WO2018113935A1 - Construction of a filtered cp-ofdm waveform - Google Patents

Abstract

The invention relates to a signal processing device, to a network node and to a user device including the signal processing device, and to a method for a signal processing device. The signal processing device comprises a processor configured to: weight current constellation symbols x _k,0 with weighting coefficients W _k , so as to provide weighted constellation symbols W _k x _k,0 ; multiplex the weighted constellation symbols W _k x _k,0 , so as to provide a weighted orthogonal frequency division multiplex symbol w-ODFM; derive a current cyclic prefix CP₀ from the current constellation symbols x _k,0 and a previous cyclic prefix CP_0-i from previous constellation symbols x _k,0-i ; filter the current cyclic prefix CP₀ and the previous cyclic prefix CP_0-i so as to provide a filtered cyclic prefix f-CP; and append the filtered cyclic prefix f-CP to the weighted orthogonal frequency division multiplex symbol w-OFDM, so as to provide a filtered cyclic prefix orthogonal frequency division multiplex symbol f-CP-OFDM.

Description

CONSTRUCTION OF A FILTERED CP-OFDM WAVEFORM Technical Field

The invention relates to signal processing device. The invention also relates to a network node and a user device. Furthermore, the invention also relates to corresponding methods, a computer program, and a computer program product implementing the method. Background

Orthogonal frequency division multiplexing (OFDM) is an air-interface used by many

communications systems of today, such as e.g. long-term evolution (LTE) systems. Among the possible candidate waveforms to be used in the fifth cellular network generation 5G, several variants of the conventional OFDM have been considered. Universal-Filtered OFDM (UF- OFDM) also known as UFMC, and filtered-OFDM (f-OFDM) are variations of a considered filtering approach, which reduce Out-Of-Band (OOB) emission of the conventional OFDM waveform. OFDM modulation converts frequency-domain constellation symbols to time-domain samples with the help of an Inverse Fast Fourier Transform (IFFT). A cyclic prefix (CP) is then added for maintaining orthogonality among OFDM subcarriers in a time-dispersive channel.

In order to filter an entire conventional OFDM symbol, the full OFDM symbol needs to be processed together with its added CP, and also taking into account the last time-samples of a previous/foregoing OFDM symbol. It is the transition region between the previous OFDM symbol and the CP of the current OFDM symbol that may cause high OOB emission, and this transition region is thus the most important part of the signal to be filtered. Also, the corresponding processing window needs to be longer than the OFDM symbol period due to the filtering of the CP and due to the impulse response of the filter.

Filtered-OFDM with longer filter design has a very heavy implementation complexity and also causes a large time overhead in downlink/uplink (DL/UL) switching.

Time convolution operations in the time domain may be more efficiently implemented as multiplications in the frequency domain, wherefore a Fast Fourier Transform is performed before the filtering of the full OFDM symbol, such that the filtering may be performed in the frequency domain. Thereafter, an IFFT is performed in order to provide a time domain filtered OFDM symbol. The number of OFDM samples to be filtered is equal to the size of the OFDM's IFFT plus the impulse response length of the filter, which must be larger than the number of allocated subcarriers. The sequential operations of the OFDM modulation, which inherently includes an IFFT operation, and filtering, including a FFT operation and another IFFT operation, results in back and forth implementation of frequency domain to time domain conversion using a cascade of several (l)FFT operations/algorithms. Such an implementation is inefficient in terms of implementation complexity. Filtered OFDM thus suffers from heavy implementation complexity, which increases for wideband transmission having a large number of subcarriers allocated for the transmission.

Potential complexity reduction of filtering could possibly be achieved if part of the processing of the constellation symbol level could be transferred into the frequency domain. However, the IFFT of the OFDM modulation and the FFT of the filtering step do not have the same size, and can thus not be directly removed. On the one hand, the OFDM modulation IFFT size is fixed and independently implemented for each OFDM symbol. One the other hand, the filtering FFT windows needs to overlap two consecutive OFDM symbols as the high OOB emission arises from the irregular transition between consecutive blocks, as mentioned above. It is this overlap that results in that the filtering FFT window size does not to match the size of OFDM modulation IFFT. This mismatch is greater with filters having a long impulse response. Summary

An object of the embodiments of the invention is to provide a solution which mitigates or at least partly solves the above mentioned drawbacks and problems.

Another object of the embodiments of the invention is to provide construction of a filtered cyclic prefix orthogonal frequency division multiplex symbol (f-CP-OFDM) at a low implementation complexity.

The above objects and further objects are achieved by the subject matter of the independent claims. Further advantageous implementation forms of the invention are defined by the dependent claims.

According to a first aspect of the invention, the above mentioned and other objects are achieved with a signal processing device, comprising a processor configured to: weight current constellation symbols x_k>0 with weighting coefficients W_k, so as to provide weighted constellation symbols W_kx_{k 0};

multiplex the weighted constellation symbols W_kx_{k 0} , so as to provide a weighted orthogonal frequency division multiplex symbol w-ODFM;

derive a current cyclic prefix CPo from the current constellation symbols x_kfi and a previous cyclic prefix CPo-i from previous constellation symbols x_ki0-i ^',

filter the current cyclic prefix CP₀ and the previous cyclic prefix CP₀-i so as to provide a filtered cyclic prefix f-CP; and

append the filtered cyclic prefix f-CP to the weighted orthogonal frequency division multiplex symbol w-OFDM, so as to provide a filtered cyclic prefix orthogonal frequency division multiplex symbol f-CP-OFDM.

Thus, the computation of the f-CP-OFDM symbol is split in two computation groups, i.e. into computation of a f-CP and computation of a w-OFDM symbol. Thus, a novel waveform built upon an OFDM waveform is provided by combining partial filtering and partial

subcarrier/constellation symbol weighting.

The f-CP samples are generated by filtering a short signal made of the current cyclic prefix samples CPo and the previous cyclic prefix samples CPo-i. The filtering computation step ensures a smooth transition between consecutive OFDM symbols, and thus ensures low OOB emission.

The subcarrier weighting computation of the w-OFDM symbol, wherein the w-OFDM symbol is generated by weighting and multiplexing the current constellation symbols x_kfl , provides for both a lower implementation complexity and a generalization with more degrees of freedom than conventional filtered-OFDM methods. The subcarrier weights may be designed as a function of the filter used for the filtered computation step, which provides for a relevant signal output. The two computation groups may be controlled by a common unit that stores the coefficients of the filter. The weights used for weighting the current constellation symbols x_ki0 may be derived based on these filter coefficients, which reduces the need for storage memory. At the end, the separately computed f-CP and w-OFDM symbol are appended to each other to form a f-CP-OFDM symbol.

A lower implementation complexity than for conventional filtered-OFDM implementations is hereby provided, since the IFFT already available in the OFDM modulation is exploited. The computation of the w-OFDM computes most of its samples with a symbol/subcarrier weighting operation which has little additional complexity compared to the conventional OFDM complexity. Most of the additional implementation complexity is added in the filtering CP step, which is motivated by the possibilities for OOB emission reduction when the f-CP-OFDM symbol is transmitted after the f-CP has been appended to the w-OFDM.

The signal processing device is notably beneficial for spectral containment for wideband transmission, and the implementation complexity scales logarithmically with the (l)FFT size.

In a first possible implementation form of the signal processing device according to the first aspect, the processor is configured to weight the current constellation symbols x_kfl with weighting coefficients W_k which are a function of Fourier coefficients F_k of a filter /„ used for filtering the current cyclic prefix CPo and the previous cyclic prefix CPo-i.

To use weighting coefficients W_k being a function of the Fourier coefficients F_k still guarantees that OOB reduction will result, and also provides for a degree of freedom in the selection of the weighting coefficient amplitudes, which allows for a trade-off between OOB reduction and improved error rate performance. Thus, the subcarrier/constellation symbol weighting coefficients may here tuned to trade OOB emission against flatten in-band distortion for improved error performance. Also, the reuse of the filter Fourier coefficients F_k results in a low implementation complexity.

In a second possible implementation form of the signal processing device according to the first implementation form of the first aspect, the weighting coefficients W_k are complex coefficients and have phases 9_k being equal to phases 9_k of corresponding Fourier coefficients F_k of the filter /„.

The weighting coefficients here have the same phases as the Fourier coefficients of the filter used in the CP filtering step, which results in a maintained low-OOB emission, since a phase- continuity between the f-CP and the w-OFDM symbol is guaranteed.

In a third possible implementation form of the signal processing device according to any one of the first and second implementation forms of the first aspect, the weighting coefficients W_k are complex coefficients, and the processor is configured to determine at least one amplitude value p_k of the weighting coefficients W_k based on an averaging of an amplitude value p_k of a corresponding Fourier coefficient F_k of the filter /„ and a positive real number K.

Hereby, the in-band attenuation of the filter response is smoothed. The smoothed in-band attenuation achieves a degree of freedom for trade-off between OOB emission and bit error performance. This may be especially important if the filter response, due to CP constraints, is too short for providing an acceptable performance. For this implementation, the resulting output signal is not equivalent to filtered-OFDM, since W_k≠ F_k .

In a fourth possible implementation form of the signal processing device according to the third implementation form of the first aspect, the processor is configured to adjust one or more of the amplitude values p_k of the complex weighting coefficients W_k to a value of one (1 ).

To not attenuate the constellation symbols/subcarriers, i.e. to weight them with a weighting coefficient having an amplitude value of one, provides for the best possible bit error

performance. Other amplitude values than one for the weights provides different trade-offs between the bit error performance and the OOB emission. For this implementation, the resulting output signal is not equivalent to filtered-OFDM, since W_k≠ F_k .

In a fifth possible implementation form of the signal processing device according to any one of the first or second implementation forms of the first aspect, the weighting coefficients W_k have values equal to corresponding Fourier coefficients F_k of the filter /„.

When the weighting coefficients W_k have equal values, i.e. equal phases and equal amplitudes, as the corresponding Fourier filtering coefficients F_k used for the CP filtering, the resulting output signal is exactly the same as a conventional implementation of filtered-OFDM. However, the hereby provided f-CP-OFDM symbol is produced with much lower implementation complexity than for the conventionally produced filtered-OFDM. The implementation complexity may here be approximately an order-of-magnitude, i.e. approximately ten times, lower than the implementation complexity of a conventional OFDM filtering implementation. This reduced complexity is obtained by exploiting the inherent structure of the CP-OFDM waveform, which has been designed to convert the time-dispersion effect of multi-path channel to frequency- selective weighting of the subcarriers/constellation symbols.

In a sixth possible implementation form of the signal processing device according to any of the first to fifth implementation forms of the first aspect, or to the first aspect as such, the processor is configured to filter the current cyclic prefix CPo and the previous cyclic prefix CPo-i using a finite impulse response FIR filter /„ having an impulse response being shorter than the current cyclic prefix CPo.

To be able to use FIR filtering with shorter impulse response than the length of the CPs reduces the implementation complexity and also reduces the time overhead at switching between downlink and uplink transmission.

In a seventh possible implementation form of the signal processing device according to any one of the first to sixth implementation forms of the first aspect, or to the first aspect as such, the processor is configured to:

select samples of a central pulse from the signal output resulting from filtering of the current cyclic prefix CPo and the previous cyclic prefix CPo-i as the filtered cyclic prefix f-CP; and discard samples CP_discr of one or more tails of the signal output resulting from the filtering.

By only selecting samples of the central pulse from the output signal, the number of samples of the f-CP are equal to the desired CP length when appending the f-CP to the w-OFDM symbol. Also, the samples of the filtered cyclic prefix f-CP is a function of both the current cyclic prefix CPo and the previous cyclic prefix CPo-i.

In an eighth possible implementation form of the signal processing device according to any one of the first to seventh implementation forms of the first aspect, or to the first aspect as such, the processor is configured to filter the current cyclic prefix CPo and the previous cyclic prefix CPo-i using a frequency domain filtering.

By filtering the current cyclic prefix CPo and the previous cyclic prefix CPo-i in the frequency domain, the filtering may be much more efficiently implemented than by use of a convolution filtering operation in the time domain, whereby a lower computational complexity is achieved.

In a ninth possible implementation form of the according to any one of the first to eight implementation forms of the first aspect, or to the first aspect as such,

the current constellation symbols x_kfl represent information to be transmitted in the filtered cyclic prefix orthogonal frequency division multiplex symbol f-CP-OFDM; and the previous constellation symbols ¾_j0_j are last preceding constellation symbols x_k __x representing information transmitted in a preceding filtered cyclic prefix orthogonal frequency division multiplex symbol being transmitted immediately before the filtered cyclic prefix orthogonal frequency division multiplex symbol f-CP-OFDM.

To provide the f-CP by filtering the current cyclic prefix CPo and the last previous cyclic prefix CP-1 , i.e. to filter the current cyclic prefix CPo derived from the current constellation symbols x_ki0 and the last previous cyclic prefix CP-i derived from last previous constellation symbols x_k -_t , is important in order to take into account the above mentioned transition between the immediately preceding/previous cyclic prefix CP-i and the current cyclic prefix CPo. When this irregular transition is taken into account, the OOB emission may be reduced.

According to a second aspect of the invention, the above mentioned and other objects are achieved with a network node configured to transmit information downlink, the network node comprising a transceiver and a signal processing device according to any one of the first to ninth implementation forms of the aspect, or to the first aspect as such, wherein the signal processing device is further configured to:

receive a plurality of constellation symbols ¾,o, ¾o-i !

and the transceiver is configured to:

transmit the filtered cyclic prefix orthogonal frequency division multiplex symbol f-CP- OFMD, e.g. included in a transmission signal r.

The advantages for any network node according to the second aspect of the present invention are the same as for the corresponding implementation form for the signal processing device according to the first aspect. According to a third aspect of the invention, the above mentioned and other objects are achieved with a user device, the user device comprising a transceiver and a signal processing device according to any one of the first to ninth implementation forms of the aspect, or to the first aspect as such, wherein the signal processing device is further configured to:

receive a plurality of constellation symbols ¾,₀, ¾ο-ί ;

and the transceiver is configured to:

transmit the filtered cyclic prefix orthogonal frequency division multiplex symbol f-CP-

OFMD. The advantages for any user device according to the third aspect of the present invention are the same as for the corresponding implementation form for the signal processing device according to the first aspect. According to a fourth aspect of the invention, the above mentioned and other objects are achieved with a method for a signal processing device, the method comprising:

weighting current constellation symbols x_ki0 with weighting coefficients W_k, so as to provide weighted constellation symbols W_kx_ki0 ;

multiplexing the weighted constellation symbols W_kx ₀ , so as to provide a weighted orthogonal frequency division multiplex symbol w-OFDM;

deriving a current cyclic prefix CPo from the current constellation symbols x_kfl and a previous cyclic prefix CP₀-i from previous constellation symbols x_kfi-i

filtering the current cyclic prefix CPo and the previous cyclic prefix CPo-i, so as to provide a filtered cyclic prefix f-CP; and

appending the filtered cyclic prefix f-CP to the weighted orthogonal frequency division multiplex symbol w-OFDM, so as to provide a filtered cyclic prefix orthogonal frequency division multiplex symbol f-CP-OFDM.

In a first possible implementation form of the method according to the fourth aspect, the method comprises weighting the current constellation symbols x_ki0 with weighting coefficients W_k which are a function of Fourier coefficients F_k of a filter /„ used for filtering the current cyclic prefix CPo and the previous cyclic prefix CPo-i.

In a second possible implementation form of the method according to the first implementation form of the fourth aspect, the weighting coefficients W_k are complex coefficients and have phases e_k being equal to phases 9_k of corresponding Fourier coefficients F_k of the filter /„.

In a third possible implementation form of the method according to any one of the first and second implementation forms of the fourth aspect, the weighting coefficients W_k are complex coefficients, and the processor is configured to determine at least one amplitude value p_k of the weighting coefficients W_k based on an averaging of an amplitude value p_k of a corresponding Fourier coefficient F_k of the filter f_n and positive real number K. In a fourth possible implementation form of the method according to the third implementation form of the fourth aspect, the method comprises adjusting one or more of the amplitude values p_k of the complex weighting coefficients W_k to a value of one (1 ). In a fifth possible implementation form of the method according to any one of the first and second implementation forms of the fourth aspect, the weighting coefficients W_k have values equal to corresponding Fourier coefficients F_k of the filter /„.

In a sixth possible implementation form of the method according to any of the first to fifth implementation forms of the fourth aspect, or to the fourth aspect as such, the method comprises filtering the current cyclic prefix CPo and the previous cyclic prefix CPo-i using a finite impulse response FIR filter /„ having an impulse response being shorter than the current cyclic prefix CPo.

In a seventh possible implementation form of the method according to any of the first to sixth implementation forms of the fourth aspect, or to the fourth aspect as such, the method comprises:

selecting samples of a central pulse from the signal output resulting from filtering of the current cyclic prefix CPo and the previous cyclic prefix CPo-i as the filtered cyclic prefix f-CP ; and discarding samples CP_discr of one or more tails of the signal output resulting from the filtering.

In an eighth possible implementation form of the method according to any of the first to seventh implementation forms of the fourth aspect, or to the fourth aspect as such, the method comprises filtering the current cyclic prefix CPo and the previous cyclic prefix CPo-i using a frequency domain filtering.

In a ninth possible implementation form of the method according to any of the first to eighth implementation forms of the fourth aspect, or to the fourth aspect as such,

the current constellation symbols x_kfl represent information to be transmitted in the filtered cyclic prefix orthogonal frequency division multiplex symbol f-CP-OFDM; and

the previous constellation symbols ¾_j0__j are last preceding constellation symbols x_k _ representing information transmitted in a preceding filtered cyclic prefix orthogonal frequency division multiplex symbol being transmitted immediately before the filtered cyclic prefix orthogonal frequency division multiplex symbol f-CP-OFDM.

In a tenth possible implementation form of the method, the method is for a network node and comprises the method according to any of the first to ninth implementation forms of the fourth aspect, or to the fourth aspect as such, the method further comprises,

receiving a plurality of constellation symbols ¾_i0, ¾₀_i ;

and

transmitting the filtered cyclic prefix orthogonal frequency division multiplex symbol f-CP- OFMD, e.g. included in a transmission signal r.

The advantages for any method according to the fourth aspect of the present invention are the same as for the corresponding implementation form for the receiving device according to the first aspect.

According to a fifth aspect of the invention, the above mentioned and other objects are achieved with a method for a user device, the method comprising:

receiving a plurality of constellation symbols (¾₀, ¾,o-i) ;

weighting current constellation symbols (x_fcj0) with weighting coefficients (W_k), so as to provide weighted constellation symbols (W_kx_{k 0}) ;

multiplexing the weighted constellation symbols (W_kx_{k 0}), so as to provide a weighted orthogonal frequency division multiplex symbol (w-OFDM);

deriving a current cyclic prefix (CPo) from the current constellation symbols (x_fcj0) and a previous cyclic prefix (CPo-i) from previous constellation symbols (x_k,₀-d ^',

filtering the current cyclic prefix (CPo) and the previous cyclic prefix (CPo-i), so as to provide a filtered cyclic prefix (f-CP) ;

appending the filtered cyclic prefix (f-CP) to the weighted orthogonal frequency division multiplex symbol (w-OFDM), so as to provide a filtered cyclic prefix orthogonal frequency division multiplex symbol (f-CP-OFDM); and

transmitting the filtered cyclic prefix orthogonal frequency division multiplex symbol (f-

CP-OFMD). The advantages for any method according to the fifth aspect of the present invention are the same as for the corresponding implementation form for the receiving device according to the first aspect. Embodiments of the invention also relate to a computer program, characterized in code means, which when run by processing means causes said processing means to execute any method according to the invention. Further, the invention also relates to a computer program product comprising a computer readable medium and said mentioned computer program, wherein said computer program is included in the computer readable medium, and comprises of one or more from the group: ROM (Read-Only Memory), PROM (Programmable ROM), EPROM (Erasable PROM), Flash memory, EEPROM (Electrically EPROM) and hard disk drive.

Further applications and advantages of the invention will be apparent from the following detailed description.

Brief Description of the Drawings

The appended drawings are intended to clarify and explain different embodiments of the invention, in which:

Fig. 1 schematically shows a network node or a user device according to an example of the invention.

Fig. 2 shows a corresponding method according to an example of the invention.

Fig. 3 schematically shows a user device and a network node of a communication system according to an example of the invention.

Fig. 4 schematically shows a signal processing device according to an example of the invention.

Fig. 5 schematically shows a method of a signal processing device according to an example of the invention.

Fig. 6 shows performance simulations for some examples of the invention.

Fig. 7 schematically shows a method of a user device or a network node according to an example of the invention.

Fig. 8 shows performance simulations for some examples of the invention.

Fig. 9 shows performance simulations for some examples of the invention.

Fig. 10 shows performance simulations for some examples of the invention.

Fig. 1 1 shows performance simulations for some examples of the invention. Detailed Description

In the following, the principles of an OFDM signal and a filtered OFDM (f-OFDM) signal, and the transmission of such signal is explained.

In the baseband domain, an OFDM symbol is constructed based on N_sub orthogonal subcarriers φ_¾(£) = ε^ι2πτ? , where T_s is the symbol period, modulating/multiplexing parallel data streams including constellation symbols {x_kii}, where i is the OFDM symbol index, and where k is the subcarrier index and j = ^T Generally, sequential constellation symbols, corresponding to information to be transmitted, are grouped together into blocks of constellation symbols {x_{k i}} by serial to parallel conversion. For each such block of constellation symbols, an OFDM symbol is constructed/derived/created. Such OFDM symbols, corresponding to sequential blocks of constellation symbols, are then sequentially transmitted.

Assuming a sampling period T_sp such that T_s = N_fft T_sp, and an FFT size of N_fft≥ N_sub , the i^th OFDM baseband discrete signal is:

with the sampling index 0≤ n≤ (N_fft - 1).

As such, this signal s^n] may be generated by an IFFT algorithm by allocating zeros symbols x_kil = 0 to the subcarrier indices N_sub≤ k < N_fft. Thus, Equation 1 is equivalent to:

The signal s^n] is then extended by a cyclic prefix (CP), i.e. by extending the set of sampling indices to - N_cp < n < (N_fft - 1) and setting s^n] = 0 otherwise. Successive OFDM symbols are then transmitted as:

y (Eq. 3) Si[n - i(N_cp + N_fft )

Consider an OFDM signal s[n] as defined in Equation 3, which is a sequential transmission of CP-OFDM symbols. This signal may be filtered by a filter / with finite impulse response (FIR) of length N_F1R in order to provide a filtered OFDM (f-OFDM) signal. The filter response may be written for any integer n as:

N_FIR -1

f[n] =

1=0 (Eq. 4)

The filtered CP-OFDM (f-CP-OFDM) transmission signal r[m] may generically be written as:

r[m] = (/ * s)[m]

^™^"1 (Eq. 5)

= f [n] s[m— n].

n=0

If the transmission signal r[m] is restricted to the output filter indices - N_cp≤m≤ (N_fft - l), this corresponds to the filtering of the symbol s₀, Equation 5 may be expanded to: m+N,

r[m] = f[n]s₀ [m— n]

n=0

N_FIR-1 (Eq.6) m - n + N_fft + N_cp] where s_₁ is the previous OFDM symbol.

A time-convolution operation as the one in Equation 5 may be more efficiently implemented in the frequency domain. Conventional low-complexity implementation methods of OFDM filtering therefore exploit the benefits of the Fast Fourier Transform (FFT) to transform a time domain convolution to frequency domain multiplications. It may be noted that the filtering window in this implementation may be split into shorter overlapping segments in order to process several smaller FFTs/IFFTs. However, both of the non-split and split implementations lead to similar implementation complexity orders.

For f-OFDM, long filter designs have been used in conventional solutions, typically with an impulse response longer than the cyclic prefix length. Filter orders from 160 to half of the OFDM symbol length have been proposed. While a long filter may create more Inter Symbol Interference (ISI) compared to a short filter, it has a more flat in-band attenuation which does not distort the in- band subcarriers. Such long filter designs show better performance than shorter filter designs for a small number of allocated subcarriers.

As mentioned above, the long filter design of f-OFDM has a heavy implementation complexity and also causes large time overheads for DL/UL switching.

The number of OFDM samples to filter is equal to the size of the IFFT of the OFDM plus the length of the filter impulse response, which should be larger than the number of allocated subcarriers. The sequential operations of OFDM modulation, including an IFFT operation, and filtering, including an FFT operation and then an IFFT operation, results in back and forth transfer between the frequency domain and the time domain, using several cascaded (l)FFT algorithms. This is inefficient in terms of implementation complexity, wherefore f-OFDM is suffering from heavy implementation-complexity, especially in wideband transmission with a large number of allocated subcarriers. Figure 1 schematically shows a signal processing device 100 included in a network node 400 or a user device 600 for e.g. a multi-carrier communication system 500. The multi-carrier communication system 500 is schematically illustrated in Figure 3, including a network node 400, such as for example an access node, base station or a eNodeB, in which the signal processing device 100 may be comprised, and user device 600, in which the signal processing device 100 may be comprised.

The signal processing device 100 comprises a processor 104 configured to weight current constellation symbols x_kfl with weighting coefficients W_k , so as to provide weighted

constellation symbols W_kx_ki0. The processor 104 is further configured to multiplex the weighted constellation symbols W_kx_ki0 , so as to provide a weighted orthogonal frequency division multiplex symbol w-ODFM. The processor 104 is also configured to derive a current cyclic prefix CPo from the current constellation symbols x_kfl and a previous cyclic prefix CPo-i from previous constellation symbols x_kfl-i- The processor 104 is also configured to filter the current cyclic prefix CPo and the previous cyclic prefix CPo-i so as to provide a filtered cyclic prefix f-CP. The processor 104 is further configured to append the filtered cyclic prefix f-CP to the weighted orthogonal frequency division multiplex symbol w-OFDM, so as to provide a filtered cyclic prefix orthogonal frequency division multiplex symbol f-CP-OFDM.

The signal processing device 100 may further comprise a transceiver 102 configured to, by the use of at least one antenna 106, transmit e.g. a multi-carrier transmission signal r[m . The network node 400 or the user device 600 may also comprise an input device 1 10 configured to provide constellation symbols x_ki0 , x_ki0-i, being based on information to be transmitted, to the signal processing device 100, and communication means 108 transferring information between the transceiver 102, the processor 104 and the input device 1 10 of the communication device network node 400 or user device 600. The constellation symbols x_ki0 , x_k,o-i may be received from an internal subunit of the network node 400 or the user device 600, or may be received from outside of the network node 400 or the user device 600.

According to an aspect, a method 200 for a signal processing device 100 is presented. The method 200, as illustrated in Figure 2,comprises a first step 204 of weighting current constellation symbols x_kfl with weighting coefficients W_k , so as to provide weighted

constellation symbols W_kx_kfi . In a second step 206, the weighted constellation symbols W_kx_{k 0} are multiplexed, so as to provide a weighted orthogonal frequency division multiplex symbol w-OFDM.

In a third step 208, a current cyclic prefix CPo is derived from the current constellation symbols x_ki0 and a previous cyclic prefix CPo-, from previous constellation symbols x_kfl-i -

In a fourth step 210, the current cyclic prefix CPo and the previous cyclic prefix CPo-i are filtered, so as to provide a filtered cyclic prefix f-CP. In a fifth step 212, the filtered cyclic prefix f-CP is appended to the weighted orthogonal frequency division multiplex symbol w-OFDM, so as to provide a filtered cyclic prefix orthogonal frequency division multiplex symbol f-CP-OFDM.

Hereby, a signal processing method 200, a signal processing device 100, and also a network node 400 transmitting downlink or a user device 600 transmitting uplink including the signal processing device 100 are provided, that offer a low complexity calculation/computation/creation of f-CP-OFDM symbols to be transmitted. Thus, a waveform based on an OFDM waveform and combining partial CP filtering and subcarrier weighting is provided. The invention is especially beneficial for providing spectral containment in wideband transmission as implementation complexity increases with the number of subcarriers used and thus increases with the size of the used (l)FFT.

Figures 4 and 5 schematically illustrate various examples of the signal processing device 100 and the corresponding methods. The related embodiments are hereafter described more in detail.

As mentioned above, a waveform constructed based on OFDM is provided by the signal processing device 100 and the methods, wherein the samples of a block of constellation symbols are split in two computation groups. The two computation groups then in different ways generate two parts of the resulting f-CP-OFDM symbols, a filtered CP (f-CP) and a weighted OFDM symbol, as is described in detail below.

Consider an OFDM signal s[n] as defined in Equation 3, which corresponds to a sequential transmission of CP-OFDM symbols. Again, it is enough to restrict the exposure to the waveform's sample indices to - N_cp≤ m≤ (N_fft - l), which corresponds to the symbol s₀. A filtered CP (f-CP) is provided for one of the two groups of constellation symbols comprising the samples of the cyclic prefix, i.e. with indices -N_cp≤m≤ -1. The current cyclic prefix CPo and the previous cyclic prefix CPo-i are derived/computed 208 based on the current constellation symbols x_kfl and on previous constellation symbols x_ki0-i, respectively.

In this document, the current constellation symbols x_kfl represent information to be transmitted in the currently computed/provided f-CP-OFDM symbol. Correspondingly, the previous constellation symbols x_kfl-i are preceding constellation symbols x_kfl-i representing information transmitted in a preceding f-CP-OFDM symbol being transmitted before the current f-CP-OFDM symbol. According to an embodiment, the previous constellation symbols x_kfl-i are the last preceding constellation symbols x_k _ representing information transmitted in a preceding f-CP- OFDM immediately before the f-CP-OFDM currently being provided/computed.

The current cyclic prefix CP₀ samples correspond to conventional OFDM CP samples and are filtered 210 together with samples corresponding to the last samples of the previous OFDM symbol, that are equal to the samples of the previous cyclic prefix CPo-i due to the symmetric appearance of the OFDM symbol.

According to an embodiment, the current cyclic prefix CPo and the previous cyclic prefix CPo-i are filtered using a finite impulse response FIR filter /„ having an impulse response being shorter than the CPs, e.g. shorter than the current cyclic prefix CP₀. Thus, filter /„ is chosen to have an impulse response at most equal to the CP length, i.e. N_F1R - 1≤ N_cp . As a result, by the cyclic property of the CPs, the last OFDM samples are equal to the previous CP samples. This CP filtering 210 may thus be performed by filtering 210 two appended CPs, i.e. the current cyclic prefix CPo and a previous cyclic prefix CPo-i, that may, according to an embodiment, be derived from current x_kfl and previous x_k _ constellation symbols to be consecutively transmitted. The filtering 210 may be implemented by a time-domain convolution

implementation or by a frequency-domain implementation.

Thus, the current cyclic prefix CPo samples and the previous cyclic prefix CPo-i samples are filtered by a filter /„ with finite impulse response (FIR) of length N_F1R having an impulse response as defined in Equation 4. The filter /„ may, as mentioned above, have an impulse response length at most equal to the CP length, i.e. N_F1R - 1≤ N_cp . The filtered CP samples with indices -N_cp≤ m≤ -1 are computed as described in Equation 6, and thus depend on the previous OFDM symbol s^ . In the second term of Equation 6, it may be noted that the last contribution of the previous OFDM symbol s_₁ occurs at m =- N_cp and n = N_F1R - 1. It may also be noted the transmission signal r [m] in Equation 6 is based on samples from

- N_F1R + l] to s^Nfft - l] . Since the filter length is shorter than the CP length, by the

circularity/symmetry appearance of the OFDM symbol, these samples are equal to the samples

+ 1] to s__! [-l] , i.e. to the samples of the last previous cyclic prefix CP0-1 , that may be derived from the last previous x_k -\ constellation symbols, wherefore: m+N_cp N_FIR -1

r [m] = ^ s₀ [m - n] + ^ s. rn - n + N_cp] ,

n=0 CPO samples n=m+N_cp +l CPO-1 samples (Eq.7) for the indices -N_cp ≤ m≤ -1.

The generated signal samples may be rewritten as an independent convolution:

N_FIR -1

^o (Eq.8) of the filter f[n] and the discrete signal c[n] =

_C; s_{n l} made by appending the samples from the current cyclic prefix CPo and the last previous cyclic prefix CP0-1 :

[ci, ... , c_{Ncp +NpiR}] =

This convolution generates a total of N_cp + 2N_FIR - 1 non-zero samples from k = 1 to k = N_cp +

2N_FIR - 1.

According to an embodiment, the filtering of the current cyclic prefix CPo and the previous cyclic prefix CPo-i is performed by the use of frequency domain filtering. A time-domain convolution operation, such as a filtering operation, may be performed by a corresponding frequency- domain operation in order to achieve a more complexity efficient implementation. Also, complexity reducing implementation methods, such as e.g. the overlap-save method, may be used for further increasing the implementation efficiency of the filtering of the current cyclic prefix CPo and the previous cyclic prefix CPo-i. According to an embodiment, samples of a central pulse of the signal output r_CP [k] resulting from the filtering 210 of the current cyclic prefix CPo and the previous cyclic prefix CPo-i are selected as the filtered cyclic prefix f-CP, and samples CP_discr of one or more tails of the signal output resulting from the filtering 210 are discarded/deleted. More in detail, the desired output f- CP from the linear convolution of Equation 8 (corresponding to Equation 7) are the indices from k = N_F1R - 1 to k = N_CP + N_F1R - 1, and the tails of the convolution are discarded/deleted. Thus, the f-CP hereby has the desired CP length and is based on the current cyclic prefix CPo and the previous cyclic prefix CPo-i convolved with the filter. The first tail of the disregarded samples CP_discr is only based on the previous cyclic prefix CPo-i , and the end tail of the disregarded samples CP_discr is only based on the the current cyclic prefix CP₀.

Based on the other computation group of constellation symbols, a weighted orthogonal frequency division multiplex symbol (w-ODFM) is computed/determined. The group of the current constellation symbols x_ki0 hereby being processed corresponds to the samples of the OFDM symbol without CP, i.e. with indices 0≤ m≤ (N_fft - 1). The waveform samples are obtained by weighting 204 the current constellation symbols x_kfi with the complex weights {W_k}^N _k^^{s _1} before OFDM modulation/multiplexing 206 is performed. The hereby obtained output signal r[m] , including weighted OFDM symbol (w-OFDM) symbols, is:

for the indices 0≤ m≤ (N_fft - l).

According to an embodiment, the weighting coefficients W_k used for weighting 204 the current constellation symbols x_ki0 have values being equal to the corresponding Fourier coefficients F_k of the filter „ used for filtering the 210 the current cyclic prefix CP₀ and the previous cyclic prefix CPo-i . Thus, the current constellation symbols x_kfi are weighted by the Fourier coefficients of the filter „ evaluated at the subcarrier frequencies, i.e. W_k = F_k where:

Hereby, the output signal r[m] is equal to a conventionally determined filtered-OFDM symbol signal. Thus, this implementation provides the same output signal r[m] as Equation 5:

f[n]s₀ [m— n]

o

s)[m] ,

where the last equality follows from 0≤ m≤ {N_fft - l) and n < N_cp . Due to the cyclic prefix, the convolution in Equation 12 for samples of the OFDM symbol depends only on the current constellation symbols x_ki0. The convolution of Equation 12 may be equivalently written as a Fourier transform of weighted constellation symbols W_kx ₀. The interpretation of this construction arises from the inherent structure of the creation of a CP- OFDM symbol, which includes transforming multipath channels to frequency selective weights for the subcarriers.

Then, by appending 212 the f-CP to the w-OFDM symbol, the generated f-CP-OFDM samples with indices - N_cp≤ m≤ {N_fft - l) are equivalent to a conventional f-CP-OFDM signal r = if * s). However, the implementation complexity for producing/deriving the f-CP-OFDM symbols according to the embodiment is considerably lower than for conventional methods used for producing/deriving f-CP-OFMD symbols.

Low-pass filtering may generally result in the so-called Gibbs effect, which is related to in-band amplification fluctuations, especially for the edge subcarriers. Normally, the shorter the filter impulse response is, the more prominent the Gibbs effect is. For this reason, longer filter impulse responses may provide better bit error performance in some scenarios. Such typical scenarios include not-so-large band allocation. The scenarios also include wideband transmission with large subcarrier spacing, which corresponds to a low number of allocated subcarriers, a small required sampling period, and a small size of the (l)FFT. Also, the design of the filter used for the CP filtering 210 is constrained to the CP length.

According to an embodiment, the weighting coefficients W_k being used for weighting 204 the current constellation symbols x_kfl are a function of Fourier coefficients F_k of the filter /„ used for filtering 210 of the current cyclic prefix CPo and the previous cyclic prefix CPo-i. Hereby, the Gibbs effect may be mitigated by use of modified amplitudes of the subcarrier weights.

According to an embodiment, the weighting coefficients W_k are complex coefficients having phases 9_k being equal to phases 9_k of the corresponding Fourier coefficients F_k of the filter /„. According to an embodiment, at least one amplitude value p_k of the weighting coefficients W_k is determined based on an averaging of an amplitude value p_k of a corresponding Fourier coefficient F_k of the filter f_n and a positive real number K. Hereby, the amplitudes may e.g. be adjusted towards a value closer to the value one (1 ). According to an embodiment, one or more of the amplitude values p_k of the complex weighting coefficients W_k are adjusted to a value of one (1 ).

The polar decomposition of the Fourier coefficient of the filter /„ may be written as F_k = p_k e^j6k . The filter weights/attenuations p_k are ideally close to one, which is typically the case for the middle subcarriers, but not necessarily for the edge subcarriers. The weights may then be selected to be:

W_k = p ~_k e**,

(Eq.13) where the phases 9_k are equal to the phases 9_k of the corresponding Fourier coefficients of the filter /„ used for the CP filtering 210. However, the weighting coefficient amplitudes p_k do not necessarily have to be equal to the filtering coefficient amplitudes p_k , as mentioned above. The new weighting amplitudes p_k may, according to an embodiment, be selected to smooth/mitigate or to totally remove the Gibbs effect on the edge subcarriers. One way to achieve this is to smooth the original weighting coefficient amplitudes, i.e. to average the amplitudes to values closer to one, e.g. as: Pk + K

If K→ oo is chosen, flat weighting coefficient amplitudes p_k = 1 are obtained, such that none of the subcarriers are attenuated. Flat weighting coefficient amplitudes provides for the best error rate performance among the herein described embodiments, but also results in the highest OOB emission. Other values of K provides different trade-offs between performance and OOB emission.

Figure 6 shows the amplitude values of the subcarrier weights p_k resulting from the above mentioned embodiments, i.e. for the original/non-averaged weighting coefficient amplitude values p_k, for the averaged/smoothed weighting coefficient amplitudes p_k, and for flat weighting coefficient amplitudes p_k = 1. As illustrated in Figure 6, an advantage of the averaging amplitude and/or flat amplitude embodiments is that they enable smoothing of the in-band attenuation of the filter response. This gives a number of degrees-of-freedom for trading-off improved error rate performance against higher OOB emission. This is relevant if the constraints on CP length for the filter results in a filter is too short for satisfactory performance. According to an aspect, the above mentioned network node 400 configured to transmit information downlink is presented. The network node 400 comprises a transceiver 1 02 and a signal processing device 100 configured as described above. The signal processing device 100 is configured to receive a plurality of constellation symbols and the transceiver 1 02 is configured to transmit the derived/created filtered cyclic prefix orthogonal frequency division multiplex symbol f-CP-OFMD included in a transmission signal r.

According to an aspect, the above mentioned user device 600 configured to transmit information uplink is presented. The user device 600 comprises a transceiver 1 02 and a signal processing device 1 00 configured as described above. The signal processing device 1 00 is further configured to receive a plurality of constellation symbols ¾,₀, ¾o-i_> ^{ancl tne} transceiver 1 02 is configured to transmit the derived/determined filtered cyclic prefix orthogonal frequency division multiplex symbol f-CP-OFMD included in a transmission signal r. A corresponding method 7200 for embodiments of the network node 400 and/or the user device 600 is shown in Figure 7.

The method 7200 includes an initial step 202 of receiving a plurality of constellation symbols ^xk,0' ^xk,0-i - The method then includes the above described first 204 to fifth 21 2 step.

The first step 204 comprises weighting current constellation symbols x_kfl with weighting coefficients W_k, so as to provide weighted constellation symbols W_kx_kfi .

The second step 206 comprises multiplexing the weighted constellation symbols W_kx_kfi , so as to provide a weighted orthogonal frequency division multiplex symbol w-OFDM.

The third step 208 comprises deriving a current cyclic prefix CPo from the current constellation symbols x_kfl and a previous cyclic prefix CPo-i from previous constellation symbols x_kfl-i - The fourth step 210 comprises filtering the current cyclic prefix CPo and the previous cyclic prefix CPo-i, so as to provide a filtered cyclic prefix f-CP.

The fifth step 212 comprises appending the filtered cyclic prefix f-CP to the weighted orthogonal frequency division multiplex symbol w-OFDM, so as to provide a filtered cyclic prefix orthogonal frequency division multiplex symbol f-CP-OFDM.

The method further comprises a final step 214 of transmitting the derived/determined filtered cyclic prefix orthogonal frequency division multiplex symbol f-CP-OFMD included in a transmission signal r.

One of the main effects of the above mentioned embodiments is that an alternative

implementation of the creation of f-CP-OFMD symbols at a reduced complexity, and also constrained to filter responses shorter than the length of the CP, is provided.

Hereafter, the different implementation approaches of the embodiments are compared in terms of number of complex multiplications required to generate a f-CP-OFDM symbol with conventional implementations using FFT and IFFT, where an FFT/IFFT computation is assumed to have an order of - - log₂(W_//t ) complex multiplications, which is a commonly used complexity evaluation.

According to a conventional Time-Domain Implementation of f-OFDM, a FIR filter / of length N_FIR is convolved with the OFDM signal s [m] . In order to filter the signal, N_FIR - 1 samples from the previous OFDM symbol need to be buffered. A direct implementation of the convolution in the time-domain would be prohibitively complex, requiring (N_fft + N_cp) N_F1R complex multiplications.

According to a conventional frequency-domain Implementation of f-OFDM, the overlap-save method splits the OFDM block in N_seg segments of size = (N_FFT + N_CP)/N_seg . In order to filter each segment, a computation window taking into account the N_F1R - 1 samples before the segment is needed. The size of this computation window is thus N_win = L + N_F1R - 1, in which the filtering will be implemented in the frequency domain by a FFT and then an IFFT. The total number of complex multiplication per window accounts for two (l)FFT computation complexities, and for the multiplications by the Fourier coefficients, which in total for one OFDM block results in:

(N_win \og₂ (N_win ) + N_win )N_seg . If this process is applied with only one segment, the number of complex multiplication is:

{N_fft + N_cp + N_FIR - 1) log₂(%_t + N_cp + N_FIR - 1) + N_fft + N_cp + N_FIR - 1.

For the herein presented embodiments, for generation of the weighted OFDM symbol w-OFDM having samples with indices 0≤ m≤ (N_fft - 1), the input data symbols are multiplied by complex weights before the IFFT operation of the OFDM modulation is performed, requiring only N_sub multiplications (and no additions).

Most of the complexity of the herein described embodiments remains in filtering of the current cyclic prefix CPo and the previous cyclic prefix CPo-i, which depends on the previous OFDM symbol. It requires a generation of the CP samples without subcarrier weighting. For this it suffices to compute N_cp original samples whose computation complexity is of the order

log₂0 //t )■ Then, the filtering of the current cyclic prefix CPo and the previous cyclic prefix

CPo i, with the frequency domain implementation gives the complexity of {N_cp + N_F1R - l)log₂(N_CP + N_FIR - 1 ) + N_CP + N_FIR - 1 multiplications. All in all, a total number of complex multiplications is obtained in the order of:

Nsub + log₂ (%t) + {N_cp + N_F1R - l)log₂(jV_cp + N_F1R - 1 ) + N_cp + N_F1R - 1.

To sum up: the evaluated implementation complexity of the different methods are listed in Table 1 .

Table 1. Implementation complexity of conventional f-OFDM and herein presented embodiment

Hereafter, the complexity comparison is also provided as a numerical evaluation.

Below, examples of the complexity-performance trade-off using LTE numerology are presented, i.e. with a symbol period of T_s = ms and a cyclic prefix duration of T_cp = ^ ms. The complexity and performance of the herein presented embodiments, which are based on a short filter length being equal to the CP length, and a conventional f-OFDM with a unconstrainsted long filter length of half the symbol duration are compared.

For both the herein presented embodiments and the conventional methods, the classical windowed-sinc filters method using an Hanning window have been used, as it has also been recently proposed for filtering OFDM signals. Taking the inverse Fourier transform of an ideal low-pass filter at cutoff frequency f_c gives the following sine function:

where sinc(x) =— , and f_sp = - - represents the sampling frequency.

This corresponds to an infinite impulse response (I IF) filter, which in practice may be implemented using a soft-truncation of its tails. Therefore, the Hanning window is considered:

In the following, the cut-off frequency is set to match the bandwidth of the OFDM signal. For a large bandwidth implementation, a large bandwidth usage with N_sub = 600 subcarriers is considered. Assuming an FFT size of N_fft = 1024 samples per T_s, this corresponds to a cyclic prefix of N_cp = 72 samples. The obtained spectrums for conventional f-OFDM and for the herein described embodiment using the Fourier coefficients of the filter as weighting coefficients; W_k = F_k are shown in Figure 8. The embodiment with W_k = F_k corresponds to an alternative implementation of f-OFDM requiring a shorter filter response. As it can be seen in Figure 8, shortening of the filter degrades the OOB emission, however at a rather small level. The filtered spectrum still has very low OOB compared to non-filtered conventional OFDM, and the transition between in-band and out-band is very sharp.

The corresponding probability for bit error rate (BER) performance is shown in Figure 9 for a transmission using 64 quadrature amplitude modulation (QAM) with turbo code rate 5/6 in an average white Gaussian noise channel for N_sub = 600 subcarriers. As shown in Figure 9, a shortening of the filter according to a herein described embodiment does not degrade the BER performance in such cases. This is because for the large bandwidth implementation, the long filter in the time domain has a narrow lobe, and has a long tail, which is negligible. As shown in the examples of Figures 8 and 9, the herein presented embodiments perform similarly as conventional f-OFDM with short and long filter. However, the herein presented embodiments have much less implementation complexity. The complexity of Table 1 with the considered numerology is shown in Table 2 below. Number of Numerical example Numerical example Multiplications N_FIR = N_CP N_FIR = 512

Conventional Time- 78 91 2 561 152

domain implementation

of f-OFDM

Conventional

Frequency-domain

13 057 18 722

implementation of f- OFDM

Herein presented 2 127 X

embodiment

Table 2. Implementation complexity comparison with N_sub = 600 subcarriers

The complexity/number of multiplications for the conventional frequency-domain implementation of the long-filter is 1 8722, while for the proposed low-complexity implementation of the short filter according to one herein presented embodiment is 21 27. This is complexity reduction by 8.8 times, i.e. almost an order of magnitude.

A corresponding numerical example for a medium-sized/not-so-large bandwidth and a non- neglectable Gibbs effect and N_sub = 144 subcarriers may also be analyzed. With a smaller bandwidth, the shortening of the filter has the consequence of creating ripples on the band edges, also known as Gibbs effect. This will have the effect to degrade the error rate performances.

Spectrums of conventional f-OFDM with long filter and for the herein presented embodiment with W_k = F_k are shown in Figure 1 0. In order to avoid the in-band rippling effect, also the herein presented embodiments for which the weighting coefficients have the same phases as the phases of the Fourier coefficients of the filter response but for which different coefficient amplitudes may be considered, as mentioned above. In Figure 1 0, the two amplitude adjustment design methods described above are shown, i.e. an embodiment having flat weighting coefficient amplitudes, and an embodiment having smoothed weighting coefficient amplitudes, as described in Equation 14 with K=0.5.

The in-band spectrum of the embodiment having flat weighting coefficient amplitudes is closer to one, which improves the BER performance, but the OOB emissions are much less attenuated. As can be verified in Figure 1 1 , the OOB transition of the embodiment having flat weighting coefficient amplitudes is nevertheless still rather sharp, and this spectrum deviates from the conventional short-filter spectrum only for attenuation below -35 dB from the in-band. For practical implementation with imperfect hardware, attenuation below a certain level such as -35 dB may actually not be achievable due to non-linearity of power amplifier that would clip the transmitted OOB emission to an error floor.

The BER performances of the conventional methods and some herein described embodiments are compared in Figure 1 1 . The conventional f-OFDM with long filter has a SNR loss of 0.3 dB at 10^"3 BER compared to the conventional OFDM system. The herein presented embodiment with W_k = F_k has 0.8 dB SNR loss compared to the conventional OFDM system. For the embodiment having flat weighting coefficient amplitudes, the SNR loss disappeared as there are no in-band fluctuations. The embodiment having smoothed weighting coefficient amplitudes provides a trade-off between the two methods.

The complexity saving from the herein described embodiments may also be determined for two cases of (l)FFT sizes. Here, the above described various embodiments having differing weighting coefficient amplitudes have the same complexity.

For an (l)FFT size of N_fft = 1024, which is the same (l)FFT size as assumed in the foregoing complexity calculations, N_fft = 1024 samples per T_s are produced. This corresponds to a cyclic prefix of N_cp = 72 samples. The complexity/number of multiplications is given in Table 3 below.

Conventional frequency- 13 057 18 722

domain implementation

of f-OFDM

Herein described 1 671 N/A

embodiment

Table 3. Implementation complexity comparison with N_sub = 144 subcarriers and Nf_ft =

1024

Here, the complexity for the conventional frequency-domain implementation of f-OFDM 13057 and 1 8722 with short and long filter, respectively, while for the herein described embodiment the complexity is 1 671 . This is a complexity reduction by 7.8 and 1 1 .2 times, i.e. about an order of magnitude.

For the above mentioned bandwidth configuration, i.e. for a N_SUB = 144 subcarrier allocation, it is possible to use a much smaller (l)FFT size. With an (l)FFT size of N_FFT = 256 samples per T_S, this corresponds to a cyclic prefix of N_CP = 18 samples. The complexity/number of

multiplications is given in Table 4 below.

Table 4. Implementation complexity comparison with N_sub = 144 subcarriers and Nf_ft =

256 Here, the complexity for the conventional frequency-domain implementation of f-OFDM is 2 673 and 3869 with short and long filter, respectively, while it for the herein described embodiment is 431 . This is a complexity reduction by 6.2 and 10.2 times, again up to an order of magnitude. The network node 400 described herein may also be denoted as an access node or an access point or a base station, e.g., a Radio Base Station (RBS), which in some networks may be referred to as transmitter, "eNB", "eNodeB", "NodeB", "gNB" or "B node", depending on the technology and terminology used. The access network nodes may be of different classes such as, e.g., macro eNodeB, home eNodeB or pico base station, based on transmission power and thereby also cell size. The access network node can be a Station (STA), which is any device that comprises an IEEE 802.1 1 -conformant Media Access Control (MAC) and Physical Layer (PHY) interface to the Wireless Medium (WM). The network node 400 may also be a node in a wired communication system. Further, standards promulgated by the IEEE, the Internet Engineering Task Force (IETF), the International Telecommunications Union (ITU), the 3GPP standards, fifth-generation (5G) standards and so forth are supported. In various embodiments, the network node 400 may communicate information according to one or more IEEE 802 standards including IEEE 802.1 1 standards (e.g., 802.1 1 a, b, g/h, j, n, and variants) for WLANs and/or 802.16 standards (e.g., 802.16-2004, 802.16.2-2004, 802.16e, 802.16†, and variants) for WMANs, and/or 3GPP LTE standards. The network node 400 may communicate information according to one or more of the Digital Video Broadcasting Terrestrial (DVB-T) broadcasting standard and the High performance radio Local Area Network (HiperLAN) standard.

A user device 600 described herein may be any of a User Equipment (UE), mobile station (MS), wireless terminal or mobile terminal which is enabled to communicate wirelessly in a wireless communication system, sometimes also referred to as a cellular radio system. The user devices may further be referred to as mobile telephones, cellular telephones, computer tablets or laptops with wireless capability. The user devices in the present context may be, for example, portable, pocket-storable, hand-held, computer-comprised, or vehicle-mounted mobile devices, enabled to communicate voice or data, via the radio access network, with another entity, such as another receiver or a server. The user device can be a Station (STA), which is any device that comprises an IEEE 802.1 1 -conformant Media Access Control (MAC) and Physical Layer (PHY) interface to the Wireless Medium (WM). Further, standards promulgated by the IEEE, the Internet Engineering Task Force (IETF), the International Telecommunications Union (ITU), the 3GPP standards, fifth-generation (5G) standards and so forth, are supported. In various embodiments, the user device 600 may communicate information according to one or more IEEE 802 standards including IEEE 802.1 1 standards (e.g., 802.1 1 a, b, g/h, j, n, and variants) for WLANs and/or 802.16 standards (e.g., 802.16-2004, 802.16.2-2004, 802.16e, 802.16†, and variants) for WMANs, and/or 3GPP LTE standards. The user device 600 may communicate information according to one or more of the Digital Video Broadcasting Terrestrial (DVB-T) broadcasting standard and the High performance radio Local Area Network (HiperLAN) standard.

Furthermore, any methods according to embodiments of the invention may be implemented in a computer program, having code means, which when run by processing means causes the processing means to execute the steps of the method. The computer program is included in a computer readable medium of a computer program product. The computer readable medium may comprise essentially any memory, such as a ROM (Read-Only Memory), a PROM

(Programmable Read-Only Memory), an EPROM (Erasable PROM), a Flash memory, an EEPROM (Electrically Erasable PROM), or a hard disk drive.

Moreover, it is realized by the skilled person that the signal processing device 100, the network node 400 and the user device 600 described herein comprise the necessary communication capabilities in the form of e.g., functions, means, units, elements, etc., for performing the present solution. Examples of other such means, units, elements and functions are: processors, memory, buffers, control logic, encoders, decoders, rate matchers, de-rate matchers, mapping units, multipliers, decision units, selecting units, switches, interleavers, de-interleavers, modulators, demodulators, inputs, outputs, antennas, amplifiers, receiver units, transmitter units, DSPs, MSDs, TCM encoder, TCM decoder, power supply units, power feeders, communication interfaces, communication protocols, etc. which are suitably arranged together for performing the present solution.

Especially, the processor 104 described herein may in an embodiment comprise, e.g., one or more instances of a Central Processing Unit (CPU), a processing unit, a processing circuit, a processor, an Application Specific Integrated Circuit (ASIC), a microprocessor, or other processing logic that may interpret and execute instructions. The expression "processor" may thus represent a processing circuitry comprising a plurality of processing circuits, such as, e.g., any, some or all of the ones mentioned above. The processing circuitry may further perform data processing functions for inputting, outputting, and processing of data comprising data buffering and device control functions, such as call processing control, user interface control, or the like.

Finally, it should be understood that the invention is not limited to the embodiments described above, but also relates to and incorporates all embodiments within the scope of the appended independent claims.

Claims

1 . A signal processing device (100), comprising a processor (104) configured to:

weight current constellation symbols (x_fcj0) with weighting coefficients (Wk), so as to provide weighted constellation symbols (W_kx_{k 0})

multiplex the weighted constellation symbols (W_kx_{k 0}), so as to provide a weighted orthogonal frequency division multiplex symbol (w-ODFM);

derive a current cyclic prefix (CPo) from the current constellation symbols (x_ki0) and a previous cyclic prefix (CPo-i) from previous constellation symbols (x_k,₀-i) ^',

filter the current cyclic prefix (CPo) and the previous cyclic prefix (CPo-i) so as to provide a filtered cyclic prefix (f-CP); and

append the filtered cyclic prefix (f-CP) to the weighted orthogonal frequency division multiplex symbol (w-OFDM), so as to provide a filtered cyclic prefix orthogonal frequency division multiplex symbol (f-CP-OFDM).

2. The signal processing device (100) according to claim 1 , wherein the processor (104) is configured to weight the current constellation symbols (x_ki0) with weighting coefficients (W_k) which are a function of Fourier coefficients (F_k) of a filter (/„) used for filtering the current cyclic prefix (CPo) and the previous cyclic prefix (CPo-i).

3. The signal processing device (100) according to claim 2, wherein the weighting coefficients (W_k) are complex coefficients and have phases (0_fc) being equal to phases (0_fc) of

corresponding Fourier coefficients (F_k) of the filter (/„).

4. The signal processing device (100) according to any one of claims 2-3, wherein the weighting coefficients (W_k) are complex coefficients, and the processor (104) is configured to determine at least one amplitude value (p_k) of the weighting coefficients (W_k) based on an averaging of an amplitude value (p_k) of a corresponding Fourier coefficient (F_k) of the filter (/„) and a positive real number K.

5. The signal processing device (100) according to claim 4, wherein the processor (104) is configured to adjust one or more of the amplitude values (p_k) of the complex weighting coefficients (W_k) to a value of one (1 ).

6. The signal processing device (100) according to any one of claims 2-3, wherein the weighting coefficients (W_k) have values equal to corresponding Fourier coefficients (F_k) of the filter (f_n).

7. The signal processing device (1 00) according to any one of claims 1 -6, wherein the processor (1 04) is configured to filter the current cyclic prefix (CPo) and the previous cyclic prefix (CPo-i) using a finite impulse response (FIR) filter („) having an impulse response being shorter than the current cyclic prefix (CPo).

8. The signal processing device (1 00) according to any one of claims 1 -7, wherein the processor (1 04) is configured to:

select samples of a central pulse from the signal output resulting from filtering of the current cyclic prefix (CPo) and the previous cyclic prefix (CPo-i) as the filtered cyclic prefix (f-CP); and

discard samples (CP_discr) of one or more tails of the signal output resulting from the filtering.

9. The signal processing device (1 00) according to any one of claims 1 -8, wherein the processor (1 04) is configured to filter the current cyclic prefix (CPo) and the previous cyclic prefix (CPo-i) using a frequency domain filtering.

1 0. The signal processing device (1 00) according to claim 1 -9, wherein

the current constellation symbols (¾₀) represent information to be transmitted in the filtered cyclic prefix orthogonal frequency division multiplex symbol (f-CP-OFDM); and

the previous constellation symbols (x_fe,₀-i) are last preceding constellation symbols representing information transmitted in a preceding filtered cyclic prefix orthogonal frequency division multiplex symbol being transmitted immediately before the filtered cyclic prefix orthogonal frequency division multiplex symbol (f-CP-OFDM).

1 1 . A network node (400) configured to transmit information downlink, the network node (400) comprising a transceiver (1 02) and a signal processing device (1 00) according to any one of claims 1 -1 0, wherein signal processing device (1 00) is further configured to:

receive a plurality of constellation symbols (¾_i0, ¾,o-i);

and the transceiver (1 02) is configured to:

transmit the filtered cyclic prefix orthogonal frequency division multiplex symbol (f-CP- OFMD).

12. A user device (600) configured to transmit information uplink, the user device (600) comprising a transceiver (1 02) and a signal processing device (1 00) according to any one of claims 1 -1 0, wherein signal processing device (1 00) is further configured to: receive a plurality of constellation symbols (¾₀- ¾,o-i);

and the transceiver (1 02) is configured to:

transmit the filtered cyclic prefix orthogonal frequency division multiplex symbol (f-CP- OFMD).

13. A method (200) for a signal processing device (100), the method (200) comprising:

weighting (204) current constellation symbols (x_fe,₀) with weighting coefficients (W_k), so as to provide weighted constellation symbols (W_kx_kfi) ;

multiplexing (206) the weighted constellation symbols (W_kx_kfi), so as to provide a weighted orthogonal frequency division multiplex symbol (w-OFDM); deriving (208) a current cyclic prefix (CPo) from the current constellation symbols (x_fcj0) and a previous cyclic prefix (CPo-i) from previous constellation symbols (x_k,0-d',

filtering (21 0) the current cyclic prefix (CPo) and the previous cyclic prefix (CPo-i), so as to provide a filtered cyclic prefix (f-CP) ; and

appending (212) the filtered cyclic prefix (f-CP) to the weighted orthogonal frequency division multiplex symbol (w-OFDM), so as to provide a filtered cyclic prefix orthogonal frequency division multiplex symbol (f-CP-OFDM).

14. A method (7200) for a user device (600), the method (7200) comprising:

receiving (202) a plurality of constellation symbols (¾,_0< ¾o-i) ;

weighting (204) current constellation symbols (x_fcj0) with weighting coefficients (W_k), so as to provide weighted constellation symbols (W_kx_{k 0}) ;

multiplexing (206) the weighted constellation symbols (W_kx_{k 0}), so as to provide a weighted orthogonal frequency division multiplex symbol (w-OFDM); deriving (208) a current cyclic prefix (CPo) from the current constellation symbols (x_fcj0) and a previous cyclic prefix (CPo-i) from previous constellation symbols (x_k,0-d',

filtering (21 0) the current cyclic prefix (CPo) and the previous cyclic prefix (CPo-i), so as to provide a filtered cyclic prefix (f-CP) ;

appending (212) the filtered cyclic prefix (f-CP) to the weighted orthogonal frequency division multiplex symbol (w-OFDM), so as to provide a filtered cyclic prefix orthogonal frequency division multiplex symbol (f-CP-OFDM); and

transmitting (214) the filtered cyclic prefix orthogonal frequency division multiplex symbol

(f-CP-OFMD).

15. Computer program with a program code for performing a method according to any one of claims 13-14 when the computer program runs on a computer.