Method, system and device for compensation of Doppler impairments in OFDM wireless communication networks

Abstract

A system, method and device to overcome the effects of mobility in OFDM wireless cellular networks. Individual beams are isolated and Doppler impairments are compensated so the constituent beams can reach the users in DL with ideally no Doppler impairments. Similarly in UL the signals corresponding to the different spatial beams are detected and their Doppler impairments compensated.

Claims

1. A method for compensating Doppler impairments in a wireless Orthogonal Frequency-Division Multiplexing, OFDM, system comprising at least one base station equipped with a two-dimensional rectangular antenna array of N.sub.1N.sub.2 antenna elements and M user equipments, M>=1, where the method comprises the following steps: a) spatially separating the received beams corresponding to different user equipments from the signals received in the uplink by the antenna array, according to their angles of arrival, and determining a set of beams characterizing the user equipments; b) estimating the Doppler shift corresponding to each beam of said set of beams characterizing the user equipments; and c) processing the received signals in each beam of said set of beams characterizing the user equipments, to compensate Doppler impairments in uplink, based on the estimated Doppler shifts of each beam of said set of beams characterizing the user equipments; where this processing is made by applying the following expression: $S_R\left[k,l,t\right]=S_{R,\mathrm{Dopp}}\left[k,l,t\right]\exp \left(-j2\frac{f_{d,\mathrm{shift}}\left[k,l\right]}{f}t\right),$ where S.sub.R,Dopp[k, l, t] denotes the Doppler-affected discrete-time samples of the received OFDM symbol at the base station, at the uplink beam characterized by coordinates (k, l), S.sub.R[k, l, t] are the corresponding samples of the received OFDM symbol at the base station after introducing said intentional Doppler shift in the beam characterized by coordinates (k, l); f is the subcarrier width; and f.sub.d,shift[k,l] is the estimated Doppler shift of the uplink beam characterized by coordinates (k, l).

2. A method according to claim 1, where the base station comprises N.sub.1 antenna elements along a perpendicular axis with a regular spacing d.sub.x and N.sub.2 antenna elements along a perpendicular axis with a regular spacing d.sub.y, and where the position of said user equipments is defined by elevation and azimuth angles (,) in a spherical coordinate system discretized trough a grid spacing u, v in an (u, v) domain where
u=sin()cos()
v=sin()sin() and where (k, l) are indices characterising beams in an (u, v) grid according to the following relations: $\begin{array}{c}{u}_k=k.Math.u;k=0,1,\mathrm{.Math.},N_1-1\\ v_l=l.Math.v;l=0,1,\mathrm{.Math.},N_2-1\end{array}.\begin{array}{c}{d}_x=\frac{}{N_{1}u}\\ d_y=\frac{}{N_{2}v}\end{array}.$ where is the wavelength of a system operating frequency.

3. A method according to claim 1 where the method further comprises: d) spatially decomposing the signals to be transmitted by the base station into individual beams in downlink direction; e) introducing, in each beam of the set of beams characterizing the user equipments for the signal to be transmitted in downlink direction, a shift equal to the opposite of the estimated Doppler shift for said beam in step b) in order to compensate Doppler impairments in downlink.

4. A method according to claim 3 where step e) includes: obtaining the time-domain OFDM transmit signals A.sub.T[n, m, t] corresponding to antenna element (n, m), which compensate Doppler impairments in downlink, by applying the following expression: $A_T\left[n,m,t\right]=\sqrt{\frac{1}{N_1{N}_2}}\underset{k=0}{\overset{N_1-1}{.Math.}}\underset{l=0}{\overset{N_2-1}{.Math.}}{P}_T\left[k,l\right]S_T\left[k,l,t\right]\exp \left(-j2\frac{f_{d,\mathrm{shift}}\left[k,l\right]}{f}t\right)\exp \left(-j\frac{2}{N_1}\mathrm{nk}\right)\exp \left(-j\frac{2}{N_2}ml\right),$ where f is a subcarrier width; S.sub.T[k, l, t] is the time-domain OFDM transmission signal corresponding to the beam with coordinates (k, l) in the (u, v) grid; P.sub.T[k,l] are the individual transmit powers assigned to the beam with coordinates (k, l); and f.sub.d,shift[k,l] is the Doppler shift of the beam with coordinates (k, l) as estimated in step b).

5. A method according to claim 3, where the signals to be transmitted in downlink direction are decomposed into individual beams by means of the following expression: $A_T\left[n,m,f\right]=\sqrt{\frac{1}{N_1{N}_2}}\underset{k=0}{\overset{N_1-1}{.Math.}}\underset{l=0}{\overset{N_2-1}{.Math.}}{P}_T\left[k,l\right]S_T\left[k,l,f\right]\exp \left(-j\frac{2}{N_1}\mathrm{nk}\right)\exp \left(-j\frac{2}{N_2}ml\right),\mathrm{with}f=0,\mathrm{.Math.},N_c-1,$ where A.sub.T[n, m, f] are the frequency-domain OFDM transmit signals corresponding to each antenna element (n, m); P.sub.T[k,l] are the individual transmit powers assigned to beam with coordinates (k, l); and S.sub.T[k, l, f] are the normalized complex baseband signals to be transmitted over the beam with coordinates (k, l).

6. A method according to claim 1 where S.sub.R,Dopp[k, l, t] is given by the following expression: $S_{R,\mathrm{Dopp}}\left[k,l,t\right]=\frac{1}{\sqrt{N_1{N}_2}}\underset{n=0}{\overset{N_1-1}{.Math.}}\underset{m=0}{\overset{N_2-1}{.Math.}}{A}_R\left[n,m,t\right]\exp \left(j\frac{2}{N_1}\mathrm{nk}\right)\exp \left(j\frac{2}{N_2}ml\right)$ where A.sub.R[n, m, t] are the uplink time-domain signals received at the antenna element (n, m), where n and m are integer indices labeling the antenna in the horizontal and vertical directions respectively.

7. A method according to claim 3 where in step d) the individual beams into which the signals to be transmitted in downlink direction are decomposed are the beams of the set of individual beams characterizing the user equipments as determined in step a).

8. A method according to claim 1, where step a) comprises obtaining the frequency components S.sub.R[k, l, f] of the signals received from the M user equipments in the uplink by applying the following transformation over the received time-domain signals A.sub.R[n, m, t] received at the antenna element (n, m), where n and m are integer indices labeling the antenna in the horizontal and vertical directions respectively, at the spatial beam in the (k, l) direction: $S_R\left[k,l,f\right]=\frac{1}{\sqrt{N_c{N}_1{N}_2}}\underset{t=0}{\overset{N_c-1}{.Math.}}\underset{n=0}{\overset{N_1-1}{.Math.}}\underset{m=0}{\overset{N_2-1}{.Math.}}{A}_R\left[n,m,t\right]\exp \left(-j\frac{2}{N_c}ft\right)\exp \left(j\frac{2}{N_1}\mathrm{nk}\right)\exp \left(j\frac{2}{N_2}ml\right)$ where N.sub.c is the number of subcarriers in the frequency domain.

9. A method according to claim 1, where step a) further comprises determining the set of beams characterizing the user equipments as the set of angular directions (k, l) at which the received powers from each of the user equipments are not zero.

10. A method according to claim 9, where in step a), from the set of beams characterizing the user equipments, those beams belonging to the set of beams of two or more different user equipments are discarded.

11. A method according to claim 1, where the steps of the method are performed by the base station.

12. A base station for compensating Doppler impairments comprising a two-dimensional rectangular antenna array of N.sub.1N.sub.2 antenna elements, the base station being wirelessly connected through a wireless Orthogonal Frequency-Division Multiplexing, OFDM, network with M user equipments, M>=1, where the base station further comprises a processing unit configured to perform the following steps: a) spatially separating the received beams corresponding to different user equipments from the signals received in the uplink by the antenna array, according to their angles of arrival, and for each user equipment determining a set of received beams characterizing the user equipments; b) estimating the Doppler shift corresponding to each beam of said set of beams characterizing the user equipments; c) processing the received signals in each beam of said set of beams characterizing the user equipments to compensate Doppler impairments in uplink, based on the estimated Doppler shifts of each beam of said set of beams characterizing the user equipments; where this processing is made by applying the following expression: $S_R\left[k,l,t\right]=S_{R,\mathrm{Dopp}}\left[k,l,t\right]\exp \left(-j2\frac{f_{d,\mathrm{shift}}\left[k,l\right]}{f}t\right),$ where S.sub.R,Dopp[k, l, t] denotes the Doppler-affected discrete-time samples of the received OFDM symbol at the base station, at the uplink beam characterized by coordinates (k, l), S.sub.R[k, l, t] are the corresponding samples of the received OFDM symbol at the base station after introducing said intentional Doppler shift in the beam characterized by coordinates (k, l); .sub.f is the subcarrier width; and f.sub.d,shift[k,l] is the estimated Doppler shift of the uplink beam characterized by coordinates (k, l).

13. A system for compensating Doppler in wireless Orthogonal Frequency-Division Multiplexing, OFDM, networks, the system comprising M user equipments, M>=1 and a base station comprising a two-dimensional rectangular antenna array of N.sub.1N.sub.2 antenna elements, and where the system further comprises a processing unit configured to perform the following steps: a) spatially separating the received beams corresponding to different user equipments from the signals received in the uplink by the antenna array, according to their angles of arrival, and for each user equipment, determining a set of beams characterizing the user equipments; b) estimating the Doppler shift corresponding to each beam of said set of beams characterizing the user equipments; c) processing the received signals in each beam of said set of beams characterizing the user equipments to compensate Doppler impairments in uplink, based on the estimated Doppler shifts of each beam of said set of beams characterizing the user equipments; where this processing is made by applying the following expression: $S_R\left[k,l,t\right]=S_{R,\mathrm{Dopp}}\left[k,l,t\right]\exp \left(-j2\frac{f_{d,\mathrm{shift}}\left[k,l\right]}{f}t\right),$ where S.sub.R,Dopp[k, l, t] denotes the Doppler-affected discrete-time samples of the received OFDM symbol at the base station, at the uplink beam characterized by coordinates (k, l), S.sub.R[k, l, t] are the corresponding samples of the received OFDM symbol at the base station after introducing said intentional Doppler shift in the beam characterized by coordinates (k, l); .sub.f is the subcarrier width; and f.sub.d,shift[k,l] is the estimated Doppler shift of the uplink beam characterized by coordinates (k, l).

14. A non-transitory computer readable medium comprising program code instructions which when loaded into a computer system controls the computer system to perform the method of claim 1.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) For the purpose of aiding the understanding of the characteristics of the disclosure, according to a preferred practical embodiment thereof and in order to complement this description, the following figures are attached as an integral part thereof, having an illustrative and non-limiting character:

(2) FIG. 1 shows a schematic block diagram of the proposed disclosure in a basic scenario with M users and a massive MIMO base station.

(3) FIG. 2 shows a schematic diagram of a basic scenario for application of the disclosure according to an embodiment of the disclosure.

(4) FIG. 3 illustrates some exemplary angular profiles where inter-user interference is avoided by not exciting common beams.

(5) FIG. 4 illustrates a geometric characterization of the receive beam width .sub.H.sup.RX, the transmitted and received signals, and the angle between the velocity vector and the transmitted signal .sub.v, taking uplink direction as a reference.

(6) FIG. 5 shows a schematic block diagram of the proposed disclosure according to an embodiment of the disclosure.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

(7) The present disclosure proposes a method, system and device to compensate the effects of Doppler impairments in wireless OFDM communications systems.

(8) FIG. 1 summarizes the basics of the proposed disclosure. A number M of moving cellular user equipments (moving at velocities v.sub.1 . . . v.sub.M) are wirelessly connected to a base station, comprising a rectangular array of N.sub.1N.sub.2 transmission/reception antennas in a massive MIMO system (with multipath wireless channels), where N.sub.1 and N.sub.2 are the amount of antennas in the horizontal and vertical direction, respectively. User mobility leads to the appearance of a certain Doppler power spectrum at the receive side, whose impact depends on the magnitude of the user's velocity and its relative orientation with respect to the angles of departure or arrival, impairing reception in both uplink and downlink directions. The present disclosure compensates said Doppler impairments by estimating Doppler shifts for each of the spatial beams in uplink and compensating said estimated Doppler shifts in uplink and downlink.

(9) FIG. 2 illustrates the basic scenario and network deployment where the proposed method would apply, comprising a MIMO base station (BS), preferably a so-called massive MIMO base station, with a rectangular antenna array of N.sub.1N.sub.2 antenna elements, with inter-antenna spacing given by d.sub.x, d.sub.y in the horizontal and vertical dimensions, respectively. M cellular user equipments are simultaneously connected to the base station and their mobility is described by the velocity vectors v.sub.1 . . . v.sub.M, which create Doppler impairments in both uplink (UL) and downlink (DL). The aim of this disclosure is to compensate Doppler effects at the BS side so that performance is optimized, while keeping baseband processing at the device side as simple as possible.

(10) Massive MIMO systems are characterized by having at least one order of magnitude higher number of antennas at the BS compared to traditional MIMO systems (see for example, T. L. Marzetta, Noncooperative Cellular Wireless with Unlimited Numbers of Base Station Antennas, IEEE Transactions on Wireless Communications, vol. 9 no. 11, November 2010 or L. Lu, G. Y. Li, A. L. Swindlehurst, A. Ashikhmin and R. Zhang, An Overview of Massive MIMO: Benefits and Challenges, in IEEE Journal of Selected Topics in Signal Processing, vol. 8, no. 5, pp. 742-758, October 2014). The additional degrees of freedom brought by the excess antennas can be exploited in two ways: Upon reception, the high number of antennas makes it possible for the base station (BS) to spatially discriminate the signals coming from multiple users by means of simple linear techniques. Upon transmission, linear precoding techniques can easily be applied so as to spatially multiplex transmissions towards the different users, provided that full channel state information (CSI) is available at the BS.

(11) The above properties make massive MIMO an ideal choice for increasing the area spectral efficiency of wireless cellular systems without further densifying the network. An important condition, though, is that the BS must have detailed CSI knowledge between each pair (antenna-user equipment) in both UL and DL. UL CSI can be easily achieved by means of pilots inserted as part of the uplink transmissions. However, DL CSI is in general only known by the user equipment unless the same frequencies are employed in UL and DL (and channel reciprocity holds). For this reason, massive MIMO systems based on full CSI are actually restricted to TDD operation. This proposal however is not restricted to TDD operation, and FDD can be supported without any channel reciprocity constraint. In a way, it can be said that the present disclosure stems from the disclosures described in patent applications EP-A1-2806576 and EP-A1-3038270 for spatially multiplexing users using orthogonal beams.

(12) Spatial Multiplexing of User Equipments by Means of Orthogonal Beams

(13) According to EP-A1-3038270 it is possible to spatially multiplex users in the DL without having detailed channel knowledge at the BS side. UL signals from users are assumed to be periodically received by the BS, for carrying either UL data or UL control pilots. Such UL signals contain enough information on the angles of arrival that can be re-used for the downlink. Reciprocity is observed between the angles of arrival and departure even if different frequencies are involved, apart from a usually small correction factor applied to the antenna excitations that accounts for the differences in UL and DL carrier frequencies. Hence, it is possible to derive the angular profile of user equipment i in UL as the set of directions (or beams (k, l)) in the (u, v) grid leading to non-zero received powers (signal energy):
.sub.i={(k.sub.j,l.sub.j),j=0, . . . ,N.sub.1N.sub.21 such that non-null signal is received by user i},
where i=0, . . . , M1, and the indices (k.sub.j, l.sub.j) relate to the discretized directional cosines which are functions of the elevation and azimuth angles (, ) in a spherical coordinate system, discretized trough a grid spacing as follows:
u=sin()cos()
v=sin()sin()

(14) A sector area is fully covered by a set of N.sub.1N.sub.2 discrete points in the (u, v) grid given by:
u.sub.k=k.Math.u;k=0,1, . . . ,N.sub.11
v.sub.l=l.Math.v;l=0,1, . . . ,N.sub.21

(15) The sampling periods u, v represent the desired granularity in the spatial domain and are related to the antenna spacing in both dimensions of the array d.sub.x, d.sub.y that ensure orthogonality between the users (orthogonal multiple access):

(16) $d_x=\frac{}{N_{1}u}$$d_y=\frac{}{N_{2}v}.$

(17) For this k=0, . . . , N.sub.11, l=0, . . . , N.sub.21 are indices characterising the beams (spatial beams) in an (u, v) grid with wavelength according to the following relations:

(18) $u_k=k.Math.u,v_l=l.Math.v,u=\frac{}{N_1{d}_x},v=\frac{}{N_2{d}_y}.$

(19) The angular profile .sub.i of each user equipment characterizes said user equipment uplink communications as it represents the set of angular directions (corresponding to the received multipaths) in which significant signal energy (or at least non-zero signal energy) is detected at the BS. The angular directions defined by the (u, v) grid can be regarded as a set of orthogonal beams. If multiple users are present and their corresponding angular profiles do not overlap in the (u, v) grid, it is possible to spatially multiplex their transmissions by performing the following precoding operation (according to the technique proposed in patent applications EP-A1-2806576 or EP-A1-3038270 but any known technique can be used to spatially separate the received beams):

(20) $A_T\left[n,m,f\right]=\sqrt{\frac{1}{N_1{N}_2}}\underset{k=0}{\overset{N_1-1}{.Math.}}\underset{l=0}{\overset{N_2-1}{.Math.}}{P}_T\left[k,l\right]S_T\left[k,l,f\right]\exp \left(-j\frac{2}{N_1}\mathrm{nk}\right)\exp \left(-j\frac{2}{N_2}\mathrm{ml}\right),\mathrm{with}\{\begin{array}{c}n=0,\mathrm{.Math.},N_1-1\\ m=0,\mathrm{.Math.},N_2-1\\ f=0,\mathrm{.Math.},N_c-1\end{array}.$

(21) The information to be sent to each user is constructed as follows:

(22) 0$S_T\left[k,l,f\right]=\{\begin{array}{c}{S}_i\left[f\right];\left(k,l\right){}_i,i=0,1,\mathrm{.Math.},M-1\\ 0;\mathrm{otherwise}\end{array},$
where A.sub.T[n, m, f] are the frequency-domain OFDM transmission signals corresponding to each antenna element (n, m) (this corresponds to the combined signal containing all the user equipments' information, as different user equipments will be addressed by means of different subsets of points in the u, v grid); N.sub.c denotes the number of subcarriers in the frequency domain; P.sub.T[k, l] are the individual transmit powers assigned to the orthogonal beams; S.sub.i[f] are the normalized (unit power) complex baseband signals corresponding to user equipment i in the frequency domain (or in other words, the frequency-domain signal for user equipment i). When no inter-user interference is present one can multiplex and de-multiplex users according to their angular profiles .sub.i without ambiguity.

(23) For detection of uplink signals, after receiving the time-domain signals A.sub.R[n, m, t], t=0, . . . , N.sub.c1, at antenna elements (n, m), the frequency contents of each beam at direction (k, l) can be obtained through the expression:

(24) $S_R\left[k,l,f\right]=\frac{1}{\sqrt{N_c{N}_1{N}_2}}\underset{t=0}{\overset{N_c-1}{.Math.}}\underset{n=0}{\overset{N_1-1}{.Math.}}\underset{m=0}{\overset{N_2-1}{.Math.}}{A}_R\left[n,m,t\right]\exp \left(-j\frac{2}{N_c}\mathrm{ft}\right)\exp \left(j\frac{2}{N_1}\mathrm{nk}\right)\exp \left(j\frac{2}{N_2}\mathrm{ml}\right)$

(25) By knowing the frequency contents (or components) or each beam, it is apparent that the angular profile (the set of beams from which the power received from each user equipment is significant or at least is not zero) can be determined.

(26) When multiple user equipments are present in the system, chances are that inter-user interference appears in urban environments as a result from reflections, diffraction and scattering. After obtaining the angular profiles .sub.i for all active users in the system, it is possible for the BS to infer which beams are shared by several users, i.e. which beams are simultaneously received by (or transmitted from) two or more users hence causing inter-user interference. As illustrated in FIG. 3 (which shows angular profiles of four exemplary users where inter-user interference is avoided by not exciting common beams), shared beams are those contained in the intersection of the angular profiles corresponding to two or more user equipments. It is then possible to avoid inter-user interference by defining new sets of directions (beams) {tilde over ()}.sub.i, i=0, . . . , M1 from .sub.i after excluding those shared beams:
{tilde over ()}.sub.i={(k.sub.j,l.sub.j).sub.i:(k.sub.j,l.sub.j).Math..sub.i,ii},i=0, . . . M1.

(27) M denotes the number of different resulting clusters (equal to the number of resolvable user equipments not suffering complete inter-user interference). The combined set of all beams contained in {tilde over ()}.sub.i, defines the angular directions where transmission from the BS takes place:

(28) $\stackrel{~}{}\stackrel{M^{}-1}{\underset{i=0}{.Math.}}{\stackrel{~}{}}_i.$

(29) As an example, in FIG. 3 the angular profiles of user (user equipment) 3 (303) and user (user equipment) 4 (304) are disjoint after avoiding two shared beams (305), while the angular profiles of user (user equipment) 1 (301) and user (user equipment) 2 (302) remain unchanged as they were already disjoint.

(30) Doppler Spectrum of the Signals Captured by the Spatial Beams, and Compensation of the Doppler Impairments of the Signals Corresponding to the Spatial Beams

(31) The described spatial multiplexing technique allows convenient separation of the users in the spatial domain. Signals received in the uplink direction can be examined in the spatial domain by obtaining the time/frequency components of the beams in the spatial directions (k, l), which characterize the users (the user equipments) according to their modified angular profiles {tilde over ()}.sub.i (avoiding inter-user experience). Each of the beams represents a well-defined direction in space, with a certain beam width that can be obtained by taking derivatives thus yielding the following expressions:

(32) $\frac{uu+vv}{\sqrt{\left(u^2+v^2\right)\left(1-u^2-v^2\right)}},\frac{uv-vu}{u^2+v^2}.$

(33) By choosing half-lambda antenna separation, we have

(34) $d_x=\frac{}{2}.Math.u=\frac{2}{N_1},d_y=\frac{}{2}.Math.v=\frac{2}{N_2},$
hence, denoting r{square root over (u.sup.2+v.sup.2)}1 as the magnitude of the vector (u, v) in the spatial domain, we have:

(35) $\frac{2}{r\sqrt{1-r^2}}\left(\frac{u}{N_1}+\frac{v}{N_2}\right),\frac{2}{r^2}\left(\frac{u}{N_2}-\frac{v}{N_1}\right).$

(36) The equations are only approximate because u and v are actually finite. The equalities only hold when u, v.fwdarw.0: in fact, vanishes at the points u=v which is unrealistic and means actually that the horizontal beam width is the smallest possible at these points.

(37) It is apparent that the beam widths are inversely proportional to the numbers of antennas N.sub.1, N.sub.2. Very small beam widths can be assumed if sufficiently large numbers of antennas are considered in both dimensions. Under these conditions, the Doppler power spectrum of a signal contained in a given beam does not follow the classical U-shaped Jakes spectrum, but resembles instead a pure Doppler shift. Taking the scenario in FIG. 4 as an exemplary reference in UL, a user equipment (411) moves at a relative velocity (v.sub.user) with respect to the direction of departure of a given ray, which after reflection, diffraction and scattering is finally captured by the base station (412). The angle between the velocity vector and the direction of departure of the ray is .sub.v, and the receive beam width is .sub.H.sup.RX. In general .sub.H.sup.RX will be equal to , or something in between depending on the plane formed by the received signal and the beam's rotational axis.

(38) If the receive beam width is sufficiently small, then the Doppler shift f.sub.d,shift and Doppler spread f.sub.d values can be well approximated by the following expressions (as stated for example in the document On the Impact of Beamforming in the Doppler Spectrum of Millimeter Wave Communications, submitted to IEEE Communications Letters, July 2016 by J. Lorca, M. Hunukumbure, and Y. Wang):

(39) $\mathrm{In}\mathrm{the}\mathrm{region}.Math.{}_v.Math.\frac{{}_H^{\mathrm{RX}}}{2}\mathrm{then}$$f_{d,\mathrm{shift}}=f_D\left(1-\frac{{}_H^{\mathrm{RX}}.Math.{}_v.Math.}{4}\right),f_d=f_D\frac{{}_H^{\mathrm{RX}}}{2}.Math.{}_v.Math.$$\mathrm{In}\mathrm{the}\mathrm{region}\frac{{}_H^{\mathrm{RX}}}{2}<.Math.{}_v.Math.-\frac{{}_H^{\mathrm{RX}}}{2}\mathrm{then}$$f_{d,\mathrm{shift}}=f_D\cos {}_v,f_d=f_D{}_H^{\mathrm{RX}}.Math.\sin {}_v.Math..\mathrm{In}\mathrm{the}\mathrm{region}-\frac{{}_H^{\mathrm{RX}}}{2}<.Math.{}_v.Math.\mathrm{then}$$f_{d,\mathrm{shift}}=-f_D\left(1-\frac{{}_H^{\mathrm{RX}}.Math.-{}_v.Math.}{4}\right),f_d=f_D\frac{{}_H^{\mathrm{RX}}}{2}.Math.-{}_v.Math..$

(40) The resulting Doppler spread values are therefore proportional to the receive beam width .sub.H.sup.RX. Hence for very small values of .sub.H.sup.RX the Doppler spectrum resembles a Doppler shift with a magnitude that depends on the magnitude of the velocity vector and its relative orientation with respect to the angle of departure. By virtue of reciprocity, all these expressions remain valid for DL direction by simply changing the roles of the transmitter and the receiver.

(41) Taking the above expressions into account, it is easy for the base station to estimate the Doppler shifts of each of the beams contained in the angular profile of a given user equipment, because said Doppler shifts are seen as complex exponential terms multiplying the received OFDM signals in the time domain. If S.sub.R,Dopp[k, l, t] denotes the Doppler-affected discrete-time samples of the received OFDM symbols at the BS (in the spatial direction (k, l)), and S.sub.R[k, l, t] are the corresponding samples without Doppler impairments, it can be written:
S.sub.R,Dopp[k,l,t]=S.sub.R[k,l,t]exp j2(f.sub.d,shift[k,l]/f)t,
where f is the subcarrier width, f.sub.d,shift[k, l] is the Doppler shift in the spatial direction (k, l) in the (u, v) grid and S.sub.R,Dopp[k, l, t] can be obtained as:

(42) $S_{R,\mathrm{Dopp}}\left[k,l,t\right]=\frac{1}{\sqrt{N_1{N}_2}}\underset{n=0}{\overset{N_1-1}{.Math.}}\underset{m=0}{\overset{N_2-1}{.Math.}}{A}_R\left[n,m,t\right]\exp \left(j\frac{2}{N_1}\mathrm{nk}\right)\exp \left(j\frac{2}{N_2}ml\right),$
where A.sub.R[n, m, t] are the time domain signals received at the antenna element (n, m).

(43) The Doppler shift f.sub.d,shift[k, l] will be seen in the frequency domain as the superposition of two components: a coarse Doppler shift f.sub.d,shift.sup.coarse[k, l], comprising an integer multiple of the subcarrier width (possibly zero),

(44) $f_{d,\mathrm{shift}}^{\mathrm{coarse}}\left[k,l\right]=.Math.\frac{f_{d,\mathrm{shift}}\left[k,l\right]}{f}.Math.f,$
(where represents the rounding towards zero operator), and a fine Doppler shift f.sub.d,shift.sup.fine[k, l], comprising a fraction of a subcarrier width,
f.sub.d,shift.sup.fine[k,l]=f.sub.d,shift[k,l]f.sub.d,shift.sup.coarse[k,l].

(45) The total Doppler shift f.sub.d,shift[k, l]=f.sub.d,shift.sup.coarse[k, l]+f.sub.d,shift.sup.fine[k, l] can be estimated at the base station side. For example, it can be done by following a two-step approach. A-priori known pilot subcarriers can yield the coarse Doppler shift by identifying their relative shift in frequency upon reception. The fine Doppler shift can be obtained by means of known techniques (for example, the techniques explained in Schmid) and D. Cox, Robust frequency and timing synchronization for OFDM, IEEE Transactions on Consumer Electronics, vol. 43, no. 3, pp. 776-783, August 1997 or in Van de Beek, M. Sandell, and P. O. Borjenson, ML Estimation of Timing and Frequency Offset in OFDM Systems, IEEE Transactions on Consumer Electronics, vol. 42, no. 10, pp. 2908-2914, October 1994). Of course, any other known technique could be used.

(46) After estimation of the Doppler shift f.sub.d,shift[k, l], it is possible to compensate Doppler in UL by a suitable processing of the received signals based on the estimated Doppler shifts, for example multiplying the signals received in spatial directions (k, l), which are affected by the Doppler shifts (S.sub.R,Dopp[k, l, t]), by a suitable time-domain complex factor:

(47) $S_R\left[k,l,t\right]=S_{R,\mathrm{Dopp}}\left[k,l,t\right]\exp \left(-j2\frac{f_{d,\mathrm{shift}}\left[k,l\right]}{f}t\right).$

(48) In downlink, it is also possible to apply the following expression that yields the antenna excitations A.sub.T[n, m, t] (the time domain OFDM transmission signals corresponding to antenna (n, m)) in order to ideally compensate Doppler:

(49) 0$A_T\left[n,m,t\right]=\sqrt{\frac{1}{N_1{N}_2}}\underset{k=0}{\overset{N_1-1}{.Math.}}\underset{l=0}{\overset{N_2-1}{.Math.}}{P}_T\left[k,l\right]S_T\left[k,l,t\right]\exp \left(-j2\frac{f_{d,\mathrm{shift}}\left[k,l\right]}{f}t\right)\exp \left(-j\frac{2}{N_1}\mathrm{nk}\right)\exp \left(-j\frac{2}{N_2}ml\right),$
where S.sub.T[k, l, t] is the time-domain OFDM transmit signal corresponding to the spatial beam with coordinates (k, l) in the (u, v) grid (the spatial beams for downlink and uplink may be considered to be the same, as they correspond to physical directions in space and the grid definition depends on the wavelength () corresponding to the system operating frequency, which is very close in UL and DL) and f.sub.d,shift[k, l] is the estimated Doppler shift of the beam characterized by coordinates (k, l) in the (u, v) grid.

(50) Hence, in this disclosure, and contrary to prior art techniques, the Doppler spectrum of the whole received signal (comprising the superposition of multiple components) is not compensated. Instead, individual beams characterizing the users (the user equipments) are isolated by exploiting the spatial multiplexing capabilities of massive MIMO and the properties of the Doppler spectrum in presence of beamforming. By applying the described disclosure, the constituent beams can reach the users in DL with ideally no Doppler impairments. Similarly in UL the signals corresponding to the different spatial beams are detected and their Doppler impairments compensated.

(51) Once the different processes have been described, an example of a mode of operation will be described below according to one embodiment of the disclosure to aid in clarifying the complete process. FIG. 5 illustrates an exemplary embodiment for application of the proposed disclosure.

(52) In this embodiment, a MIMO base station (51) (preferably a massive MIMO base station) comprises a rectangular array of N.sub.1N.sub.2 transmit/receive antennas (56), and M user equipments (57) are wirelessly connected exhibiting user velocities v.sub.1, v.sub.2, . . . , v.sub.M respectively. The user equipments (UE) may be mobile phones, smartphones, laptops, tablets . . . and generally speaking any electronic device which can be wirelessly connected to the base station, allowing the user to communicate through the telecommunications network to which the base station belongs.

(53) The massive MIMO base station is capable of spatially multiplexing up to N.sub.1N.sub.2 orthogonal beams aimed at the M user equipments. Signals received in UL by the antenna array (56) are first processed (52) so as to determine a set of beams characterizing the uplink signals (communications) received from each user equipment (e.g angular profiles) {.sub.i, i=0, . . . , M1} for the M user equipments. This can be achieved e.g. with the aid of signatures or pilot sequences that can identify them unambiguously, but other techniques are not precluded. Optionally, any interfering beams may be identified and discarded from the angular profiles (53), hence yielding M non-overlapping clusters {{acute over ()}.sub.i, i=0, . . . , M1}. These steps (52, 53) may be done using the techniques proposed in patent applications EP-A1-2806576 or EP-A1-3038270, but other known techniques are not precluded.

(54) The individual Doppler shifts corresponding to the spatial beams contained in {{tilde over ()}.sub.i} are estimated in the uplink (54), following the process previously explained. Doppler shifts in UL are compensated (55), and DL signals are generated by ideally compensating the estimated Doppler shifts (following the process previously explained). As a result, the beams (58) aimed towards each of the user equipments 1 . . . M (57) will exhibit no Doppler impairments at the device side (user equipment side).

(55) Summarizing, the present disclosure proposes a novel technique to overcome the effects of mobility in OFDM wireless cellular networks. The spatial multiplexing capabilities of massive MIMO are exploited in order to decompose the signals received from, and transmitted to, a set of users into orthogonal spatial beams, in such a way that beams corresponding to each user are detected and inter-user interference is ideally avoided. The impact of Doppler within each spatial beam can be well approximated by a simple Doppler shift whenever the beam widths of the spatial beams are sufficiently small. Individual Doppler shifts can then be estimated in UL, and further compensated in UL and DL so that the combined signals do not suffer from any Doppler impairment.

(56) The proposed disclosure can have great relevance in wireless cellular communications where Doppler effects are strong, either because user speeds are significant or because the carrier frequency is high (e.g. in millimeter-wave communications). Doppler effects in OFDM can limit performance to the point that no communication is possible beyond a given user speed. Moreover, Doppler exhibits a Doppler spread whenever the received signals are uniformly distributed in azimuth, hence being much more difficult to compensate at the receiver side. The proposed disclosure transforms Doppler spread into the superposition of multiple Doppler shifts at each of the spatial beams, which can be effectively compensated at the BS side. The proposed disclosure is applicable in both FDD and TDD as no detailed channel knowledge is required at the base station side.

(57) In this text, for simplicity sometimes the terms user or cellular user are employed to refer to the concept of user equipment (also called user station or user device), that is the electronic device wirelessly connected to a base station in a wireless OFDM communications system which is employed by a user to communicate through the wireless OFDM communications system.

(58) The present disclosure can be used in any type of OFDM communication system, especially in OFDM communication systems such as mobile (cellular) telecommunication networks, Long-Term Evolution (LTE) wireless cellular system, an IEEE 802.11, WiFi system, an IEEE 802.16, WiMAX (Wireless Microwave Access) system or any other type of OFDM communications system.

(59) The proposed embodiments can be implemented by means of software elements, hardware elements, firmware elements, or any suitable combination of them.

(60) Note that in this text, the term comprises and its derivations (such as comprising, etc.) should not be understood in an excluding sense, that is, these terms should not be interpreted as excluding the possibility that what is described and defined may include further elements, steps, etc.

(61) The matters defined in this detailed description are provided to assist in a comprehensive understanding of the disclosure. Accordingly, those of ordinary skill in the art will recognize that variation changes and modifications of the embodiments described herein can be made without departing from the scope of the disclosure. Also, description of well-known functions and elements are omitted for clarity and conciseness. Of course, the embodiments of the disclosure can be implemented in a variety of architectural platforms, operating and server systems, devices, systems, or applications. Any particular architectural layout or implementation presented herein is provided for purposes of illustration and comprehension only and is not intended to limit aspects of the disclosure.