-mMIMO type; [Fig.1b], described above in relation to the prior art, illustrates a radiocommunications network implementing APs according to a technology of the scalable CF-mMIMO type; [Fig.2] represents different functional modules implemented in a transmitter of an AP according to an embodiment of the invention, such an AP being able to be implemented eg in the network of [Fig.1a] or in the network of [Fig.1b]; [Fig.3] represents an example of a device structure being able to be implemented in the transmitter of [Fig.2] and allowing the implementation of the steps of the method for reducing the crest factor of [Fig.4] according to an embodiment of the invention; [Fig.4] represents the steps of a method for reducing the crest factor of an OFDM type signal according to an embodiment of the invention.Detailed description of embodiments of the invention The general principle of the invention is based on the use of spatial coding of the distortion signal linked to the clipping of the OFDM signal transmitted by an AP 110 so that the distortion signal in question is transmitted in one (or more) directions of a 100w receiver for which the estimated propagation channel, between the 100w receiver and the AP 110 considered, corresponds to a propagation loss greater than a predetermined threshold. Thus, the distortion signal is transmitted as a priority to the 100w receivers furthest from the AP 110 considered. Indeed, it is likely that in a system dense in APs 110, as in a system of the scalable CF-mMIMO type, such 100w receivers distant from the AP 110 considered are located near another AP 110.It is thus likely that the transmission of the distortion linked to clipping to such 100w receivers will not penalize their performance, the latter also receiving their data via another AP 110. Furthermore, the transmission of the distortion signal to 100w receivers connected to the AP 110 considered rather than in a direction in which no terminal 100 is present makes it possible to overcome the problem of the absence of degrees of freedom available when the number of connected terminals 100 is greater than the number of transmission antennas of the AP 110 considered. The present technique is thus particularly suited to a system of the scalable CF-mMIMO type. We now present, in relation to [Fig.2] different functional modules implemented in a 110tx transmitter of an AP 110 according to an embodiment of the invention.Such modules implement in particular the functionalities implemented in the crest factor reduction method of [Fig.4]. In this way, depending on the implementations considered, such modules can be software or hardware modules as described further below in relation to [Fig.3]. Returning to [Fig.2], the transmitter 110tx is configured to generate an OFDM type signal comprising N subcarriers. More particularly, the signal in question results from the superposition of M spatial components each emitted by a respective antenna 250 of the radiofrequency transmitter 110tx. The signal thus generated is emitted to a plurality of receivers 100w, 100s, eg receivers of 100 user terminals. According to the present technique, 100w, 100s receivers are differentiated according to the estimated propagation loss between the considered 100w, 100s receiver and the 110tx transmitter.More specifically: - some 100w receivers, called weak receivers, correspond to a propagation loss greater than a predetermined threshold. In other words, the weak 100w receivers are estimated, via the estimation of the propagation channel, as being the furthest from the 110tx transmitter; and - other 100s receivers, called strong receivers, correspond to a propagation loss lower than said predetermined threshold. In other words, the strong 100s receivers are estimated, via the estimation of the propagation channel, as being the closest to the 110tx transmitter. Returning to [Fig.2], the 110tx transmitter comprises a spatial precoding module 200 operating on N vectors ^. ^ ,…, ^ ^ of ^ ^ modulation symbols to deliver M vectors ^^ ^ ,^ , of N precoded symbols. Each component of a given vector of N precoded symbols being intended to be carried by a corresponding subcarrier of a spatial component of the OFDM type signal. According to the present notations: - ^ represents an identifier of the AP 110, or equivalently of the transmitter 110tx; and - ^ ^ represents a maximum number of different pilot signals present in an uplink frame implemented between the terminals 100 implementing the receivers 100w, 100s and the AP 110 implementing the transmitter 110tx. The pilot signals in question make it possible to estimate the propagation channel between the receivers 100w, 100s and the AP 110 in the uplink direction. For example, when the number K of receivers 100w, 100s connected to the AP 110 is greater than the maximum number of different pilot signals, ^ ^, the same channel is estimated for all the 100w, 100s receivers using the same pilot signal. In this case, the same spatial precoding, as described below in relation to the module 200, is implemented for all the 100w, 100s receivers using the same pilot signal. Indirectly, such an estimation of the propagation channel between the 100w, 100s receivers and the AP 110 in the uplink direction also makes it possible to estimate the propagation channel between the 100w, 100s receivers and the 110tx transmitter in the downlink direction, e.g. in a TDD (Time-Division Duplex) type system in which the same frequency band is used for the uplink and the downlink.More particularly, the module 200 implements a spatial precoding of the M spatial components of the OFDM type signal on the basis of the estimated propagation channel between the receivers 100w, 100s and the transmitter 110tx to compensate said propagation channel during the propagation of the OFDM type signal to the receivers 100w, 100s. For example, according to a zero-forcing equalization approach, we seek to have for each vector ^ , ^. ^ of ^ ^ symbols to be transmitted, the same symbol vector received at the 100w, 100s receivers. In other words, we seek to have, for the subcarrier of index ^ of the OFDM type signal: [Math.1] Where, ^ being an identifier of the 110tx transmitter: - ^ ^,^ denotes the spatial precoding operator to be determined; and - ^ ^ ^ ^,^denotes the operator modeling the estimated propagation channel between the 110tx transmitter and the 100w, 100s receivers, i.e. in the downlink direction. The optimal solution to equation [Math.1] is given by: [Math.2] Where ^ ^ ^,^ denotes the operator modeling the estimated propagation channel between the 100w, 100s receivers and the 110tx transmitter, i.e. in the uplink direction. Indeed, it can be verified that: [Math.3] ^ ^ ^ ^,^^^,^ = ^^ ^ ^,^ ^^ ^,^ ^^^^ ^,^ ^ ^ ^,^^ ^^ = ^ ^^,^^ Where: - ^ ^^,^^ denotes the identity matrix of rank ^ ^ ; And - ^ ^ ^ ^,^^ ^ ^,^ represents an operator, called receiver operator, of rank ^ ^. More specifically, a diagonal element of given index of this receiver operator represents the propagation losses between the transmitter 110tx and the receiver(s) 100w, 100s using the pilot signal corresponding to the index considered on the uplink. The off-diagonal elements of this receiver operator represent the coupling between the receivers using the two pilot signals corresponding to the indices of the considered off-diagonal element. Returning to [Fig.2], the module 200 implements N spatial coding modules 200a as such. Each of the N modules implements an operator processing a vector ^ ^ of ^ ^ symbols and outputs a vector ^ ^,^ of M elements. The operator in question is for example the ^ operator ^,^defined by equation [Math.2]. However, in other embodiments, other equalization techniques than the zero-forcing technique are considered in order to obtain the spatial coding operator. Returning to [Fig.2], the module 200 also implements a module 200b for reorganizing the N vectors ^ ^,^ ,…, ^ ^,^ of M elements in order to deliver the M vectors ^^ ^ ,^ ,…, of N precoded symbols, each vector ^^ ^ ,^ being associated with an antenna 250 of the transmitter 110tx. More particularly, the ^-th element of the vector ^^ ^ ,^ corresponds to the ^-th element of the vector ^ ^,^ , ^ an integer varying from 1 to N and ^ an integer varying from 1 to M. The transmitter 110tx comprises a module 270 delivering, for an antenna 250 indexed ^ of the transmitter 110tx, an input vector resulting from the sum between, on the one hand, the vector ^^ ^ ,^of N elements and, on the other hand, a vector of N elements comprising reduction signals each applying to a corresponding subcarrier of the spatial component transmitted by said antenna indexed ^ of the transmitter 110tx. Such an input vector is obtained for each of the M antennas 250 of the transmitter 110tx. Obtaining the vectors ^ …, ^ ^ by the module 260 is detailed further below. The transmitter 110tx comprises, for an antenna 250 indexed ^ of the transmitter 110tx, ^ an integer varying from 1 to M, a module 220 for generating an OFDM symbol of N samples from the corresponding N-element input vector. Such an OFDM symbol is obtained for each of the M antennas 250 of the transmitter 110tx. A given generation module 220 implements, for example, the inverse Fourier transform of a corresponding input vector. The transmitter 110tx comprises, for an antenna 250 indexed ^ of the transmitter 110tx, ^ an integer varying from 1 to M, a module 230 for clipping the OFDM symbol delivering a clipped OFDM symbol ^,^ corresponding. For example, clipping implements a threshold ^ beyond which an amplitude of the OFDM symbol ^ ,^ is made constant equal to ^. For example, according to some implementations the threshold is given by: [Math.4] with: - ^ ^ a variance of the spatial components transmitted by the 250 antennas of the 110tx transmitter; - ^ ^ the maximum number of pilot signals as defined above; and - ^ ^the number of low 100w receivers. The threshold ^ as defined by equation [Math.4] allows for optimal performance with respect to crest factor reduction. ^ Returning to [Fig.2], such a clipped OFDM symbol ^ ^,^ is obtained for each of the M antennas 250 of the transmitter 110tx. Furthermore, the transmitter 110tx comprises, for an antenna 250 indexed ^ of the transmitter 110tx, ^ an integer varying from 1 to M, a transmission module 240 delivering the spatial component transmitted by the antenna in question. Such a transmission module 240 implements the known, mixed or analog, functionalities of a transmitter. These are, for example, the digital / analog conversion, filtering, frequency conversion and power amplification functionalities. Such a spatial component is obtained for each of the M antennas 250 of the transmitter 110tx. In order to obtain the vectors ^^ ^ , the module 260 comprises a Fourier transform module 260a. More particularly, for an antenna 250 indexed ^ of the transmitter 110tx, ^ an integer varying from 1 to M, the module 260a implements a Fourier transform of an error vector ^ depending on a difference between the clipped OFDM symbol ^ ^,^ and the OFDM symbol delivering a transformed error vector ^ of N error signals. The Fourier transform is repeated for each transmitter antenna delivering M transformed error vectors ^ , ^^ ^ of N error signals. The module 260 comprises a module 260b for concatenating the error signals associated with the subcarrier of index ^ in each of the M transformed error vectors ^ ^ , ^ ^ delivering an error vector, called the subcarrier error vector ^ ^ , of M error signals, each error signal in the subcarrier error vector ^ ^being associated with a respective antenna. The module 260 comprises a module 260c for projecting the subcarrier error vector ^ ^delivering a vector of M crest factor reduction signals associated with the subcarrier of index ^. Each crest factor reduction signal in the vector of M crest factor reduction signals being associated with a respective antenna. Furthermore, the modules 260b and 260c are implemented for all or part of the subcarriers of the OFDM type signal generated and transmitted by the transmitter 110tx as described below in relation to [Fig. 4]. For example, the modules 260b and 260c are implemented to obtain the vectors of M crest factor reduction signals associated with the active subcarriers of the OFDM type signal, the crest factor reduction signals associated with the non-active subcarriers of the OFDM type signal being set to zero. Whatever the values of the crest factor reduction signals, the vectors ^ , ^ ^are obtained by rearranging the vectors of M crest factor reduction signals associated with the different subcarriers. More specifically, a vector of N elements ^ ^ ^ , ^ an integer varying from 1 to M, comprises the reduction signals applying to each corresponding subcarrier of the spatial component transmitted by the antenna indexed ^ of the transmitter 110tx. More particularly, the spatial coding implemented by the module 200 makes it possible to compensate for the propagation channel during the propagation of the OFDM type signal from the transmitter 110tx to the different receivers 100w, 100s connected to the AP 110. Conversely, the projection implemented in the module 260c implements, for the subcarriers concerned, a spatial coding of the M error signals of the subcarrier error vector ^ ^ , based on the estimated propagation channel ^, so that the distortion signal related to the difference between the clipped OFDM symbols ^ ^,^and OFDM symbols ^^ ^ ,^is transmitted by the transmitter 110tx in at least one direction of a weak 100w receiver. Thus, the distortion signal 290d is transmitted in at least one direction of a weak 100w receiver while the signal 290u carrying the useful data is transmitted to all the connected 100w, 100s receivers. We now present, in relation to [Fig.3], an example of a structure of an electronic device 300 allowing the execution of the steps of the method for reducing the crest factor of [Fig.4] according to an embodiment of the invention. The device 300 allows in particular the implementation of the corresponding modules described above in relation to [Fig.2]. More particularly, the device 300 comprises a random access memory 303 (for example a RAM memory), a processing unit 302 equipped for example with a processor, and controlled by a computer program stored in a read-only memory 301 (for example a ROM memory or a hard disk).At initialization, the code instructions of the computer program are for example loaded into the RAM 303 before being executed by the processor of the processing unit 302. This [Fig. 3] illustrates only one particular way, among several possible ones, of producing the device 300 so that it performs certain steps of the method for reducing the crest factor of [Fig. 4] (according to any one of the embodiments described below in relation to [Fig. 4]). Indeed, these steps can be carried out indifferently on a reprogrammable computing machine (a PC computer, a DSP processor or a microcontroller) executing a program comprising a sequence of instructions, or on a dedicated computing machine (for example a set of logic gates such as an FPGA or an ASIC, or any other hardware module).In the case where the device 300 is produced with a reprogrammable computing machine, the corresponding program (i.e. the sequence of instructions) may be stored in a removable storage medium (such as for example a CD-ROM, a DVD-ROM, a USB key) or not, this storage medium being partially or totally readable by a computer or a processor. In certain embodiments, the device 300 is included in a transmitter 110tx, eg a transmitter 110tx of an AP 110. We now present, in relation to [Fig. 4], the steps of a method for reducing the crest factor of an OFDM type signal according to an embodiment of the invention. More particularly, during a step E400, the device 300 executes an obtaining of M ^ ^ clipped OFDM symbols ^. , ^ ^,^each intended to be a temporal portion of a spatial component transmitted by a respective antenna 250 of the transmitter 110tx. More particularly, step E400 comprises a step E400a of spatial precoding of N vectors ^ ^ ,…, ^ ^ of ^ ^ modulation symbols to deliver M vectors ^^ ^ ,^,…, of N precoded symbols. Each component of a given vector of N precoded symbols being intended to be carried by a corresponding subcarrier of a spatial component of the OFDM type signal. More particularly, step E400a implements the functionalities of the module 200 described above in relation to [Fig.2]. In particular, the spatial precoding of the M spatial components is based on the estimated propagation channel between the receivers 100w, 100s and the transmitter 110tx to compensate for the propagation channel during the propagation of the OFDM type signal to the receivers 100w, 100s. For example, the spatial precoding implements an operator processing each vector ^ ^ , ^ an integer ranging from 1 to N, of ^ ^ symbols and outputs a vector ^ ^,^ of M elements. The operator in question is for example the ^ operator ^,^defined by equation [Math.2]. However, in other embodiments, other equalization techniques than the zero-forcing technique are considered in order to obtain the spatial coding operator. Returning to [Fig.4], step E400 comprises, for at least one antenna 250 indexed ^ of the transmitter 110tx, ^ an integer varying from 1 to M: - a step E400b of generating an OFDM symbol by implementing an inverse Fourier transform applied to the input vector as a function of the vector of N precoded symbols. Each component of the input vector is intended to be carried by a corresponding subcarrier of a spatial component of the OFDM type signal; and - a step E400c of clipping the OFDM symbol ^ ,^ delivering a clipped OFDM symbol ^ ^ ^,^intended to be a temporal portion of the spatial component transmitted by said antenna 250 indexed ^; Step E400b and step E400c repeated for each antenna 250 of the transmitter 110tx deliver M clipped OFDM symbols More particularly, step E400b implements the functionalities of the module 220 described above in relation to [Fig.2] and step E400c implements the functionalities of the module 230 described above in relation to [Fig.2]. In particular, as described above in relation to [Fig.2], the input vector associated with the antenna 250 indexed ^ results from the sum between, on the one hand, the vector ^^ ^ ,^ of N elements and, on the other hand, a vector of N elements comprising reduction signals each applying to a corresponding subcarrier of the spatial component transmitted by said antenna indexed ^ of the transmitter 110tx. Such an input vector is obtained for each of the M antennas 250 of the transmitter 110tx. Obtaining the vectors ,…, ^^ ^ is detailed further below in relation to steps E410, E420 and E430. As described above in relation to [Fig.2], the addition of the reduction signals to the input elements of the inverse Fourier transform implemented in step E400b allows the ^ transmission of the distortion signal linked to the difference between the clipped OFDM symbols ^ ^,^ and OFDM symbols in at least one direction of a weak 100w receiver. Furthermore, in certain embodiments, the spatial precoding step E400a is not implemented. Indeed, the emission of the distortion signal linked to the clipping of the OFDM signal transmitted by the AP 110 in one (or more) directions of a weak 100w terminal is obtained independently of such spatial precoding of the useful data. Only the addition of the reduction signals to the input elements of the inverse Fourier transform implemented during step E400b to generate the OFDM symbols is necessary to obtain this effect. In such embodiments, said inverse Fourier transform implemented during step E400b is applied to an input vector which is a direct function of vectors of N modulation symbols and not a function of the vectors of N precoded symbols. Returning to [Fig.4], in order to obtain the vectors ,…, ^^ ^ comprising the reduction signals, the device 300 executes, for at least one antenna 250 indexed ^ of the transmitter 110tx, ^ an integer varying from 1 to M, a step E410 of Fourier transformation of an error vector ^ function of a difference between the clipped OFDM symbol ^ ^,^ and the OFDM symbol ^^ ^ ,^ associated with the 250 antenna indexed ^, delivering a transformed error vector of N error signals. The Fourier transform is repeated for each transmitter antenna delivering M transformed error vectors error signals. More particularly, step E410 implements the functionalities of the module 260a described above in relation to [Fig.2]. Returning to [Fig.4], the device 300 executes, for at least one subcarrier of index ^, ^ an integer varying from 1 to N: - a step E420 of concatenation of the error signals associated with the given subcarrier in each of the M transformed error vectors ^ ,…, ^ ^ delivering the subcarrier error vector ^ ^ , of M error signals. Each error signal in the subcarrier error vector being associated with a respective antenna; and - a step E430 of projecting the subcarrier error vector ^ ^ delivering a vector of M crest factor reduction signals associated with the subcarrier of index ^. Each crest factor reduction signal in the vector of M reduction signals is associated with a respective antenna. More particularly, during step E430, the projection implements a spatial coding of the M error signals of the subcarrier error vector ^ ^ based on the estimated propagation channel between the 100w, 100s receivers and the 110tx transmitter so that the distortion signal related to the ^ ^ difference between the clipped OFDM symbols ^ …, ^ ^,^ and OFDM symbols ^ , ^ ^,^is transmitted by the transmitter 110tx in at least one direction of a weak 100w. According to the embodiments considered, step E420 and step E430 are implemented for all or part of the subcarriers of the OFDM type signal generated and transmitted by the transmitter 110tx. For example, step E420 and step E430 are implemented to obtain the vectors of M crest factor reduction signals associated with the active subcarriers of the OFDM type signal, the crest factor reduction signals associated with the non-active subcarriers of the OFDM type signal being set to zero. For example, step E420 and step E430 are not implemented for the non-active subcarriers of the OFDM type signal. Furthermore, in certain embodiments, said at least one predetermined direction does not comprise at least one direction of a strong receiver 100s. In some embodiments, during step E430, the projection implements an operator ^ ^,^of the spatial coding expressed as the identity operator from which a normalized modified spatial coding operator is subtracted. The normalized modified spatial coding operator is a function of a composition between a modified spatial precoding operator and the operator modeling the estimated propagation channel between the 110tx transmitter and the 100w, 100s receivers. The modified spatial precoding operator is a function of a receivers operator, from which a regularization operator is subtracted. The receivers operator, following the definition given above in relation to [Fig.2], is a function of a composition between the operator modeling the estimated propagation channel between the 100w, 100s receivers and the 100tx transmitter (i.e. in the uplink direction) and the operator modeling the estimated propagation channel between the 100tx transmitter and the 100w, 100s receivers (i.e. in the downlink direction).Each diagonal element of the receivers operator is representative of a power received by the corresponding receiver. The regularization operator is of the diagonal type, each diagonal element of the regularization operator is associated with a corresponding 100w, 100s receiver. An amplitude of each diagonal element of the regularization operator allows to control the level of distortion related to the difference ^ ^ ^ ^ between the OFDM symbols ^. ^,^ ,…, ^ ^,^ and clipped OFDM symbols ^ , ^ ^,^transmitted in the direction of the corresponding 100w, 100s receiver. The modified spatial precoding operator reduces, when the regularization operator reduces to the zero operator, to a spatial precoding operator, eg as implemented in known MIMO techniques. For example, in some embodiments, at least one magnitude of a diagonal element of the regularization operator for controlling the level of distortion transmitted in the direction of a given 100w weak receiver is inversely proportional to the power allocated, by the 110tx transmitter, to the given 100w weak receiver within the OFDM type signal. Such power is eg calculated as a function of the propagation loss corresponding to the estimated propagation channel between the given 100w weak receiver and the 110tx transmitter. Such a calculation of the allocated power is performed eg according to a power allocation mechanism implemented at the 110tx transmitter.Similarly, in some embodiments, at least one amplitude of a diagonal element of the regularization operator for controlling the level of distortion transmitted in the direction of a given strong receiver 100s is zero. For example, in some embodiments, the modified spatial precoding operator reduces, when the regularization operator reduces to the zero operator, to the operator implemented during the precoding step E400a. More particularly, in the case taken as an illustrative example above in connection with the description of [Fig.2] of spatial precoding according to a channel equalization approach of equalization by forcing to zero, the modified spatial precoding operator is expressed as: [Math.5]. with, ^ being an index of said given subcarrier and ^ an identifier of the 110tx transmitter: - ^ ^ ^,^the operator modeling the estimated propagation channel between the 100w, 100s receivers and the 110tx transmitter, i.e. in the uplink direction; - ^ ^ ^ ^,^ the operator modeling said estimated propagation channel between the 110tx transmitter and the 100w, 100s receivers, i.e. in the downlink direction; - ^ ^ ^ ^ ,^ ^ ^ ^,^ the receiver operator; and regularization. Thus, the operator ^ ^,^ spatial coding is expressed in this case as: [Math.6] Thus, in the case where the regularization operator ^ ^ is zero, the ^ operator ^,^ reduces to: [Math.7] We can then verify that: [Math.8] In other words, the construction as described above of the ^ operator ^,^ implemented during step E430 is such that no distortion signal related to the difference between the clipped OFDM symbols ^,^ and OFDM symbols ^^ ^,^ is transmitted in the direction of a 100w receiver, 100s corresponding to a diagonal element of the regularization operator ^ ^which is zero. Conversely, a non-zero amplitude of a given diagonal element of the regularization operator makes it possible to transmit the distortion in question in the direction of the corresponding 100w, 100s receiver and to control its level. This result applies regardless of the nature of the spatial precoding operator on which the modified spatial precoding operator is based, i.e. whether the spatial precoding operator is based on a zero-forcing propagation channel equalization technique, as considered as an example above, or on another equalization technique. Furthermore, in certain embodiments, the crest factor reduction method (according to any of the embodiments described above) is implemented iteratively.An OFDM symbol and the clipped OFDM symbol obtained during a given rank iteration being based on an input vector that is a function of reduction signals determined, via the execution of steps E410, E420 and E430, from an OFDM symbol and a clipped OFDM symbol of a previous rank iteration. For example, during the first iteration, the reduction signals are initialized to a zero value. In some embodiments, during step E430, the projection comprises a normalization of the vector of M crest factor reduction signals to make said vector of M crest factor reduction signals and the subcarrier error vector ^ similar. ^ . Such normalization allows in particular a faster convergence when the method is implemented in iterative form. For example, the normalization implements a weighting of the vectors of M signals of reduction of the crest factor by a weighting factor ^ ^given by: [Math.9] with, ^ being an index of said given subcarrier, ^ an identifier of the 110tx transmitter and ^ an index indexing the antennas of the 110tx transmitter: - ^ ^ the subcarrier error vector; and - ^ ^,^ ^ ^ the vector of M reduction signals.
Claims
CLAIMS 1. Method for reducing the crest factor of an OFDM type signal comprising N subcarriers, said signal resulting from the superposition of M spatial components each emitted by a respective antenna (250) of a radiofrequency transmitter (110tx) to a plurality of receivers (100w, 100s), in which an electronic device (300) performs an obtaining (E400) of M clipped OFDM symbols each intended to be a temporal portion of a spatial component transmitted by a respective antenna of the transmitter, said obtaining comprising, for at least one antenna of the transmitter: - a generation (E400b) of an OFDM symbol by implementing an inverse Fourier transformation applied to an input vector which is a function of modulation symbols,each component of the input vector being intended to be carried by a corresponding subcarrier of a spatial component of the OFDM type signal; and - a clipping (E400c) of the OFDM symbol delivering a clipped OFDM symbol intended to be a temporal portion of the spatial component transmitted by said antenna; said generation and said clipping repeated for each antenna of the transmitter delivering said M clipped OFDM symbols, in which the electronic device executes, for at least one given antenna of the transmitter: - a Fourier transformation (E410) of an error vector depending on a difference between the clipped OFDM symbol and the OFDM symbol associated with the given antenna, delivering an error vector transformed by N error signals, said Fourier transformation repeated for each antenna of the transmitter delivering M error vectors transformed by N error signals, in which the electronic device executes,for at least one given subcarrier: - a concatenation (E420) of the error signals associated with the given subcarrier in each of the M transformed error vectors delivering an error vector, called subcarrier error vector, of M error signals, each error signal in the subcarrier error vector being associated with a respective antenna; and - a projection (E430) of said subcarrier error vector delivering a vector of M crest factor reduction signals associated with the given subcarrier, each crest factor reduction signal in said vector of M reduction signals being associated with a respective antenna; wherein the electronic device executes a new implementation of said obtaining, of M clipped OFDM symbols to generate M updated clipped OFDM symbols, wherein said generation, for at least one antenna of the transmitter, of an OFDM symbol implements said inverse Fourier transformation applied to an updated input vector, the updated input vector being a function of N new modulation symbols, the crest factor reduction signal of the vector of M reduction signals corresponding to said antenna and associated with the given subcarrier being added to the new modulation symbol intended to be carried by said given subcarrier in the updated input vector;wherein said projection implements a spatial coding of said M error signals of the subcarrier error vector on the basis of an estimated propagation channel between said receivers and said transmitter so that the distortion signal linked to the difference between the clipped OFDM symbols and the OFDM symbols is transmitted by the transmitter in at least one direction of a receiver (100w), called weak receiver, for which the estimated propagation channel corresponds to a propagation loss greater than a predetermined threshold, characterized in that said projection implements an operator ^; ^,^said spatial coding being expressed as the identity operator from which is subtracted a modified normalized spatial coding operator, the modified normalized spatial coding operator being a function of a composition between a modified spatial precoding operator and an operator modeling said estimated propagation channel between said transmitter and said receivers, the modified spatial precoding operator being a function of an operator, called receivers operator, from which is subtracted a regularization operator, the receivers operator being a function of a composition between an operator modeling said estimated propagation channel between said receivers and said transmitter and said operator modeling an estimated propagation channel between said transmitter and said receivers, each diagonal element of said receivers operator being representative of a power received by the corresponding receiver, the regularization operator being of the diagonal type,each diagonal element of said regularization operator being associated with a corresponding receiver, an amplitude of each diagonal element of said regularization operator making it possible to control the level of distortion linked to the difference between the OFDM symbols and the clipped OFDM symbols transmitted in the direction of the corresponding receiver., 2. Method according to claim 1, wherein said at least one predetermined direction does not include at least one direction of a receiver (100s), called a strong receiver, for which the estimated propagation channel corresponds to a propagation loss lower than said predetermined threshold.
3. Method according to claim 1 or 2, wherein said obtaining of M clipped OFDM symbols comprises: - a spatial precoding (E400a) of N vectors of ^ ^modulation symbols delivering M vectors of N precoded symbols, each component of a given vector of N precoded symbols being intended to be carried by a corresponding subcarrier of a spatial component of the OFDM type signal, said generation of an OFDM symbol implementing, for each antenna of the transmitter, an inverse Fourier transformation applied to an input vector which is a function of a respective vector of N precoded symbols, said precoding implementing a spatial precoding of said M spatial components on the basis of said estimated propagation channel between said receivers and said transmitter to compensate for said propagation channel during the propagation of said OFDM type signal to said receivers.
4. Method according to any one of claims 1 to 3, in which the modified spatial precoding operator is expressed as: with, ^ being an index of said given subcarrier and ^ an identifier of the transmitter: - ^ ^ ^,^ said operator modeling said estimated propagation channel between said receivers and said transmitter; - ^ ^ ^ ^,^ said operator modeling said estimated propagation channel between said transmitter and said receivers; - ^ ^ ^ ^ ,^ ^ ^ ^,^ said receiver operator; and said diagonal type regularization operator.
5. Method according to any one of claims 1 to 4, wherein at least one amplitude of a diagonal element of said regularization operator for controlling the level of distortion transmitted in the direction of a given weak receiver is inversely proportional to the power allocated to the given weak receiver, the allocated power being calculated as a function of the propagation loss corresponding to the propagation channel estimated between the given weak receiver and the transmitter.
6. Method according to claim 2 or according to any one of claims 3 to 5 in that it depends on claim 2, wherein at least one amplitude of a diagonal element of said regularization operator for controlling the level of distortion transmitted in the direction of a given strong receiver is zero.
7. Method according to claim 3 or according to any one of claims 4 to 6 in that it depends on claim 3, wherein the modified spatial precoding operator reduces, when the regularization operator reduces to the zero operator, to an operator implemented during said precoding step.
8. Method according to any one of claims 1 to 7, wherein said at least one given subcarrier corresponds to a modulated subcarrier of said OFDM type signal. 9.A method according to any one of claims 1 to 8, wherein said clipping implements a threshold ^ beyond which an amplitude of said OFDM symbol is made constant equal to ^, said threshold being given by:. with: - ^ ^ a variance of the spatial components transmitted by the transmitter antennas; - ^ ^ a maximum number of different pilot signals present in an uplink frame implemented between the receivers and the transmitter; and - ^ ^a low number of receivers.
10. A method according to any one of claims 1 to 9, said method being implemented iteratively, the updated OFDM symbol and the updated clipped OFDM symbol obtained during a given rank iteration corresponding respectively to the OFDM symbol and the clipped OFDM symbol of a following rank iteration.
11. A method according to any one of claims 1 to 10, wherein said projection comprises a normalization of said vector of M reduction signals to make similar said vector of M reduction signals and said subcarrier error vector.
12. The method of claim 11, wherein said normalization implements a weighting of said vector of M reduction signals by a weighting factor ^ ^ given by: with, ^ being an index of said given subcarrier, ^ an identifier of the transmitter and m an index indexing the transmitter antennas: - ^^ said subcarrier error vector; and - ^ ^,^ ^ ^said vector of M reduction signals.
13. Computer program product comprising program code instructions for implementing a method according to any one of claims 1 to 12, when said program is executed on a computer.
14. Electronic device (300) for reducing the crest factor of an OFDM type signal comprising N subcarriers, said signal resulting from the superposition of M spatial components each emitted by a respective antenna (250) of a radiofrequency transmitter (110tx) to a plurality of receivers (100w, 100s), said electronic device comprising a reprogrammable computing machine (302) or a dedicated computing machine configured to perform an obtaining (E400) of M clipped OFDM symbols each intended to be a temporal portion of a spatial component transmitted by a respective antenna of the transmitter, said obtaining comprising,for at least one antenna of the transmitter: - a generation (E400b) of an OFDM symbol by implementing an inverse Fourier transformation applied to an input vector which is a function of modulation symbols, each component of the input vector being intended to be carried by a corresponding sub-carrier of a spatial component of the OFDM type signal; and - a clipping (E400c) of the OFDM symbol delivering a clipped OFDM symbol intended to be a temporal portion of the spatial component transmitted by said antenna; said generation and said clipping repeated for each antenna of the transmitter delivering said M clipped OFDM symbols, in which said reprogrammable computing machine or said dedicated computing machine is, configured to perform, for at least one given antenna of the transmitter: - a Fourier transformation (E410) of an error vector depending on a difference between the clipped OFDM symbol and the OFDM symbol associated with the given antenna, delivering a transformed error vector of N error signals, said Fourier transformation repeated for each antenna of the transmitter delivering M transformed error vectors of N error signals, wherein said reprogrammable computing machine or said dedicated computing machine is configured to perform, for at least one given subcarrier: - a concatenation (E420) of the error signals associated with the given subcarrier in each of the M transformed error vectors delivering an error vector, called subcarrier error vector, of M error signals, each error signal in the subcarrier error vector being associated with a respective antenna;and - a projection (E430) of said subcarrier error vector delivering a vector of M crest factor reduction signals associated with the given subcarrier, each crest factor reduction signal in said vector of M reduction signals being associated with a respective antenna;wherein said reprogrammable computing machine or said dedicated computing machine is configured to perform a new implementation of said obtaining of M clipped OFDM symbols to generate M updated clipped OFDM symbols, wherein said generation, for at least one antenna of the transmitter, of an OFDM symbol implements said inverse Fourier transformation applied to an updated input vector, the updated input vector being a function of N new modulation symbols, the crest factor reduction signal of the vector of M reduction signals corresponding to said antenna and associated with the given subcarrier being added to the new modulation symbol intended to be carried by said given subcarrier in the updated input vector;wherein said projection implements a spatial coding of said M error signals of the subcarrier error vector on the basis of an estimated propagation channel between said receivers and said transmitter so that the distortion signal linked to the difference between the clipped OFDM symbols and the OFDM symbols is transmitted by the transmitter in at least one direction of a receiver (100w), called weak receiver, for which the estimated propagation channel corresponds to a propagation loss greater than a predetermined threshold, characterized in that said projection implements an operator ^; ^,^ said spatial coding being expressed as the identity operator from which is subtracted a normalized operator of modified spatial coding, the normalized modified spatial coding operator being a function of a composition between a modified spatial precoding operator and an operator modeling said estimated propagation channel between said transmitter and said receivers, the modified spatial precoding operator being a function of an operator, called receivers operator, from which a regularization operator is subtracted, the receivers operator being a function of a composition between an operator modeling said estimated propagation channel between said receivers and said transmitter and said operator modeling an estimated propagation channel between said transmitter and said receivers, each diagonal element of said receivers operator being representative of a power received by the corresponding receiver, the regularization operator being of the diagonal type, each diagonal element of said regularization operator being associated with a corresponding receiver,an amplitude of each diagonal element of said regularization operator making it possible to control the level of distortion linked to the difference between the OFDM symbols and the clipped OFDM symbols transmitted in the direction of the corresponding receiver.
15. Radiofrequency transmitter (110tx) characterized in that it comprises a device according to claim 14.,