EP4655924A1

EP4655924A1 - Efficient peak-to-average power ratio reduction for orthogonal frequency divison multiplexed transmissions

Info

Publication number: EP4655924A1
Application number: EP23702921.0A
Authority: EP
Inventors: Selahattin Gokceli; Karthik Upadhya; Dani Johannes KORPI; Mikko Aleksi Uusitalo
Original assignee: Nokia Solutions and Networks Oy
Current assignee: Nokia Solutions and Networks Oy
Priority date: 2023-01-26
Filing date: 2023-01-26
Publication date: 2025-12-03
Also published as: WO2024157049A1

Abstract

Systems, methods, apparatuses, and computer program products for efficient peak-to-average-power ratio reduction methods and systems, which may be applicable to orthogonal frequency division multiplexed transmissions are provided. For example, a method can include performing phase extraction on data symbols and inverse discrete Fourier transform coefficients to obtain phase values. The method can also include generating octants and cardinality of the obtained phase values and detecting peaks based on the octants and cardinality, without performing Inverse fast Fourier transform. The method can further include generating a clipping noise signal based on the detected peaks and summing the clipping noise signal and the data symbols to provide an output signal.

Description

EFFICIENT PEAK-TO-AVERAGE POWER RATIO REDUCTION FOR ORTHOGONAL FREQUENCY DIVISON MULTIPLEXED TRANSMISSIONS TECHNICAL FIELD [0001] Some example embodiments may generally relate to communications including mobile or wireless telecommunication systems, such as Long Term Evolution (LTE) or fifth generation (5G) radio access technology or new radio (NR) access technology, or other communications systems including subsequent generations of the same or similar standards. For example, certain example embodiments may generally relate to efficient peak-to-average- power ratio reduction methods and systems, which may be applicable to orthogonal frequency division multiplexed transmissions. BACKGROUND [0002] Examples of mobile or wireless telecommunication systems may include the Universal Mobile Telecommunications System (UMTS) Terrestrial Radio Access Network (UTRAN), Long Term Evolution (LTE) Evolved UTRAN (E-UTRAN), LTE-Advanced (LTE-A), MulteFire, LTE-A Pro, and/or fifth generation (5G) radio access technology or new radio (NR) access technology. 5G wireless systems refer to the next generation (NG) of radio systems and network architecture. A 5G system is mostly built on a 5G new radio (NR), but a 5G (or NG) network can also build on the E-UTRA radio. From release 18 (Rel-18) onward, 5G is referred to as 5G advanced. It is estimated that NR provides bitrates on the order of 10-20 Gbit/s or higher, and can support at least service categories such as enhanced mobile broadband (eMBB) and ultra-reliable low-latency-communication (URLLC) as well as massive machine type communication (mMTC). NR is expected to deliver extreme broadband and ultra-robust, low latency connectivity and massive networking to support the Internet of Things (IoT). With IoT and machine-to- machine (M2M) communication becoming more widespread, there will be a growing need for networks that meet the needs of lower power, low data rate, and long battery life. The next generation radio access network (NG-RAN) represents the RAN for 5G, which can provide both NR and LTE (and LTE- Advanced) radio accesses. It is noted that, in 5G, the nodes that can provide radio access functionality to a user equipment (i.e., similar to the Node B, NB, in UTRAN or the evolved NB, eNB, in LTE) may be named next-generation NB (gNB) when built on NR radio and may be named next-generation eNB (NG-eNB) when built on E-UTRA radio. 6G is currently under development and may replace 5G and 5G advanced. SUMMARY [0003] An embodiment may be directed to an apparatus. The apparatus may include at least one processor and at least memory storing instructions. The instructions, when executed by the at least one processor, may cause the apparatus at least to perform phase extraction on data symbols and inverse discrete Fourier transform coefficients to obtain phase values, generate octants and cardinality of the obtained phase values, and detect peaks based on the octants and cardinality by approximating inverse fast Fourier transform without performing inverse fast Fourier transform. The apparatus may also generate a clipping noise signal based on the detected peaks and may sum the clipping noise signal and the data symbols to provide an output signal.. [0004] An embodiment may be directed to a method. The method can include performing phase extraction on data symbols and inverse discrete Fourier transform coefficients to obtain phase values and generating octants and cardinality of the obtained phase values. The method may also include detecting peaks based on the octants and cardinality by approximating inverse fast Fourier transform without performing inverse fast Fourier transform. The method may further include generating a clipping noise signal based on the detected peaks and summing the clipping noise signal and the data symbols to provide an output signal. [0005] An embodiment can be directed to an apparatus. The apparatus can include means for performing phase extraction on data symbols and inverse discrete Fourier transform coefficients to obtain phase values. The apparatus may also include means for generating octants and cardinality of the obtained phase values. The apparatus may further include means for detecting peaks based on the octants and cardinality by approximating inverse fast Fourier transform without performing inverse fast Fourier transform. The method may additionally include means for generating a clipping noise signal based on the detected peaks. The method may also include means for summing the clipping noise signal and the data symbols to provide an output signal. BRIEF DESCRIPTION OF THE DRAWINGS [0006] For proper understanding of example embodiments, reference should be made to the accompanying drawings, wherein: [0007] FIG.1 illustrates a block diagram of transmitter processing, according to certain embodiments; [0008] FIG. 2 illustrates amplitude groups for 16 level quadrature amplitude modulation, according to certain embodiments; [0009] FIG. 3 illustrates the considered octants in the complex plane, according to certain embodiments; [0010] FIG. 4 illustrates example cardinality values in the complex plane, according to certain embodiments; [0011] FIG. 5 illustrates example cardinality values obtained after a subtraction stage and shown in the complex plane, according to certain embodiments; [0012] FIG. 6A illustrates a comparison of peak-to-average-power ratio for various signals, including some according to certain embodiments; [0013] FIG. 6B illustrates a comparison of mean squared error for various signals, including some according to certain embodiments; [0014] FIG.7 illustrates a method according to certain embodiments; and [0015] FIG. 8 illustrates an example block diagram of a system, according to an embodiment. DETAILED DESCRIPTION [0016] It will be readily understood that the components of certain example embodiments, as generally described and illustrated in the figures herein, may be arranged and designed in a wide variety of different configurations. Thus, the following detailed description of some example embodiments of systems, methods, apparatuses, and computer program products for providing efficient peak-to-average-power ratio reduction methods and systems, which may be applicable to orthogonal frequency division multiplexed transmissions, is not intended to limit the scope of certain embodiments but is representative of selected example embodiments. [0017] The features, structures, or characteristics of example embodiments described throughout this specification may be combined in any suitable manner in one or more example embodiments. For example, the usage of the phrases “certain embodiments,” “some embodiments,” or other similar language, throughout this specification refers to the fact that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment. Thus, appearances of the phrases “in certain embodiments,” “in some embodiments,” “in other embodiments,” or other similar language, throughout this specification do not necessarily all refer to the same group of embodiments, and the described features, structures, or characteristics may be combined in any suitable manner in one or more example embodiments. [0018] Certain embodiments may have various aspects and features. These aspects and features may be applied alone or in any desired combination with one another. Other features, procedures, and elements may also be applied in combination with some or all of the aspects and features disclosed herein. [0019] Additionally, if desired, the different functions or procedures discussed below may be performed in a different order and/or concurrently with each other. Furthermore, if desired, one or more of the described functions or procedures may be optional or may be combined. As such, the following description should be considered as illustrative of the principles and teachings of certain example embodiments, and not in limitation thereof. [0020] Energy and spectral efficiency are important for next-generation wireless networks. High carrier frequencies may offer high capacity and data rate. Accordingly, carrier frequencies up to 52.6 GHz are supported by the existing third generation partnership project (3GPP) standardization, which refers to fifth generation (5G) new radio (NR) release 15 (Rel-15). Frequencies above the already standard level are being studied by 3GPP radio access network (RAN), and may become an integral part of future sixth generation (6G) specifications. [0021] Some of the potential mm-wave bands to be introduced for 5G and beyond are 70/80/92-114 GHz. Physical layer and waveform design for operation above 52.6 GHz may aim for efficient transceiver design, including power efficiency and complexity, improvement of coverage to cope with extreme propagation loss, and re-use of physical layer channel design. [0022] High frequencies may experience higher path loss and hardware challenges due to radio frequency (RF) components such as power amplifiers (PAs). Higher PA efficiency and transmission power may enhance performance. [0023] Terahertz-frequency bands may be important in 6G, due to an increase in the available spectrum and associated benefits. Furthermore, sustainability may be a design criterion for next-generation waveform design, as power efficiency may help to realize sustainable communication systems. In accordance with these, power efficient waveforms may be beneficial for high frequency communications to realize the potential benefits, while minimizing PA efficiency issues. [0024] Low PA efficiency matters because power consumed by the PA can correspond to a large percentage of the total power consumed by the transceivers. The cyclic prefix (CP) orthogonal frequency division multiplexing (OFDM), which is the main waveform of physical layer of 5G NR, is particularly susceptible to this issue, as the CP-OFDM has quite high peak to average power ratio (PAPR), which decreases PA efficiency significantly. Hence, certain embodiments may provide improvements for OFDM. [0025] There are PAPR reduction methods such as iterative clipping and filtering (ICF), partial transmit sequence, selected mapping, and tone reservation (TR), each with different advantages and trade-offs. However, these methods each have high computational complexity. For example, most of them execute iterative operations on the long oversampled signals. [0026] An efficient and effective PAPR reduction solution for OFDM waveform can be used to make the OFDM waveform suitable for 6G networks. On the other hand, low-complexity PAPR reduction solutions for OFDM may be challenging, because the peaks may be somewhat random due to inverse fast Fourier transform (IFFT) operation being applied to a group of many random quadrature amplitude modulation (QAM) symbols and IFFT operation may lead to coherent summation of these symbols for certain time- domain indices if corresponding IDFT coefficients lead to similar phase values for each QAM symbol. Therefore, PAPR reduction methods may execute at least one oversampled IFFT to detect the time-domain peaks and may use more oversampled IFFT/FFT operations to reduce the PAPR. [0027] There are ways to reduce PAPR, which may offer various advantages and trade-offs, as mentioned above. Methods may target the OFDM waveform, which has relatively high PAPR. ICF may provide effective PAPR reduction performance and relatively reasonable computational complexity compared to some other approaches. [0028] In ICF, time-domain clipping and frequency-domain out-of-band (OOB) emission filtering can be iteratively applied to reduce the PAPR of the digital waveform and to control the OOB emissions. On the other hand, since these clipping and filtering operations are applied in different domains, consecutive IFFT and FFT operations on the oversampled signals may need to change domains. Domain switching, particularly when performed iteratively, can lead to high computational complexity with respect to original OFDM waveform processing. Thus, ICF may be deemed a complex method due to having significantly higher complexity compared to the original OFDM waveform generation. [0029] The guard-band tone reservation (GTR) method, is one relevant reference method. In GTR, the potential time-domain peaks can be estimated in the data domain by utilizing a peak-detection filter, and the required peak- cancellation signals can be generated at the IFFT output by utilizing the guard- band tones. GTR may efficiently provide good PAPR reduction. The GTR method may achieve these results because of the specific implementation. GTR is for the DFT-s-OFDM waveform. GTR may reduce PAPR complexity by exploiting a certain relation between data symbols and the time-domain peaks. Unfortunately, such a pattern does not exist in OFDM waveform processing. Thus, it may be unsuitable to use GTR with the OFDM waveform because of the more random characteristics of the OFDM waveform. [0030] This invention proposes an efficient PAPR reduction method for OFDM, which estimates the potential large time domain peaks already in frequency domain efficiently by using the proposed peak detection algorithm, before creating the full waveform in time domain. It then distorts the data subcarriers by adding the clipping noise samples, which lead to the required peak cancellation signals after IFFT. These peak cancellation signals are generated also efficiently to keep the complexity of PAPR reduction stage low. [0031] Certain embodiments may provide an efficient PAPR reduction method for OFDM. For example, certain embodiments may provide a unique peak detection mechanism, which may approximate IFFT operation with much more efficient processing. By exploiting the structure in the QAM constellation map, a process that requires much lower multiplications and additions than IFFT processing may be implemented to overcome the complexity trade-offs associated with PAPR reduction approaches. [0032] In certain embodiments of peak detection, phase values of the data symbols and IDFT coefficients are processed, while a grouping is also applied based on the amplitude levels of the QAM symbols. This way, integer numbers may be processed. In IFFT, numbers with high number of decimal places are processed, which may require higher hardware implementation complexity. [0033] A precomputed Gaussian pulse can be utilized to reduce the PAPR. The frequency domain samples of this precomputed Gaussian pulse can be modified to shift the peak location of the pulse and tune the amplitude and/or phase values in accordance with the detected peaks. This processing can be done in frequency-domain rather than in time-domain, making it a very efficient PAPR reduction processing. [0034] Although OFDM is used as an example, certain embodiments can be applied all the possible M-ary QAM modulation schemes. Certain embodiments may, for example, bring increasingly large advantages when higher-order QAM modulations are used. Higher-order can refer to 256- QAM and greater. [0035] OFDM waveform processing can start with data symbol generation that is realized by converting bits to M-QAM or M-PSK symbols. Accordingly, ^th sample of time-domain OFDM waveform can be denoted as [0037] where ^ is the active subcarrier index with ^ ∈ { −#_$%& ^⁄ 2 , −#_$%& ^⁄ 2 + 1, … , #_$%& ^⁄ 2 − 1} , and ^^{^}^^{^} is the ^ th data symbol in frequency domain. Moreover, # is the total number of samples, #_$%& is the total number of active subcarriers and #/#_$%& denotes the oversampling factor, while # − #_$%& frequency-domain bins are zero. Then, the final OFDM signal can be obtained with CP addition and parallel-to-serial conversion. This procedure can be represented, using matrix notation, as [0038] , = vec^{^}01^{^^}2^{^}, ^2^ [0039] where 2, 1^{^^} , and 0 are the # × 4 frequency-domain data symbol matrix with 4 OFDM symbols, # × # IDFT matrix, and (# + #₅₆^ × # CP insertion matrix, respectively. Moreover, vec^∙^ denotes the vectorization operation. [0040] In some PAPR reduction procedures, PAPR of the OFDM waveform is computed. In methods such as ICF, multiple iterations may be used to converge to the desired PAPR level. In such methods, PAPR computation may be repeated at every iteration. The iteration index 8 ∈ {1,2, … , 9} can index the number of iterations of the process. Accordingly, sample-wise PAPR of the generated = ^,^{^:^ ^:^ ^:^} ; , ,_^ , … , ,_<^^ ^ can be computed as [0042] where max {∙} represents the maximum operator and |^| is the absolute value of a complex number ^. Then, soft limiter-based clipping is applied to reduce the PAPR, which can be expressed for target PAPR level X_&$YZ[& (X_&$YZ[&,\] for dB scale) as [0044] where ∠^ is the phase value of a complex number ^, ^̅^{^:^^}^^{^} represents the clipped is the amplitude threshold, which is computed as [0046] with E^∙^ denotes the expectation operator. Since clipping operation distributes clipping noise over all available subcarriers, in order to prevent undesired emissions, a filtering operation can be implemented in frequency domain. [0047] After the clipping operation, clipped time-domain signal can be transformed to frequency domain with FFT and then frequency-domain filtered clipping noise signal that is obtained at the 8th iteration, which can be expressed for the ^th subcarrier as ^[0048] _^ ^{^:^^} _^ ^{^} _{= r} ^{^} _^ ^{^} _^ ^{s^:^^} _^ ^{^} _, ^{^} ₆ ^{^} [0049] where is the ^th data symbol that is obtained at 8th iteration from clipped signal through FFT. The ICF filter H^^^ can be defined for ^th subcarrier as [0052] where κ_G^k^^n and κ_P^:: represent the subcarrier sets that contain the active subcarriers and non-active ones. Then, PAPR reduced CP-OFDM signal can be obtained after IFFT and CP addition as [0053] A^{^:^} = ^^^@^^^{^^}^^{^:^}B. ^{^}8^{^} [0054] The system model of ICF that corresponds to equations (4) to (8), can be a computationally expensive model, especially when a high number of iterations is run. One iteration generally does not lead to the desired PAPR value, and a high number of iterations may accordingly be used. Since every iteration contains one full FFT and one full IFFT, computational complexity grows significantly with each iteration. Such methods generally utilize oversampled FFT or IFFTs to have a good peak resolution, hence complexity that emerges due to FFT or IFFT is further magnified due to the oversampling. Hence, an ICF-like solutions may be impractical. [0055] Certain embodiments provide for less complex PAPR reduction solutions. For example, the following method can be implemented. The PAPR reduction procedure can be unconventionally divided into two stages that are peak detection and PAPR reduction. This division may help to allow efficient PAPR reduction. There can be frequency domain processing of these stages, rather than processing an oversampled time-domain signal. The latter approach may be inefficient due to at least one IFFT and also due to the long signal length caused by oversampling. In line with this, the low-complexity version of ICF can be implemented by using only one extra IFFT to detect the peaks and then applying some efficient peak cancellation mechanism that will be described below to replace the clipping operation that is done in the time domain, which can necessitate at least one extra FFT for frequency domain clipping noise filtering. [0056] First, to generate the sinc pulse to be used later in PAPR reduction stage, active subcarriers can be configured as [0057] ^_;^^^ = >_^^^ , ^9^ [0058] where >_^^^ is the EVM margin considered for each peak cancellation signal’s samples. So, each sample can be simply a real number. Due to having a limited number of active subcarriers, a perfect pulse cannot be created in time domain, meaning that the created pulse may resemble a sinc pulse when transformed to time-domain with IFFT. [0059] After generating the time domain signal, peak detection can be straightforward because for any time index ^, the peak indices are stored in subcarrier set κ_^ as follows denotes the assignment operator. Because the tolerable EVM margin for the clipping noise is usually limited, this operation can be limited to particular high-amplitude peaks. Next, for each detected peak, the peak cancellation signals can be shifted and also their phase values can be changed in accordance with detected peaks, which can be expressed as [0063] where ^_^^ denotes the scaling factor that is used to control the total EVM degradation caused by the term Z^{^}^^{^}, where amplitude level determined based on the EVM limit and number of peaks. To be more precise, the term ∑_^ ^_^^^^^^^^ is equal to phase value of the corresponding time-domain peak, i.e. ∑_^ ^_^^^^^^^^ = ∠^^^κ_^^a^^ . The term Z^^^ can then be added to data subcarrier ^^^^ and as in (1), IFFT is taken to generate the PAPR-reduced time domain signal [0065] This peak cancellation procedure may be more efficient than the frequency-domain clipping noise filtering as consecutive transforms may be needed. However, there may still be an extra IFFT taken to detect the peaks, which may double the computational complexity of OFDM signal generation. [0066] Certain embodiments may also avoid the extra IFFT. [0067] FIG.1 illustrates a block diagram of transmitter processing, according to certain embodiments. FIG. 1 may be considered as a functional block diagram, method flow chart, or both. As shown in FIG. 1, first, the data symbols, ^^^^ and all needed IDFT coefficients, ^_P ^{^}^^{^} can be given to phase extraction blocks 110a and 110b. Then the obtained phase values can be added together and output can be fed into the octant generation block 120 to generate the octants and also the cardinality for each set. The information about the cardinalities of the sets can be given to efficient peak detection block 130, where the peaks are estimated efficiently by efficient peak detection block 130 and the obtained information is given to clipping noise generation block 140, which can then generate the clipping noise signal based on the given information. The generated clipping noise signal is next summed in, at 150, with the original data symbols. In the end, IDFT operation 160 is realized to create the PAPR reduced OFDM signal A^_P. CP addition can be performed at 170 before the power amplifier 180 amplifies the signal and provides it to antenna 190 for transmission over the air, for example over air interface Uu. [0068] To minimize multiplication, certain embodiments provide an efficient peak detection mechanism that focuses on the phase values of the data symbols and the associated IDFT coefficients. Since the phase value of product of two complex numbers can be represented as the addition of individual phase values, following definition can be made for the multiplication of data symbols and IFFT coefficients for the nth time-domain sample and sth OFDM symbol [0069] ^_P^^^ = ∠^{^}^_P^^^^{^} + ∠^{^}^_^^^^^{^}, ^13^ [0070] where, 1_P and 2_^ represent the nth row vector of IDFT matrix 1^{^^} and sth row vector of data matrix 2^{^} , respectively. Index k denotes subcarriers within an OFDM symbol. Phase values of two matrices can be summed in equation (13) to obtain the phase values of the multiplication outputs that can be obtained by multiplying the 1_P and the sth column vector of 2. Amplitude values can be neglected, because the direct multiplication may involve a high number of complex multiplications and also numbers with many decimals being processed, which would complicate the hardware implementation. Moreover, the OFDM signal generation has at least one structure that can be exploited for even more efficient realization of IDFT than IFFT. [0071] FIG. 2 illustrates amplitude groups for 16 level quadrature amplitude modulation, according to certain embodiments. As shown in FIG. 2, groups 1, 2, and 3 are shown with different symbols. The constellation points can be grouped based on the amplitude values. For example, if a modulation that is higher order than QAM is utilized, the constellation points can be separated as outer (circles), middle (crosses) and inner (boxes) constellation points in line with the amplitudes of these symbols. [0072] In the case of 16-QAM which is visualized in FIG. 2, 3 amplitude groups are considered. Here, inner, middle and outer constellation points correspond to first, second and third groups shown in Fig. 2, respectively. If the modulation order is higher, middle constellation points can be separated into multiple groups based on the complexity requirements. In yet another alternative embodiment, the same approach can be applied to arbitrary constellation shapes. In that case, the amplitude groups can be defined based on upper and lower bounds, as the constellation shape might not have discrete amplitude values. [0073] As another aspect of the method, for each amplitude group, the phase values obtained with (13) are grouped in octants, where the octants in the complex plane are visualized in FIG.3. Thus, FIG.3 illustrates the considered octants in the complex plane, according to certain embodiments. As shown in FIG. 3, the groups may be arranged such that groups 1 and 5 are opposite, 2 and 6 are opposite, and so forth. [0074] The octants may be realized per amplitude group. Thus, in the 16- QAM case, octant grouping may be realized three times for the three amplitude groups shown in FIG. 2. [0075] For ^ th amplitude group where ^ denotes the total number of amplitude groups considered, an octant set that contains subcarrier indices can be created as [0077] where ¤ ∈ {1, 2, … ,7,8} and ^_^,P^^] corresponds to the kth element of ¥_^,P, which denotes vector that contains phase values obtained using the M- QAM symbols from ^th amplitude group. So, for each amplitude group, there can be eight different sets corresponding to the octants shown in FIG. 3. The subcarrier indices can be assigned to the sets based on the phase values obtained with (13). Once these sets have been created, cardinality can be computed for each set and cardinalities of the opposite octants can be subtracted from each other to reduce the number of octants to half. Cardinality can refer to the number of elements in a set. [0078] FIG. 4 illustrates example cardinality values in the complex plane, according to certain embodiments. The octant pairs 1 and 5, 2 and 6, 3 and 7, and 4 and 8 can be considered together in the subtraction stage. The resulting four cardinality values for each amplitude group can provide information about the complex time domain peak value, which would be obtained after an exact IFFT. Certain embodiments exploit this term to approximate the exact output, rather than calculating the exact output. [0079] FIG. 4 provides an example to illustrate the operation by considering only the outer constellation points of a 16-QAM. In FIG.4, cardinality values are shown for each octant in the corresponding octant. As seen, the number of elements in each octant can be counted and these are then subtracted from respective octants that are in the opposite side in the complex plane, which is visualized in Fig. 5. Thus, FIG. 5 illustrates example cardinality values obtained after a subtraction stage and shown in the complex plane, according to certain embodiments. Accordingly, for octant pairs 1-5, 2-6, 3-7 and 4-8, the respective subtraction leads to values 4, -7, 6 and -6. These example numerical results indicate that, in this specific non-limiting example, the most significant of the outer constellation points are in the 6^th octant, because that is the octant with seven more constellation points than its opposite octet, as visible in FIG. 5. On absolute terms, the third octet has the most outer constellation points with 14, as visible in FIG.4. The number of octants to be processed may be reduced to half, where a negative sign in the cardinality values means that the octants with negative imaginary values are the dominant ones of the corresponding pairs. [0080] The problem of peak detection can be formulated with respect to a linear system and the weights that to be used for multiplying the set of 4 cardinalities can be computed. In line with this, for each OFDM symbol, ¦th amplitude group and ^th time sample, the vector that uses the cardinality of each sample set can be created as [0081] §_^,P = ¨ card@κ_^,P,^B, card@κ_^,P,^B, … , card@κ_^,P,«B, card^κ_^,P,¬^ , ^15^ [0082] where card^{^}. ^{^} denotes the cardinality of the set. After subtracting the corresponding octant pairs, the following vector can be created to formulate the linear system [0084] here, ®_P is of dimension 1 × 4^, and for the ^th time sample and hth OFDM symbol, following equation can be formulated as [0085] ®_P² = ,_P , ^17^ [0086] where, ² and ,_P are the vector of octant weights of size 4^ × 1 and ^th column vector of time domain OFDM signal matrix ,.This way, optimal weights for optimal combination of the elements in ®_P can be approximated to provide a good approximation to actual time domain samples. As this is a linear system, QR factorization can be used. [0087] Furthermore, amplitude groups’ weights in ² may be the same if they are normalized in accordance with the average amplitude levels of the amplitude groups. So, by exploiting this additional feature, certain embodiments can provide multiplication of weights and the vector ®_P. [0088] As the last aspect of the method of certain embodiments, there can be a threshold for certain elements of ®_P that correspond to outer constellation points, because the outer constellation points may have the highest contribution to the large peak values due to the high amplitude value they have. In this way, the processing can be skipped for many IDFT coefficients, thereby further improving efficiency. The threshold can be determined as [0090] where > is the amplitude threshold computed in (5) based on the clipping level and ·^{^}^_¸ ^{^} is the weight corresponding to outer constellation points’ amplitude group, whose index is denoted by ^_¸. This approach may compute the minimum number of outer constellation point symbols needed to reach the clipping level after the multiplication in equation (17). Then, for the amplitude group ^_¸, the time domain indices with peaks can be computed as [0093] As a further step, for ^ ∈ κ_^ , equation (17) can be computed and approximate peak values can be obtained. [0094] To explain better how certain embodiments work and can be practically implemented, a numerical example follows. This example is non- limiting and illustrative. To generate this example, a sample simulation can consider 20 MHz 5G NR bandwidth configuration, with 16-QAM modulation, subcarrier spacing of 60 kHz and oversampling factor of 4. This configuration leads to 288 active subcarriers and IFFT length of 2048. In addition, clipping level of 7 dB is targeted with the algorithm. Some Matlab commands are used in the example to give some insight about how algorithm can be implemented. [0095] First, random 16-QAM symbols are generated, which correspond to a first row index of 2^{^} (by considering one OFDM symbol and active part for simplicity): [0096] 2_^ = [0.1581 - 0.4743i 0.4743 + 0.1581i 0.4743 + 0.1581i -0.4743 - 0.1581i 0.4743 - 0.4743i 0.1581 - 0.1581i 0.4743 + 0.1581i -0.1581 + 0.4743i…]. [0097] Then, IDFT coefficients time domain index are extracted from the matrix 1^{^^} , which can be represented as (time index 11 is chosen arbitrarily): [0098] 1_^^ = 1.0e-03 x [0.4883 + 0.0000i 0.4881 + 0.0150i 0.4874 + 0.0299i 0.4862 + 0.0449i 0.4846 + 0.0598i 0.4825 + 0.0746i 0.4800 + 0.0894i 0.4771 + 0.1041i …]. [0099] Next, phase values are created for both terms. The phase values can directly be generated without fully generating the data symbols and IDFT coefficients. These terms are presented to help the readers’ understanding of the relation between different terms. The phase values can be represented as [0100] ∠^{^}2_^ ^{^} = ^288.44 18.44 18.44 198.44 315 315 18.44 108.44 288.44 225 … ^, [0101] ∠^{^}1_^^ ^{^} = ^0 1.76 3.52 5.27 7.03 8.79 10.55 12.30 14.06 15.82 …]. [0102] These terms are then added as [0103] ¥_^^ = ^288.44 20.19 21.95 203.71 322.03 323.79 28.98 120.74302.50 240.82 … ^ . [0104] A next stage is the octant generation stage. In the 16-QAM case, there can be 3 amplitude groups, 4 outer constellation points, 12 middle ones and 4 inner ones are grouped into these 3 separate groups. And since there are 8 octants, this octant generation stage leads to 24 cardinality values, similar to [0105] §_^^ = ^9 6 4 6 11 8 6 9 27 17 23 18 24 17 21 14 15 9 5 9 7 9 9 5 . [0106] By using this term, ®_^^ that was defined in (15) , is obtained as [0107] ®_^^ = ^−2 − 2 − 2 − 3 3 0 2 4 8 0 − 4 4^. [0108] In efficient processing, the high amplitude constellation points alone can be considered. Hence, first two amplitude groups are considered in the 16-QAM case and the first 8 elements of ®_^^ are used, which correspond to these amplitude groups. Same weights are used for both real and imaginary parts, but with different order. For real part, the octant weights corresponding to these 8 elements are [0109] ² = ^2.4 1 − 1 − 2.1 1.8 0.8 − 0.8 − 1.8^ [0110] and for imaginary part [0111] ² = ^1 2.4 2.4 1 0.8 1.8 1.8 0.8^. [0112] This is not the original weight set because the weight set has been normalized using a normalization factor to have simpler multiplication procedure with fewer floating numbers. [0113] Since some weights are 1, multiplication is not needed for multiplying these weights with particular elements of ®_^^. Moreover, as seen, weights are the same for certain index pairs. Hence, the multiplication ®_P² can be realized efficiently by first summing these pairs of ®_^^, and multiplying the sum with unique weights. Moreover, for each amplitude group, when the real part is calculated, the fourth element in the octant set is subtracted from first element, as fourth quadrant corresponds to the negative real axis of the complex plane. [0114] Accordingly, operation of equation (17) can be realized efficiently for both real and imaginary parts. In this case, 1^st, 2^nd, 5^th and 6^th elements of ®_^^ correspond to real part, and rest is used for the imaginary part. This leads to real value [0115] [ −2 − 2 − 2 − 3 ] × ^{^}2.41 1 − 1 − 2.41 ^{^º} + [3 0 2 4 ] × ^{^}1.80 0.75 − 0.75 − 1.80 ^{^º} = -0.88, [0116] and imaginary value [0117] [−2 − 2 − 2 − 3 ] × ^{^}1 2.41 2.41 1 ^{^º} + [3 0 2 4 ] × ^{^}0.75 1.80 1.80 0.75 ^{^º} = -5.83. [0118] Then, two values are converted to positive numbers and summed, and compared against the determined threshold to decide if peak occurs or not [0119] 0.88+5.83 < ³, [0120] where ³ = 78.84 which is computed as in equation (17). Hence, no additional operation is done for this time domain index, as the sum value is less than the threshold. If the sum value is higher than the threshold, real and imaginary values are also created for other amplitude groups and these are added to the values obtained already. Then, both real and imaginary numbers are multiplied with the normalization factor obtained in the 7^th step, and finally, complex values are created. [0121] For example, for this generated OFDM symbol, the time index 1341 leads to a sum value that is higher than the peak threshold. In this case, the obtained complex value is 82.21 -40.05i, and since the normalization factor is 0.002, this leads to final value 0.17 - 0.08i. The original time sample has the value 0.166 - 0.08i, and a quite close approximation is usually obtained for most of the samples as well. [0122] For the detected peaks, peak cancellation signals can be calculated as in equation (11) and then these can be added to the data subcarriers at the IFFT input. Note that this processing can be realized in frequency domain, thanks to the peak detection realized in frequency domain, and quite efficient PAPR reduction can be achieved this way. [0123] It can be seen from the given numerical example that the approach of certain embodiments can utilize a low number of multiplications. It can also be seen that processing can be built on numbers with quite a low number of decimal places, which is not the case in IFFT processing. If conceptually even simpler operation is preferred, then after the 6^th step, equation (17) can directly be realized and with equation (17), peak decision can be obtained at the expense of a higher number of multiplications than the procedure illustrated in this example. [0124] Clipping noise generation can be realized in frequency domain as in equations (9)-(12) in both alternative approaches. However, in one alternative approach, another possibility is to realize this in time domain, as IFFT is already taken in the peak detection stage, and time domain OFDM signal is obtained. In this case, peak cancellation signals can be generated in a straightforward manner in time domain, as the peaks can be accurately found by processing this full time domain signal. However, certain embodiments use frequency domain processing due to the potential complexity advantages, as when this is realized in time domain, each peak cancellation signal may have the size equal to oversampled waveform’s size, and since multiple signals are processed, it would mean processing a high number of samples. Also, frequency domain processing has the advantage of accurate tuning of the active subcarriers and, in this way, any potential emissions in adjacent channels or exceeding the EVM threshold can be prevented. [0125] FIG. 6A illustrates a comparison of peak-to-average-power ratio for various signals, including some according to certain embodiments. FIG. 6B illustrates a comparison of mean squared error for various signals, including some according to certain embodiments. [0126] In order to show performance benefits of certain embodiments, numerical evaluations were conducted by considering a 20 MHz 5G NR bandwidth configuration, with subcarrier spacing of 60 kHz and oversampling factor of 4. In addition, clipping level of 7 dB was targeted. As EVM limit for the clipping noise, 10% EVM was considered. For each OFDM symbol, 8 largest peaks out of 2048 samples were targeted for cancellation. In the evaluations, three cases were considered, which are a baseline method utilizing one IFFT for peak detection, an embodiment with direct realization of equation (17) without considering the more efficient peak detection, and an embodiment with efficient peak detection. [0127] The results for PAPR and MSE are shown in FIGs.6A and 6B. As seen from FIG. 6A, each of the approaches provides around 2 dB improvement in PAPR with respect to original OFDM waveform at CCDF probability level of 10^-4. Moreover, certain embodiments of an efficient method can improve the PAPR of the original OFDM waveform by 1 dB at CCDF probability level of 10^-4 while running only one iteration. In addition, the efficient method can provide more or less the same PAPR performance as the baseline, demonstrating the effectiveness of the efficient peak detection processing. Also, the direct multiplication case can provide the same performance. Thus, from a complexity point of view, the efficient method can be considered even more advantageous. [0128] As can be seen from MSE results shown in FIG. 6B, the advantage of the baseline approach may be is visible as it provides the lowest MSE among all three methods, which is around -25 dB or around 6%. Proposed method with direct multiplication provides around -24 dB MSE or 6.5% and the efficient case provides -23.5 dB MSE or 7% EVM. However, the difference between these methods in terms of MSE or EVM is quite small and it can be claimed that they have the almost same PAPR and MSE performance [0129] Additionally, the various methods can be evaluated in terms of computational complexity. According to simulations, the baseline processing leads to 32 real multiplications and 606 real additions per time domain sample. On the other hand, the direct multiplication and efficient peak detection approaches lead to 12 real multiplications / 34 real additions and 4 real multiplications / 45 real additions, respectively. Hence, in terms of real multiplications, these cases reduce the complexity to approximately 38% and 13%, respectively. In terms of additions, the complexity is 6% and 7% that of the baseline, respectively. [0130] Due to realization of 2 dB PAPR improvement with 7% EVM and 87% improvement in terms of real multiplications, and since the 5G NR EVM threshold for 16-QAM is 12.5%, the illustrated methods may provide a good tradeoff in terms of PAPR, MSE and complexity. The baseline method might have a lower-latency processing, while certain embodiments may have a more efficient hardware implementation, as certain embodiments may avoid processing complex numbers or numbers with high number of decimal places, unlike in the baseline processing. [0131] FIG. 7 illustrates a method according to certain embodiments. The method illustrated in FIG. 7 can be implemented in hardware or software running on hardware. Such hardware may be implemented as an application specific integrated circuit and may be characterized as including a hardware processor and hardware memory. The method may include, at 710, receiving data symbols and corresponding inverse discrete Fourier transform coefficients. The method may also include, at 720, performing phase extraction on the data symbols and the inverse discrete Fourier transform coefficients to obtain phase values. The method may further include, at 730, generating octants and cardinality of the obtained phase values. [0132] The method may also include, at 740, detecting peaks based on the octants and cardinality, without performing Inverse fast Fourier transform. The method may further include, at 750, generating a clipping noise signal based on the detected peaks. The method may additionally include, at 760, summing the clipping noise signal and the data symbols to provide an output signal. The resultant signal can be output at 770. [0133] In this example method, the detection of the peaks can be based on the phase values of the data symbols and associated inverse discrete Fourier transform coefficients. Moreover, the detection of the peaks can be performed in the frequency domain, before a waveform of the data symbols is formed in the time domain. The detection of the peaks can include approximating an inverse fast Fourier transform. The detection of the peaks can exploit a structure of a quadrature amplitude modulation constellation map. [0134] In certain embodiments of the method, a precomputed Gaussian pulse can be used to reduce peak-to-average-power ratio. Frequency domain samples of the precomputed Gaussian pulse can be modified to shift the peak location of the precomputed Gaussian pulse and tune the amplitude and phase values in accordance with the detected peaks. [0135] The detection of the peaks can include grouping the data symbols based on respective amplitude values of respective data symbols of the data symbols. The grouping comprises grouping into outer constellation points, inner constellation points, and middle constellation points. The grouping includes grouping into three or more amplitude groups, each amplitude group including a plurality of the data symbols. The detection of the peaks can include grouping the octants on a per amplitude group basis to form eight sets. The eight sets can correspond to eight octants, respectively. The cardinality can be based on a number of elements in each set of the eight sets. [0136] The example of using three or more amplitude groups is just one example. The number of amplitude groups may be different at different modulation orders. For example, for 4-QAM, a single amplitude group may be sufficient. Likewise, the number of sets may vary according to implementation. For example, any symmetric number of sets can be used, such as four sets, six sets, eight sets (as in this example), ten sets, twelve sets, and so on. [0137] Cardinalities of opposite octants can be subtracted from one another, thereby halving a number of the octants, resulting in four cardinalities for each amplitude group. The detection of the peaks can include solving a linear system based on the four cardinalities. The detection of the peaks can include setting a threshold specific to outer constellation point symbols based on a minimum number of outer constellation point symbols needed to reach a clipping level. [0138] FIG. 8 illustrates an example of a system that includes an apparatus 10, according to an embodiment. In an embodiment, apparatus 10 may be a node, host, or server in a communications network or serving such a network. For example, apparatus 10 may be a network node, satellite, base station, a Node B, an evolved Node B (eNB), 5G Node B or access point, next generation Node B (NG-NB or gNB), TRP, HAPS, integrated access and backhaul (IAB) node, and/or a WLAN access point, associated with a radio access network, such as an LTE network, 5G or NR. In some example embodiments, apparatus 10 may be gNB or other similar radio node, for instance. [0139] It should be understood that, in some example embodiments, apparatus 10 may include an edge cloud server as a distributed computing system where the server and the radio node may be stand-alone apparatuses communicating with each other via a radio path or via a wired connection, or they may be located in a same entity communicating via a wired connection. For instance, in certain example embodiments where apparatus 10 represents a gNB, it may be configured in a central unit (CU) and distributed unit (DU) architecture that divides the gNB functionality. In such an architecture, the CU may be a logical node that includes gNB functions such as transfer of user data, mobility control, radio access network sharing, positioning, and/or session management, etc. The CU may control the operation of DU(s) over a mid- haul interface, referred to as an F1 interface, and the DU(s) may have one or more radio unit (RU) connected with the DU(s) over a front-haul interface. The DU may be a logical node that includes a subset of the gNB functions, depending on the functional split option. It should be noted that one of ordinary skill in the art would understand that apparatus 10 may include components or features not shown in FIG.8. [0140] As illustrated in the example of FIG. 8, apparatus 10 may include a processor 12 for processing information and executing instructions or operations. Processor 12 may be any type of general or specific purpose processor. In fact, processor 12 may include one or more of general-purpose computers, special purpose computers, microprocessors, digital signal processors (DSPs), field-programmable gate arrays (FPGAs), application- specific integrated circuits (ASICs), and processors based on a multi-core processor architecture, or any other processing means, as examples. While a single processor 12 is shown in FIG. 8, multiple processors may be utilized according to other embodiments. For example, it should be understood that, in certain embodiments, apparatus 10 may include two or more processors that may form a multiprocessor system (e.g., in this case processor 12 may represent a multiprocessor) that may support multiprocessing. In certain embodiments, the multiprocessor system may be tightly coupled or loosely coupled (e.g., to form a computer cluster). [0141] Processor 12 may perform functions associated with the operation of apparatus 10, which may include, for example, precoding of antenna gain/phase parameters, encoding and decoding of individual bits forming a communication message, formatting of information, and overall control of the apparatus 10, including processes related to efficient peak-to-average-power ratio reduction methods and systems, which may be applicable to orthogonal frequency division multiplexed transmissions. [0142] Apparatus 10 may further include or be coupled to a memory 14 (internal or external), which may be coupled to processor 12, for storing information and instructions that may be executed by processor 12. Memory 14 may be one or more memories and of any type suitable to the local application environment, and may be implemented using any suitable volatile or nonvolatile data storage technology such as a semiconductor-based memory device, a magnetic memory device and system, an optical memory device and system, fixed memory, and/or removable memory. For example, memory 14 can be include any combination of random access memory (RAM), read only memory (ROM), static storage such as a magnetic or optical disk, hard disk drive (HDD), or any other type of non-transitory machine or computer readable media, or other appropriate storing means. The instructions stored in memory 14 may include program instructions or computer program code that, when executed by processor 12, enable the apparatus 10 to perform tasks as described herein. [0143] In an embodiment, apparatus 10 may further include or be coupled to (internal or external) a drive or port that is configured to accept and read an external computer readable storage medium, such as an optical disc, USB drive, flash drive, or any other storage medium. For example, the external computer readable storage medium may store a computer program or software for execution by processor 12 and/or apparatus 10. [0144] In some embodiments, apparatus 10 may also include or be coupled to one or more antennas 15 for transmitting and receiving signals and/or data to and from apparatus 10. Apparatus 10 may further include or be coupled to a transceiver 18 configured to transmit and receive information. The transceiver 18 may include, for example, a plurality of radio interfaces that may be coupled to the antenna(s) 15, or may include any other appropriate transceiving means. The radio interfaces may correspond to a plurality of radio access technologies including one or more of global system for mobile communications (GSM), narrow band Internet of Things (NB-IoT), LTE, 5G, WLAN, Bluetooth (BT), Bluetooth Low Energy (BT-LE), near-field communication (NFC), radio frequency identifier (RFID), ultrawideband (UWB), MulteFire, and the like. The radio interface may include components, such as filters, converters (for example, digital-to-analog converters and the like), mappers, a Fast Fourier Transform (FFT) module, and the like, to generate symbols for a transmission via one or more downlinks and to receive symbols (via an uplink, for example). [0145] As such, transceiver 18 may be configured to modulate information on to a carrier waveform for transmission by the antenna(s) 15 and demodulate information received via the antenna(s) 15 for further processing by other elements of apparatus 10. In other embodiments, transceiver 18 may be capable of transmitting and receiving signals or data directly. Additionally or alternatively, in some embodiments, apparatus 10 may include an input and/or output device (I/O device), or an input/output means. [0146] In an embodiment, memory 14 may store software modules that provide functionality when executed by processor 12. The modules may include, for example, an operating system that provides operating system functionality for apparatus 10. The memory may also store one or more functional modules, such as an application or program, to provide additional functionality for apparatus 10. The components of apparatus 10 may be implemented in hardware, or as any suitable combination of hardware and software. [0147] According to some embodiments, processor 12 and memory 14 may be included in or may form a part of processing circuitry/means or control circuitry/means. In addition, in some embodiments, transceiver 18 may be included in or may form a part of transceiver circuitry/means. [0148] As used herein, the term “circuitry” may refer to hardware-only circuitry implementations (e.g., analog and/or digital circuitry), combinations of hardware circuits and software, combinations of analog and/or digital hardware circuits with software/firmware, any portions of hardware processor(s) with software (including digital signal processors) that work together to cause an apparatus (e.g., apparatus 10) to perform various functions, and/or hardware circuit(s) and/or processor(s), or portions thereof, that use software for operation but where the software may not be present when it is not needed for operation. As a further example, as used herein, the term “circuitry” may also cover an implementation of merely a hardware circuit or processor (or multiple processors), or portion of a hardware circuit or processor, and its accompanying software and/or firmware. The term circuitry may also cover, for example, a baseband integrated circuit in a server, cellular network node or device, or other computing or network device. [0149] As introduced above, in certain embodiments, apparatus 10 may be or may be a part of a network element or RAN node, such as a base station, access point, Node B, eNB, gNB, TRP, HAPS, IAB node, relay node, WLAN access point, satellite, or the like. In one example embodiment, apparatus 10 may be a gNB or other radio node, or may be a CU and/or DU of a gNB. According to certain embodiments, apparatus 10 may be controlled by memory 14 and processor 12 to perform the functions associated with any of the embodiments described herein. For example, in some embodiments, apparatus 10 may be configured to perform one or more of the processes depicted in any of the flow charts or signaling diagrams described herein, such as those illustrated in FIGs. 1 to 7, or any other method described herein. In some embodiments, as discussed herein, apparatus 10 may be configured to perform a procedure relating to providing efficient peak-to-average-power ratio reduction methods and systems, which may be applicable to orthogonal frequency division multiplexed transmissions, for example. [0150] FIG. 8 further illustrates an example of an apparatus 20, according to an embodiment. In an embodiment, apparatus 20 may be a node or element in a communications network or associated with such a network, such as a UE, communication node, mobile equipment (ME), mobile station, mobile device, stationary device, IoT device, or other device. As described herein, a UE may alternatively be referred to as, for example, a mobile station, mobile equipment, mobile unit, mobile device, user device, subscriber station, wireless terminal, tablet, smart phone, IoT device, sensor or NB-IoT device, a watch or other wearable, a head-mounted display (HMD), a vehicle, a drone, a medical device and applications thereof (e.g., remote surgery), an industrial device and applications thereof (e.g., a robot and/or other wireless devices operating in an industrial and/or an automated processing chain context), a consumer electronics device, a device operating on commercial and/or industrial wireless networks, or the like. As one example, apparatus 20 may be implemented in, for instance, a wireless handheld device, a wireless plug- in accessory, or the like. [0151] In some example embodiments, apparatus 20 may include one or more processors, one or more computer-readable storage medium (for example, memory, storage, or the like), one or more radio access components (for example, a modem, a transceiver, or the like), and/or a user interface. In some embodiments, apparatus 20 may be configured to operate using one or more radio access technologies, such as GSM, LTE, LTE-A, NR, 5G, WLAN, WiFi, NB-IoT, Bluetooth, NFC, MulteFire, and/or any other radio access technologies. It should be noted that one of ordinary skill in the art would understand that apparatus 20 may include components or features not shown in FIG.8. [0152] As illustrated in the example of FIG.8, apparatus 20 may include or be coupled to a processor 22 for processing information and executing instructions or operations. Processor 22 may be any type of general or specific purpose processor. In fact, processor 22 may include one or more of general- purpose computers, special purpose computers, microprocessors, digital signal processors (DSPs), field-programmable gate arrays (FPGAs), application-specific integrated circuits (ASICs), and processors based on a multi-core processor architecture, as examples. While a single processor 22 is shown in FIG. 8, multiple processors may be utilized according to other embodiments. For example, it should be understood that, in certain embodiments, apparatus 20 may include two or more processors that may form a multiprocessor system (e.g., in this case processor 22 may represent a multiprocessor) that may support multiprocessing. In certain embodiments, the multiprocessor system may be tightly coupled or loosely coupled (e.g., to form a computer cluster). [0153] Processor 22 may perform functions associated with the operation of apparatus 20 including, as some examples, precoding of antenna gain/phase parameters, encoding and decoding of individual bits forming a communication message, formatting of information, and overall control of the apparatus 20, including processes related to management of communication resources. [0154] Apparatus 20 may further include or be coupled to a memory 24 (internal or external), which may be coupled to processor 22, for storing information and instructions that may be executed by processor 22. Memory 24 may be one or more memories and of any type suitable to the local application environment, and may be implemented using any suitable volatile or nonvolatile data storage technology such as a semiconductor-based memory device, a magnetic memory device and system, an optical memory device and system, fixed memory, and/or removable memory. For example, memory 24 can include any combination of random access memory (RAM), read only memory (ROM), static storage such as a magnetic or optical disk, hard disk drive (HDD), or any other type of non-transitory machine or computer readable media. The instructions stored in memory 24 may include program instructions or computer program code that, when executed by processor 22, enable the apparatus 20 to perform tasks as described herein. [0155] In an embodiment, apparatus 20 may further include or be coupled to (internal or external) a drive or port that is configured to accept and read an external computer readable storage medium, such as an optical disc, USB drive, flash drive, or any other storage medium. For example, the external computer readable storage medium may store a computer program or software for execution by processor 22 and/or apparatus 20. [0156] In some embodiments, apparatus 20 may also include or be coupled to one or more antennas 25 for receiving a downlink signal and for transmitting via an uplink from apparatus 20. Apparatus 20 may further include a transceiver 28 configured to transmit and receive information. The transceiver 28 may also include a radio interface (e.g., a modem) coupled to the antenna 25. The radio interface may correspond to a plurality of radio access technologies including one or more of GSM, LTE, LTE-A, 5G, NR, WLAN, NB-IoT, Bluetooth, BT-LE, NFC, RFID, UWB, and the like. The radio interface may include other components, such as filters, converters (for example, digital-to-analog converters and the like), symbol demappers, signal shaping components, an Inverse Fast Fourier Transform (IFFT) module, and the like, to process symbols, such as OFDM symbols, carried by a downlink or an uplink. [0157] For instance, transceiver 28 may be configured to modulate information on to a carrier waveform for transmission by the antenna(s) 25 and demodulate information received via the antenna(s) 25 for further processing by other elements of apparatus 20. In other embodiments, transceiver 28 may be capable of transmitting and receiving signals or data directly. Additionally or alternatively, in some embodiments, apparatus 20 may include an input and/or output device (I/O device). In certain embodiments, apparatus 20 may further include a user interface, such as a graphical user interface or touchscreen. [0158] In an embodiment, memory 24 stores software modules that provide functionality when executed by processor 22. The modules may include, for example, an operating system that provides operating system functionality for apparatus 20. The memory may also store one or more functional modules, such as an application or program, to provide additional functionality for apparatus 20. The components of apparatus 20 may be implemented in hardware, or as any suitable combination of hardware and software. According to an example embodiment, apparatus 20 may optionally be configured to communicate with apparatus 10 via a wireless or wired communications link 70 according to any radio access technology, such as NR. [0159] According to some embodiments, processor 22 and memory 24 may be included in or may form a part of processing circuitry or control circuitry. In addition, in some embodiments, transceiver 28 may be included in or may form a part of transceiving circuitry. [0160] As discussed above, according to some embodiments, apparatus 20 may be a UE, SL UE, relay UE, mobile device, mobile station, ME, IoT device and/or NB-IoT device, or the like, for example. According to certain embodiments, apparatus 20 may be controlled by memory 24 and processor 22 to perform the functions associated with any of the embodiments described herein, such as one or more of the operations illustrated in, or described with respect to, FIGs. 1 to 7, or any other method described herein. For example, in an embodiment, apparatus 20 may be controlled to perform a process relating to providing efficient peak-to-average-power ratio reduction methods and systems, which may be applicable to orthogonal frequency division multiplexed transmissions, as described in detail elsewhere herein. [0161] In some embodiments, an apparatus (e.g., apparatus 10 and/or apparatus 20) may include means for performing a method, a process, or any of the variants discussed herein. Examples of the means may include one or more processors, memory, controllers, transmitters, receivers, and/or computer program code for causing the performance of any of the operations discussed herein. [0162] In view of the foregoing, certain example embodiments provide several technological improvements, enhancements, and/or advantages over existing technological processes and constitute an improvement at least to the technological field of wireless network control and/or management. Certain embodiments may have various benefits and/or advantages. For example, certain embodiments of a PAPR reduction technique may provide good quality PAPR performance, with only 0.3 dB worse performance at the complementary cumulative distribution function (CCDF) probability level of 10-4 with respect to a reference algorithm, where peak detection is realized by using one full IFFT. In addition, certain embodiments provide good PAPR and EVM performance, with error vector magnitude (EVM) performance that is slightly better than a reference algorithm. Compared to PAPR performance of the original OFDM waveform, certain embodiments can provide up to 2 dB improvement in PAPR at the CCDF probability level of 10-4. Also, performance gains at such low probability levels indicate that certain embodiments can accurately detect the significant peaks despite non-optimal processing. Certain embodiments may provide huge improvements in overall energy efficiency, as certain embodiments may reduce PAPR through a low- complexity processing. Accordingly, compared to efficient implementation of IFFT used in reference methods, certain embodiments may reduce the real multiplications and real additions to approximately 13% and 8% that of IFFT, respectively. IFFT is sometimes viewed as the most efficient way of realizing IDFT. Certain embodiments, however, may outperform IFFT by exploiting the structure in QAM constellation map. The latency of processing of certain embodiments may be higher than the IFFT, but may be more suitable to hardware implementation from a fixed-point conversion point of view. Thus, certain embodiments may be more suitable for hardware implementation, and may improve energy efficiency significantly. Certain embodiments of PAPR reduction method has closed-form solution as it will be shown, it can be formulated as a linear system and the solution can simply be found by using the inverse matrix approach. And the solution is dependent only on the used M-QAM modulation. Hence, it is quite flexible in terms of support for multiple bandwidth configuration cases. [0163] In some example embodiments, the functionality of any of the methods, processes, signaling diagrams, algorithms or flow charts described herein may be implemented by software and/or computer program code or portions of code stored in memory or other computer readable or tangible media, and may be executed by a processor. [0164] In some example embodiments, an apparatus may include or be associated with at least one software application, module, unit or entity configured as arithmetic operation(s), or as a program or portions of programs (including an added or updated software routine), which may be executed by at least one operation processor or controller. Programs, also called program products or computer programs, including software routines, applets and macros, may be stored in any apparatus-readable data storage medium and may include program instructions to perform particular tasks. A computer program product may include one or more computer-executable components which, when the program is run, are configured to carry out some example embodiments. The one or more computer-executable components may be at least one software code or portions of code. Modifications and configurations required for implementing the functionality of an example embodiment may be performed as routine(s), which may be implemented as added or updated software routine(s). In one example, software routine(s) may be downloaded into the apparatus. [0165] As an example, software or computer program code or portions of code may be in source code form, object code form, or in some intermediate form, and may be stored in some sort of carrier, distribution medium, or computer readable medium, which may be any entity or device capable of carrying the program. Such carriers may include a record medium, computer memory, read-only memory, photoelectrical and/or electrical carrier signal, telecommunications signal, and/or software distribution package, for example. Depending on the processing power needed, the computer program may be executed in a single electronic digital computer or it may be distributed amongst a number of computers. The computer readable medium or computer readable storage medium may be a non-transitory medium. The term “non-transitory” as used herein, is a limitation of the medium itself (i.e. tangible, not a signal) as opposed to a limitation on data storage persistency (e.g. RAM vs. ROM). [0166] In other example embodiments, the functionality of example embodiments may be performed by hardware or circuitry included in an apparatus, for example through the use of an application specific integrated circuit (ASIC), a programmable gate array (PGA), a field programmable gate array (FPGA), or any other combination of hardware and software. In yet another example embodiment, the functionality of example embodiments may be implemented as a signal, such as a non-tangible means, that can be carried by an electromagnetic signal downloaded from the Internet or other network. [0167] According to an example embodiment, an apparatus, such as a node, device, or a corresponding component, may be configured as circuitry, a computer or a microprocessor, such as single-chip computer element, or as a chipset, which may include at least a memory for providing storage capacity used for arithmetic operation(s) and/or an operation processor for executing the arithmetic operation(s). [0168] Example embodiments described herein may apply to both singular and plural implementations, regardless of whether singular or plural language is used in connection with describing certain embodiments. For example, an embodiment that describes operations of a single network node may also apply to example embodiments that include multiple instances of the network node, and vice versa. [0169] One having ordinary skill in the art will readily understand that the example embodiments as discussed above may be practiced with procedures in a different order, and/or with hardware elements in configurations which are different than those which are disclosed. Therefore, although some embodiments have been described based upon these example embodiments, it would be apparent to those of skill in the art that certain modifications, variations, and alternative constructions would be apparent, while remaining within the spirit and scope of example embodiments.

Claims

CLAIMS 1. An apparatus, comprising: at least one processor; and at least one memory storing instructions that, when executed by the at least one processor, cause the apparatus at least to: perform phase extraction on data symbols and inverse discrete Fourier transform coefficients to obtain phase values; generate octants and cardinality of the obtained phase values; detect peaks based on the octants and cardinality by approximating inverse fast Fourier transform without performing inverse fast Fourier transform; generate a clipping noise signal based on the detected peaks; and sum the clipping noise signal and the data symbols to provide an output signal.

2. The apparatus of claim 1, wherein the detection of the peaks is based on the phase values of the data symbols and associated inverse discrete Fourier transform coefficients.

3. The apparatus of claim 1, wherein the detection of the peaks is performed in frequency domain, before a waveform of the data symbols is formed in time domain.

4. The apparatus of claim 1, wherein the detection of the peaks comprises approximating an inverse fast Fourier transform.

5. The apparatus of claim 1, wherein the detection of the peaks exploits a structure of a quadrature amplitude modulation constellation map.

6. The apparatus of claim 1, wherein a precomputed Gaussian pulse is used to reduce peak-to-average-power ratio, wherein frequency domain samples of the precomputed Gaussian pulse are modified to shift the peak location of the precomputed Gaussian pulse and tune the amplitude and phase values in accordance with the detected peaks.

7. The apparatus of claim 1, wherein the detection of the peaks comprises grouping the data symbols based on respective amplitude values of respective data symbols of the data symbols.

8. The apparatus of claim 7, wherein the grouping comprises grouping into outer constellation points, inner constellation points, and middle constellation points.

9. The apparatus of claim 7, wherein the grouping comprises grouping into one or more amplitude groups, each amplitude group comprising a plurality of the data symbols.

10. The apparatus of claim 9, wherein the grouping comprises grouping into three or more amplitude groups.

11. The apparatus of claim 9, wherein the detection of the peaks comprises grouping the octants on a per amplitude group basis to form a plurality of sets.

12. The apparatus of claim 11, wherein the plurality of sets is eight sets.

13. The apparatus of claim 11, wherein the cardinality is based on a number of elements in each set of the plurality of sets.

14. The apparatus of claim 13, wherein cardinalities of opposite octants are subtracted from one another, thereby halving a number of the octants, resulting in a plurality of cardinalities for each amplitude group.

15. The apparatus of claim 14, wherein the detection of the peaks comprises solving a linear system based on the plurality of cardinalities.

16. The apparatus of claim 14, wherein the detection of the peaks comprises setting a threshold specific to outer constellation point symbols based on a minimum number of outer constellation point symbols needed to reach a clipping level.

17. A method, comprising: performing phase extraction on data symbols and inverse discrete Fourier transform coefficients to obtain phase values; generating octants and cardinality of the obtained phase values; detecting peaks based on the octants and cardinality by approximating inverse fast Fourier transform without performing inverse fast Fourier transform; generating a clipping noise signal based on the detected peaks; and summing the clipping noise signal and the data symbols to provide an output signal.

18. The method of claim 17, wherein the detection of the peaks is based on the phase values of the data symbols and associated inverse discrete Fourier transform coefficients.

19. The method of claim 17, wherein the detection of the peaks is performed in frequency domain, before a waveform of the data symbols is formed in time domain.

20. The method of claim 17, wherein the detection of the peaks comprises approximating an inverse fast Fourier transform.

21. The method of claim 17, wherein the detection of the peaks exploits a structure of a quadrature amplitude modulation constellation map.

22. The method of claim 17, wherein a precomputed Gaussian pulse is used to reduce peak-to-average-power ratio, wherein frequency domain samples of the precomputed Gaussian pulse are modified to shift the peak location of the precomputed Gaussian pulse and tune the amplitude and phase values in accordance with the detected peaks.

23. The method of claim 17, wherein the detection of the peaks comprises grouping the data symbols based on respective amplitude values of respective data symbols of the data symbols.

24. The method of claim 23, wherein the grouping comprises grouping into outer constellation points, inner constellation points, and middle constellation points.

25. The method of claim 23, wherein the grouping comprises grouping into one or more amplitude groups, each amplitude group comprising a plurality of the data symbols.

26. The method of claim 25, wherein the grouping comprises grouping into three or more amplitude groups.

27. The method of claim 25, wherein the detection of the peaks comprises grouping the octants on a per amplitude group basis to form a plurality of sets.

28. The method of claim 27, wherein the plurality of sets is eight sets.

29. The method of claim 27, wherein the cardinality is based on a number of elements in each set of the plurality of sets.

30. The method of claim 29, wherein cardinalities of opposite octants are subtracted from one another, thereby halving a number of the octants, resulting in a plurality of cardinalities for each amplitude group.

31. The method of claim 30, wherein the detection of the peaks comprises solving a linear system based on the plurality of cardinalities.

32. The method of claim 30, wherein the detection of the peaks comprises setting a threshold specific to outer constellation point symbols based on a minimum number of outer constellation point symbols needed to reach a clipping level.

33. An apparatus, comprising: means for performing phase extraction on data symbols and inverse discrete Fourier transform coefficients to obtain phase values; means for generating octants and cardinality of the obtained phase values; means for detecting peaks based on the octants and cardinality by approximating inverse fast Fourier transform without performing inverse fast Fourier transform; means for generating a clipping noise signal based on the detected peaks; and means for summing the clipping noise signal and the data symbols to provide an output signal.

34. The apparatus of claim 33, wherein the detection of the peaks is based on the phase values of the data symbols and associated inverse discrete Fourier transform coefficients.

35. The apparatus of claim 33, wherein the detection of the peaks is performed in frequency domain, before a waveform of the data symbols is formed in time domain.

36. The apparatus of claim 33, wherein the detection of the peaks comprises approximating an inverse fast Fourier transform.

37. The apparatus of claim 33, wherein the detection of the peaks exploits a structure of a quadrature amplitude modulation constellation map.

38. The apparatus of claim 33, wherein a precomputed Gaussian pulse is used to reduce peak-to-average-power ratio, wherein frequency domain samples of the precomputed Gaussian pulse are modified to shift the peak location of the precomputed Gaussian pulse and tune the amplitude and phase values in accordance with the detected peaks.

39. The apparatus of claim 33, wherein the detection of the peaks comprises grouping the data symbols based on respective amplitude values of respective data symbols of the data symbols.

40. The apparatus of claim 39, wherein the grouping comprises grouping into outer constellation points, inner constellation points, and middle constellation points.

41. The apparatus of claim 39, wherein the grouping comprises grouping into one or more amplitude groups, each amplitude group comprising a plurality of the data symbols.

42. The apparatus of claim 41, wherein the grouping comprises grouping into three or more amplitude groups.

43. The apparatus of claim 41, wherein the detection of the peaks comprises grouping the octants on a per amplitude group basis to form a plurality of sets.

44. The apparatus of claim 43, wherein the plurality of sets is eight sets.

45. The apparatus of claim 43, wherein the cardinality is based on a number of elements in each set of the plurality of sets.

46. The apparatus of claim 45, wherein cardinalities of opposite octants are subtracted from one another, thereby halving a number of the octants, resulting in a plurality of cardinalities for each amplitude group.

47. The apparatus of claim 46, wherein the detection of the peaks comprises solving a linear system based on the plurality of cardinalities.

48. The apparatus of claim 46, wherein the detection of the peaks comprises setting a threshold specific to outer constellation point symbols based on a minimum number of outer constellation point symbols needed to reach a clipping level.

49. A computer program product encoding instructions for performing the method of any of claims 17-32.

50. A non-transitory computer-readable medium encoded with instructions that, when executed in hardware, perform the method of any of claims 17-32.