TECHNICAL FIELD

The present invention is directed to a method for generating pulse shapes, a pulse shape generated by performing the method, a multicarrier modulation system configured to perform the method, a usage of the pulse shape in the multicarrier modulation system, a computer program for executing the method and a system comprising the multicarrier modulation system and a communication device. In particular, the aspects of the present invention relate to a wireless communication based on Filter Bank Multi Carrier (FBMC) systems, in particular for QAM symbol transmission. Further, the present invention is suitable to the forward compatible 5 G air interface focusing on supporting the enhanced Mobile Broad Band (eMBB), Massive Machine-type Communications (MMC), and Ultra-Reliable and low-latency Communications (URC). The present invention can be utilized in Multiple Input Multiple Output (MIMO) channels.

BACKGROUND In the real world, a physical channel is exposed to two kinds of dispersion, namely a time dispersion due to multipath propagation and a frequency dispersion due to

Doppler shift. With respect to the time dispersion, due to multipath propagation, when a signal, whether in the form of electromagnetic or acoustic waves, is transmitted from a transmitter to a receiver in a wireless communication system, it may interact with objects in the environment. Due to such interaction, the receiver may receive multiple copies of the original signal, each with its own propagation delay and attenuation factor. This situation is referred to as a multipath propagation. Multipath propagation may cause Inter-Symbol Interference (ISI) in time domain, which is related to frequency selectivity in frequency domain. Further, with respect to the frequency dispersion, due to the Doppler shift, when a relative distance among a transmitter, a receiver and interfering objects is varying, the frequency of the wave may be shifted. This effect is known as Doppler shift, which may lead to Inter-Carrier Interference (ICI). In fact, in the real world, if a signal propagates within a linear time-variant (LTV) channel h(t, τ), the transmitted signal s(t) suffers both, multipath propagation and Doppler shift. When denoting the general operator as H and neglecting the additive noise throughout the present patent application, the received signal r(t) is

r(t) = (Hs)(t) = J h(t _f T)s(t ~ τ)άτ

If H is modeled as wide-sense stationary with uncorrelated scattering (WSSUS), the corresponding channel scattering function C ₃ (T, U) can be given by

In the present patent application for simplifying the analysis, the system causality is ignored in the rest of the application.

Further, the basic idea of multi carrier (MC) modulation is shown in FIG. 1, wherein there it is shown that the principle idea is to divide a wideband channel with high frequency selectivity into M narrowband sub-channels with nearly flat frequency response. Further, g(t) and γ(ί) represent the transmit and receive prototype filters, respectively. In order to model the transmitted signal s(t), first the QAM symbol sampling lattice is defined as (T, F) with the density condition TF>1, wherein T represents a symbol duration of a signal and F represents the inter-carrier spacing. Then, s(t) is given by

wherein _f i (t) is the transmit filter bank defined At the receiver side, the demodulated symbol ¾ is obtained by correlating the received signal r(t) with the receive filter bank r _^ s) = y(t - Τ)ε^ ^2πτηΡ ^ ^~ηΤ ^ , that is

Two essential properties should be fulfilled by g(t) and γ(ί). The first one is

orthogonality. For a perfect reconstruction at the receiver side multicarrier transmission requires the orthogonality between g^ i ) and f^ _n ii) to fight ISI and ICI.

Furthermore, a T - F localization should be presented to avoid the symbol energy "smearing out" over the channel and distributing the neighboring symbols during a doubly dispersive transmission and therefore a good localization of g(t) and γ(ί) is also required.

In the prior art, two types of MC modulation are used, namely Orthogonal Frequency Division Multiplexing (OFDM) and Filter Bank Multi Carrier (FBMC), whose main difference lies in the choice of g(t) and γ(ί). In OFDM there is no doubt that OFDM is currently the most popular MC architecture in which both, g(t) and γ(ί) are selected as rectangular pulses. By applying an Inverse Fast Fourier Transform (IFFT) and a Fast Fourier Transform (FFT) the modulation and demodulation can be trivially performed. Moreover, a Cyclic Prefix (CP, e.g. CP-OFDM) helps to effectively avoid ISI. Although OFDM offers several advantages, it results in having large side lobes resulting from the rectangular pulses in time domain, which lead to its poor performance in certain applications such as uplink transmission in multicarrier systems where a subset of subcarriers is allocated to each user.

With respect to FBMC, in order to avoid ICI, FBMC is also an active search area. Most of the design algorithms in the prior art consider symmetric prototype functions, i.e. g(t) = γ(ί). In FBMC, the duration of g(t) is usually an integer of T, which results in better T-F localization properties as in OFDM. There are two distinct classes of FBMC, namely FBMC/OQAM and FBMC/QAM, which are designed to transmit real- valued and complex- valued data symbols, respectively. In the present patent application, only FBMC/QAM is considered. Further, based on frame theory, the "Gaussian orthogonalization" is one of the most popular methods. However, for arbitrary bandwidth efficiency requirements, e.g. LTE, the length of a generated pulse may be very long.

As mentioned above, MC modulation schemes being OFDM or FBMC face their own problems. Up to now a lot of efforts have been spent in these two areas. For instance, windowed OFDM has been proposed for OFDM as a variant to optimize the frequency response. However, when the transition periods at the beginning and end are short, for achieving high bandwidth efficiency, the prototype filter still suffers poor frequency response. In order to find a satisfying alternative, the target of the present invention is to design a numerical algorithm, which can derive pulse shapes with adjustable length, orthogonality and TF localization property in particular for FBMC/QAM systems.

In the prior art, within CP-OFDM, the transmitter and the receiver perform the "add ψ

CP" and "remove CP" operations, respectively, wherein furthermore TF = holds. As shown in FIG. 2, the transmit and receive prototype filters g _cp ofdm(t) and Ycpofdm(t) are selected as rectangular pulses and are given by

i pofdm Ct) = . 2 ' 2.

otherwise

T 1 T I _cp T I T l _cp 1

for t G

cprfdm ^{' 1} crp

otherwise

Further, when neglecting the system causality, the CP-OFDM can be modeled as "half prefix and half suffix OFDM", but still named as "CP-OFDM". While successively preventing the time dispersion up to T _cpt CP-OFDM cannot combat ICI, because of its poor spectral containment.

Furthermore, in order to deal with the large side lobes in CP-OFDM, windowed OFDM is introduced, in which the rectangular pulses are replaced by a window function with soft transition at both ends. In practice, g(t) and y(t) are usually chosen as the root-raised cosine (RRC) pulses as shown in FIG. 3. In this context, it is noted that such an improvement of a frequency response can only be achieved when the soft transition is relatively long. However, if taking the bandwidth efficiency into consideration, one cannot select long transition periods (see for example the left figure of FIG. 3).

Therefore, the RRC pulse shape may still suffer a bad spectral containment.

Furthermore, the method of "orthogonalized Gaussian", differing from OFDM and its variants, directly focuses on constructing a TF well-localized pulse as its prototype filter. Starting from a Gaussian g _ga uss(t) with good TF localization property and linearly independent _« _ J£^"( the corresponding orthonormal system can be constructed as ffortkft) = TF (s- ^1/2 ¾ _amsE )Ct) Here, (Sx)(t) =∑»,„ _Ε2 Μ^¾^ ^{is the frame} operator associated to the dual frame Sm ^of fl T ^E · ^For simplicity it is written as

A numerical solution can be efficiently obtained by a matrix factorization method. The derived pulses for TF = 1,07 and TF = 1,25 are illustrated in FIG. 4. For g _or th, one problem is that for an arbitrary bandwidth efficiency requirement, e.g. LTE for TF = 1.07, the length of generated pulse may be long (see left side figure of FIG. 4). One can directly truncate the pulse to the required length, but may lose its orthogonality and TF localization.

Furthermore, short PR FMT can be used to better balance between TF localization and filter length, wherein short pulse shapes satisfy perfect reconstruction (PR) condition, with relatively good TF localization property. In this context, two analytical methods for computing the optimal PR Filtered Multi-Tone (FMT) prototype filters have been proposed in the prior art. One is for minimizing the Out-of-Band (OOB) energy and the other is for maximizing the TF localization. Nevertheless, these two algorithms are limited to N N M

= 1

gcd{¾,M) gcd(jV,M) with time shift j

N =—

F* and number of sub-channels M—— where Fs represents the sampling frequency. Further, gooB(t) and gTFi for TF = 1.25 are illustrated in FIG. 5. Therefore, in the prior art, there is no universal approach for producing orthogonal prototype filters with arbitrary length as well as good TF localization property.

Therefore, the present invention is in particular directed to a method for generating pulse shapes, which are well-localized in the T-F domain, at least approximately orthogonal and have arbitrary length. A further problem is to provide a corresponding pulse shape generated by the herewith described generating method, a corresponding multicarrier modulation system configured to perform the claimed method, a usage of the pulse shape in a multicarrier modulation system, a computer program for executing processing for performing the claimed method and a corresponding system comprising the multicarrier modulation system and a communication device.

These problems are solved by the subject matter of the independent claims.

Advantageous implementations of the present invention are further defined in the respective dependent claims.

A first aspect of the present invention is directed to a method for generating pulse shapes comprising the steps of: obtaining a pulse shape g(t), performing an optimization on the obtained pulse shape g(t), generating an optimized pulse shape by truncating the optimized pulse shape, determining if the generated pulse shape meets at least one predefined requirement, if the generated pulse shape meets at least one predefined requirement outputting the generated pulse shape, otherwise repeating the method steps of optimization and truncating by using the generated pulse shape as the obtained pulse shape.

Therefore, according to the first aspect, an iterative method is provided for designing pulses with adjustable length, orthogonality and localization properties. Therefore, it is possible to provide at least approximately orthogonal transmit and receive prototype filters having at the same time a good T-F localization property.

In a first implementation form of the first aspect, the optimization is an

orthogonalization and the orthogonalization is performed by calculating orth{g(t), T, F} is the dual Gabor frame

operator associated with the dual frame of a filter bank, wherein T is a symbol duration of an input signal and F is an inter-carrier spacing. Therewith, a specific implementation form of performing the optimization is provided, which resembles a very easy and effective method for performing an orthogonalization on a certain obtained pulse shape.

In a second implementation form of the first aspect, the truncating of the optimized pulse shape is performed by multiplying the optimized pulse shape with a truncating window.

This contributes for providing an effective method for generating at least approximately orthogonal pulse shapes.

In a third implementation form of the first aspect, the truncating window is fixed for the whole method.

In a fourth implementation form of the first aspect, the truncating window is a rectangular window, RECT, a raised-cosine window, RC(P), or a root-raised cosine window, RRC(P), wherein beta is a roll-off factor with β>0. In a fifth implementation form of the first aspect, the truncating window is varied every time the truncating step is performed.

In a sixth implementation form of the first aspect, the obtained pulse shape g(t) is polynominally localized or sub-exponentially localized.

In a seventh implementation form of the first aspect, the polynominally localized pulse shape g(t) is a spline-type pulse shape and the sub-exponentially localized pulse shape g(t) is a Gaussian pulse shape.

In an eighth implementation form of the first aspect, the sequence of the method steps of optimization and truncating forms one iteration and in a first alternative the at least one predefined requirement comprises that a difference between the generated pulse shape of an iteration and a generated pulse shape of a previous iteration is below a threshold or in a second alternative the at least one predefined requirement comprises exceeding a maximum number of iterations. Thereby, a very effective and easy criteria for stopping the iterative method are provided.

In a second aspect of the present invention, a pulse shape is provided being generated by performing any of the above methods.

In a third aspect of the present invention, a multicarrier modulation system is provided being configured to perform any of the above methods. In an implementation form of the third aspect, the multicarrier system is a filter bank.

In a fourth aspect of the present invention, a pulse shape according to the above- mentioned method is used in a multicarrier modulation system, in particular in a filter bank.

In a fifth aspect of the present invention, a computer program is provided for executing processing according to any of the above methods. In a sixth aspect of the present invention, a system is provided comprising a multicarrier modulation system according to the third aspect or the implementation form of the third aspect and a communication device, wherein the multicarrier modulation system is configured to update the obtained pulse shape g(t) by performing a communication between the multicarrier modulation system and the communication device according to a communication protocol.

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

BRIEF DESCRIPTION OF THE DRAWINGS The above-described aspects and implementation forms of the present invention will be explained in the following description of specific embodiments in relation to the enclosed drawings in which:

FIG. 1 shows a unified block diagram of OFDM and FBMC transceivers.

FIG. 2 shows CP-OFDM prototype filters at the transmitter (solid line) and receiver (dashed line). FIG. 3 shows the function gRR _C for TF = 1.07 (left figure) and TF = 1.25 (right figure).

FIG. 4 shows gorth for TF = 1.07 (left figure) and TF = 1.25 (right figure).

FIG. 5 shows gooB (left figure) and gTFL (right figure) for TF = 1.25.

FIG. 6 shows an embodiment of an iterative method according to the present invention.

FIG. 7 shows an implementation form of the iterative method of Fig. 6 of the present invention.

FIG. 8 shows impulse and frequency responses of gcpofdm and gi _ter for TF = 1.07

(upper half) and TF = 1.25 (lower half).

FIG. 9 shows the ambiguity surface of gcpofdm (left figures) and giter (right

figures) for TF = 1.07 (upper half) and TF = 1.25 (lower half). FIG. 10 shows an SIR contour for gcpofdm (solid curve) and giter (dashed curve) for

TF = 1.07 (left figure) and TF = 1.25 (right figure).

FIG. 11 shows giter converging to gTFL (left figure) and gooB (right figure) for TF

= 1.25 and K = 1.

FIG. 12 shows g _ite r for TF = 1.07 and K = 1.

FIG. 13 shows the SIR contour of gcpofdm (solid curve) and giter (dashed curve) for

TF = 1.07 (left figure) and TF = 1.25 (right figure).

FIG. 14 shows a scenario of uplink TA-free access.

FIG. 15 shows a scenario of HST-V2V with a high mobility. FIG. 16 shows a scenario of one symbol per TTI.

FIG. 6 shows an embodiment of the iterative method according to the present invention for designing pulse shapes with adjustable length, orthogonality and localization properties.

There, in a step 600 an initial well-localized pulse shape g ⁽⁰⁾ (t) is provided. g ⁽⁰⁾ (t) can be well-localized in the T-F domain and can be, for example, a sub-exponentially localized pulse shape, e.g. a Gaussian-type pulse, or a polynominally localized pulse shape, e.g. a spline-type pulse. Here, in the present invention, a Gaussian pulse

5gns _E ⁼ (2σ) ^1/ β~ ^πσ * can be chosen as g ⁽⁰⁾ (t), where g ⁽⁰⁾ (t) is preset, and σ is the decaying factor. In this context, can be shrunk or dilated to match the channel

F

doubly dispersive property. In this context, σ = - a. With a given symbol duration T and frequency spacing F, σ > 1 makes g^„ _Eg decays faster in the time domain while a < 1 makes it faster in the frequency domain. Given T and F, α>1 makes decays faster in the time domain, wherein α<1 decays are faster in the frequency domain.

In particular, g ⁽⁰⁾ (t) can be localized in the time domain (e.g. rectangular pulse) or T-F domain (e.g. Gaussian pulse). For § _{s mBB} it can be shrunk or dilated to match the channel doubly dispersive property.

After inputting the initial pulse shape g ⁽⁰⁾ (t) an orthogonalization procedure is performed on the initial pulse shape g ⁽⁰⁾ (t) as can be seen in step 610 of FIG. 6 and a iteration index is set to n = 1. In this context, the orthogonalization procedure performed in step 610 can be the same as discussed and mentioned above with respect to the orthogonalized Gaussian. That means, an optimized pulse shape g ⁽¹⁾ (t) is generated by an optimization procedure. This orthogonalization might not be a perfect

orthogonalization, but after performing step 610 some regularizations might still remain. Further, the orthogonalization might further be performed on the original or the dual time-frequency lattice. In this context the optimized pulse shape g ⁽¹⁾ (t) is calculated by using the general formula g ⁽ⁿ⁾ = orth{ g ^{(n l)} , T, F} with n = 1 and can for example be a Weyl-Heisenberg Riesz sequence construction. Subsequently, as can be seen in FIG. 6 in a step 620, is truncated by a truncating window gw ⁽ⁿ⁾ with n =1 by multiplying g ⁽¹⁾ (t) with gw ⁽¹⁾ , thereby arriving at a truncated pulse shape gt ⁽¹⁾ (t). Thereafter, a resetting is performed by g ⁽¹⁾ (t) <— gt ⁽¹⁾ (t). In this context, the truncating window g _w ⁽ⁿ⁾ can be changed every time the truncating is performed or can be the same for the whole iteration method. Common windows include the rectangular (RECT), raised-cosine (RC(P)) or the root-raised cosine (RRC(P) windows, where beta is the roll-off factor. For β→ 0 , RC(P) and RRC(P) converge to REC. For example, one can only consider in FIG. 6 a fixed window g _w with a non-zero duration D^ il + β) , where Z? _r(K1 = KT is the required time interval and K 1. For K=4, numerical results show that RC (0.25) may be a good choice. In this context one iteration (loop) in Fig. 6 is defined as a sequence of method steps 610 and 620 and the iteration index n counts the number of iterations (iteration loops) performed in the method of Fig. 6. Further, in a step 630, it is checked if the generated pulse shape g ⁽¹⁾ (t) generated in method step 620 meets at least one predefined requirement. In this context, it is checked if ll(g ⁽ⁿ⁾ - g ^(n_1) ) II /II g ^(n_1) II < ε with n = 1 holds, wherein ε is the predefined requirement being a threshold, in particular a convergence coefficient ε with ε > 0. There, the convergence coefficient ε controls the orthogonality and TF localization properties of the outputted pulse shape output in step 640. A large ε can put more weight on TF localization, while a small ε pursues orthogonality. Alternatively, the predefined requirement can also be the number of performed iterations exceeding a certain maximum number of iterations. Further, also a combination of several predefined requirements is conceivable, for example a combination of the convergence coefficient ε together with the maximum number of iterations.

If the above condition of step 630 holds, then g ⁽¹⁾ (t) is output, otherwise the iteration index is increased by 1 in steps 635 and it is returned to step 610 of performing an orthogonalization procedure, now on g ⁽¹⁾ (t) and not on g ⁽⁰⁾ (t) as indicated in step 610 of FIG. 6, thereby calculating g ⁽²⁾ (t) by calculating g ⁽ⁿ⁾ = orth{g ^(n_1) , T, F} with n = 2.

Thereafter, method step 620 and 630 are again performed. If the condition of step 630 holds, then g ⁽²⁾ (t) is output, otherwise the iteration index is increased by one and again method steps 610 , 620, 630 are performed until the condition of method step 630 holds. Then, the final generated pulse shape is output.

Furthermore, FIG. 7 shows an implementation form of the method of FIG. 6, wherein the method step of the orthogonalization of step 610 is further detailed by calculating in step 710

wherein § is the above defined frame operator associated with the frame 9 ^{' " ^{' 1}} and n is the iteration index. Further, all other steps 720, 730, 735, 740 in the flow diagram of FIG. 7 correspond to steps 620, 630, 635 and 640 in the flow diagram of FIG. 6, respectively.

Further, the below Algorithm 1 shows the iterative method for designing pulses with adjustable length, orthogonality and localization procedures, which can be implemented in a computer program.

Algorithm 1

Since several parameters in the iterative method of FIGS. 6 and 7 can be adjusted, the algorithm of the present invention holds flexibility and is feasible to any proposed requirement. Further, the method of FIGS. 6 and 7 can be performed by a multicarrier modulation system, in particular by a filter bank. Further, the multicarrier modulation system can be a transmitter, receiver or other devices with computing ability, which can perform the methods of FIGS. 6 and 7 online or offline, that means being connected to a further system (online), for example via the Internet, or not being connected with the further system (offline). In another embodiment the pulse shape generated by the method of FIGS. 6 and 7 can also be, after the generation, used in a multicarrier modulation system, in particular in a filter bank. Of course, a computer program can also store commands for being executed on a computer, which performs the herewith presented methods of FIGS. 6 and 7. Further, a computer program can also be configured to use the pulse shapes generated by the methods of FIGS. 6 and 7 subsequently after its generation. In a further embodiment, also a system can be provided comprising a multicarrier modulation system configured to perform the method of FIGS. 6 and 7 and a communication device, wherein the multicarrier modulation system is configured to update the obtained pulse shape g ^(o) (t) by performing a communication between the multicarrier modulation system and the communication device according to a communication protocol.

In the following, a performance analysis of the herewith presented invention according to FIGS. 6 and 7 is shown. Besides common impulse and frequency responses, performance analysis also includes orthogonality and self-interference in the following.

The orthogonality between gm.n(t and f _m , _« (t) is described by the cross-ambiguity function defined as where τ, v represent the time delay and frequency shift, respectively. Further, the ambiguity surface is chosen to intuitively look at the ambiguity function. For a perfect reconstruction, one needs n, m = (0,0)

A _giY (:nT _t mF) =

otherwise Furthermore, self-interference is introduced in a TF dispersive channel H and represented by the cross-ambiguity function Α _{ΰ γ} (τ,υ) and computed as

with Ε _Η (τ, υ) ∑ _(r¾n)3:(0, o ₎ Cgir - nT,!/ - m ). For a given scattering function

C _h (T, U) = ff{r— τ ₀ , ι>— υ ₀ ) with normalized support (¾, i¾), the derived SIR contour

SIR(H) is of great importance, since it indicates the self-interference of the pulse when a signal carried on it is undergoing a proportional misalignment in time and frequency domain.

Furthermore, the performance analysis in the present invention can be done by evaluating the performance of the pulse gi _ter and compare it with CP-OFDM for the case of TF = 1.07 and TF = 1.25, respectively. All other essential simulation parameters are listed in Table 1.

Table 1

Furthermore, the impulse and frequency response can also be clearly seen in FIG. 8 of the present patent application. Furthermore, an orthogonality comparison is also performed in terms of SIR (dB, see Table 2) and the ambiguity surface (see FIG. 9), respectively. For both transmission schemes, the ambiguity function Α _{α γ} {τ,υ) regularly crosses zeros at the grid points τ = nT and u = mF for nonzero integers n and m, and as a result guarantees a 1ST and ICI-free transmission over an ideal channel. Moreover, compared with S _cpo fdm, the spreading of g _iter along the frequency axes is smaller, especially for TF = 1.2 S . Table 2: SIR (dB) comparison between g„^ _im and

Furthermore, a mismatching loss is also checked, wherein a CP-OFDM has a mismatching loss ξ _άΒ » 0.3dB for TF = 1.07 and ξ _ΛΒ ¾ IdB for TF = 1.25 . g _iter does not have such loss.

Furthermore, by using the method of FIGS. 6 or 7, the method can converge to gTFL and gooB for TF = 1.25 (see in particular FIG. 11). Further, Table 3 below lists the essential parameters for achieving such a universality. Moreover, since there is no limitation on the relationship between n and m, a pulse shape for TF = 1.07 and K = 1 is first derived in the literature (see FIG. 12).

Table 3: Parameters setting for g _lw∑ converging to g _T n and

In this context, it is noted that K = 1 is for a special scenario called one symbol per Transmission Time Interval (TTI), in which guard periods are inserted between the uplink and downlink transmission and hence in this case there is no ISI. In order to analyze the self-interference prototype with respect to ICI of giter the SIR contour SIR(B) for TF = 1.07 and TF = 1.25 is respectively shown, both of which are compared to gcpofdm.

Furthermore, the present application can be applied for various scenarios. For example, the present invention can be applied with respect to an uplink timing adjustment-free access. In the uplink transmission, due to the propagation delay signals arrive at the base station with timing misalignments. For a cell with a radius of 800 m, for example, such timing offset is as high as 5.4 μβ. To solve this problem, closed-loop Timing Adjustment (TA) is adopted. However, if each user equipment only uses to send a small data packet in a relatively long period of time, TA becomes a large overhead. For the purpose of easing the burden, uplink TA-free access or relaxed TA transmission is enabled as illustrated in FIG. 14. As presented above, the proposed pulse with good orthogonality is more robust to time dispersion and hence can be used in this scenario.

Furthermore, FIG. 15 shows a scenario of High Speed Train (HST) and Vehicle-to- Vehicle (V2V) with high mobility. In this scenario, objects are moving at a high velocity, which leads to a more "doubly dispersive" channel then other scenarios. For example, when a car moves towards the BS with a speed of 20 m/s, the corresponding Doppler shift is 173 Hz for carrier frequency f _c =2,6GHz. In traditional CP-OFDM, longer Cyclic Prefix is adopted to handle this double dispersion but inevitably increases the mismatching loss, e.g., for TF = 1.25 , ξ _ύΒ ¾ IdB . However, as shown in FIG. 15, using the proposed pulse in the present invention in such challenging scenario may be more reasonable to maintain a reliable performance without incurring any mismatching loss.

Further, FIG. 16 illustrates a scenario of one symbol per TTI. As shown in FIG. 16, the pulses of the present invention can be an appealing alternative to gcpofdm, especially for TF = 1.25, since its TF support contour is much larger than CP-OFDM in this case.

Furthermore, in the following Table 4 some applicable parameter settings for the aforementioned scenarios are presented.

Table 4: Exampled parameter settings

The invention has been described in conjunction with various embodiments herein. However, other variations to the enclosed embodiments can be readily understood and effected by those skilled in the art and practicing the claimed invention from a study of the drawings, the disclosure and the appended claims. In the claims, the word

"comprising" does not exclude other elements or steps, and the indefinite article "a" or "an" does not exclude a plurality. A single processor of the entity may fulfil the functions of several items recited in the claims. The mere fact that certain measures are recited in mutually different dependent claims does not initiate that a combination of these measures cannot be used to advantage. A computer program may be

stored/distributed on a suitable medium, such as an optical storage medium or a solid state medium, supplied together with or as part of other hardware, but may be also distributed in other forms, such as via the internet or other wired or wireless telecommunication systems.