METHOD AND APPARATUS FOR CHANNEL PREDICTION FOR 5G UPLINK/DOWNLINK MASSIVE MIMO SYSTEM FOR OPEN RADIO ACCESS NETWORKS

Abstract

A method for channel prediction for uplink (UL) and downlink (DL) massive Multiple Input Multiple Output (MIMO) systems for Open Radio Access Network (0-RAN) fronthaul Split 7.2 networks enables prediction of a channel that is seen by the UL slot. The pre-processing matrix is computed by the distributed unit (DU) based on this predicted channel and sent to the radio unit (RU) for minimizing the effects of channel aging. A channel corresponding to sounding reference signal (SRS) symbol closest to uplink slot being decoded can be predicted from previous SRS symbols and can be used as a combining matrix. Alternatively, the channel of the uplink slot itself can be predicted from past SRS symbols, and a combining matrix can be generated based on the predicted channel.

Claims

1. A method of linear channel prediction (LCP) in an Open Radio Access Network (0-RAN) massive Multiple Input Multiple Output (MIMO) system, comprising: predicting a channel associated with a target uplink (UL) slot to be decoded, wherein said predicting is performed based on at least one previous SRS symbol; and using the predicted channel as a basis for a combining matrix to be applied in a radio unit (RU) for decoding the target UL slot.

2. The method according to claim 1, wherein the predicting comprises: predicting a channel corresponding to a sounding reference signal (SRS) symbol closest to a target uplink (UL) slot to be decoded.

3. The method according to claim 2, wherein the predicted channel is used as the combining matrix to be applied in the RU for decoding the target UL slot.

4. The method according to claim 3, wherein the predicting comprises: training with a latest SRS symbol as the desired channel and past SRS symbols as inputs to a prediction module.

5. The method according to claim 4, wherein prediction coefficients are obtained by the training.

6. The method according to claim 5, wherein the predicting further comprises: using the prediction coefficients to predict at least one future SRS symbol based on the at least one previous SRS symbol.

7. The method according to claim 6, wherein the predicted SRS symbol is used to derive the combining matrix to be applied in the RU for decoding the target UL slot.

8. The method according to claim 1, wherein the predicting comprises: predicting a channel of the target uplink slot from at least previous SRS symbols.

9. The method according to claim 8, wherein the combining matrix is built based on the predicted channel of the target uplink slot.

10. The method according to claim 1, wherein the predicting comprises: training for predicting a channel between two periodic SRS symbols; and decoding the target UL slot using a combining matrix based on a predicted channel corresponding to the target UL slot located between slots containing the two periodic SRS symbols.

11. The method according to claim 11, further comprising: prior to the training for predicting, sampling a channel between two periodic SRS symbols for reconstructing the channel between two periodic SRS symbols.

12. The method according to claim 11, wherein the sampling the channel is performed at a frequency greater than the Nyquist sampling frequency.

13. The method according to claim 11, wherein prediction coefficients are obtained by the training.

14. The method according to claim 13, wherein the prediction coefficients are learned by an adaptive filter configured as one of a normalized least mean square (NLMS) filter, affine projection (AP) filter, and recursive least squares (RLS) filter.

15. The method according to claim 13, wherein the prediction coefficients are learned by a Kalman filter.

16. The method according to claim 11, wherein fractional delay infinite impulse response (IR) filter is used for reconstructing the channel between two periodic SRS symbols.

17. The method according to claim 5, wherein the prediction coefficients are learned by an adaptive filter configured as one of a normalized least mean square (NLMS) filter, affine projection (AP) filter, and recursive least squares (RLS) filter.

18. The method according to claim 5, wherein the prediction coefficients are learned by a Kalman filter.

19. The method according to claim 2, wherein the predicting comprises: training with a latest SRS symbol as the desired channel and past SRS symbols as inputs to a prediction module.

20. The method according to claim 19, wherein prediction coefficients are obtained by the training, and the prediction coefficients are used to predict at least one future SRS symbol based on the at least one previous SRS symbol.

Description

BRIEF DESCRIPTION OF THE FIGURES

[0017] FIG. 1 illustrates the architecture of O-RAN Split 7.3 and Split 7.2.

[0018] FIG. 2 illustrates various processing and scheduling associated with reception of an uplink slot in a DSUUU slot pattern.

[0019] FIG. 3 illustrates three physical sites and their cells/sectors classified as desired, intra-site and inter-site cells/sectors.

[0020] FIG. 4 illustrates the effect of using predictions of both LCP methods vs. not using the LCP methods.

[0021] FIG. 5 illustrates channel reconstruction error associated with Nyquist sampling/reconstruction of LCP Method 2.

[0022] FIG. 6 illustrates Split 7.3 and Split 7.2 having same performance and compares it with other methods for FUS.

[0023] FIG. 7 illustrates that LCP Method 2 overcomes limitations of LCP Method 1 for TUS.

[0024] FIG. 8 illustrates the comparisons between LCP Methods 1 and 2 for FUS and TUS.

DETAILED DESCRIPTION

[0025] The present disclosure provides an improved mechanism to overcome the loss of performance arising from the channel aging issue. An example embodiment of a method according to the present disclosure, based on linear channel prediction, ensures that Split 7.2 and 7.3 achieve substantially the same performance.

[0026] The present disclosure provides a mechanism for channel prediction for uplink and downlink massive MIMO systems for O-RAN fronthaul Split 7.2 networks. In traditional networks, which include co-located RU and DU, although the advantages of ORAN fronthaul split 7.2 are not available, the channel estimates can be based on the DMRS present in the UL slots, and hence the channel aging problem is not an issue. On the other hand, in O-RAN fronthaul Split 7.2 networks, because of the separation of RU and DU, UL slots have to be pre-processed in the RU before sending to DU to minimize the FH requirements. This means the last estimated SRS channel is used in the DU to determine the combining weights which are sent to RU for pre-processing the incoming UL slots, thereby resulting in performance degradation due to channel aging.

[0027] In the present disclosure, channel prediction techniques are provided to predict the channel that is seen by the UL slot. The pre-processing matrix is computed by the DU based on this predicted channel and sent to RU for minimizing the effects of channel aging. In an example embodiment, a channel corresponding to SRS symbol closest to uplink slot being decoded is predicted from previous SRS symbols and is used as a combining matrix. In yet another example embodiment, the channel of the uplink slot itself is predicted from past SRS symbols, and a combining matrix is built based on the predicted channel. Low-complexity, implementation-friendly versions of the linear predictor is implemented using adaptive filters, Kalman filters and/or estimating speed of users via SRS symbols.

[0028] As an example, a pattern of repeated slots is considered, denoted by DSUUU, where D, S and U are downlink, special, and uplink slots, respectively. A downlink slot has only downlink OFDM symbols, and an uplink slot has only uplink OFDM symbols. A special slot has a combination of downlink, flexible and uplink OFDM symbols, in that order. The quantities D,, S,, U, denote downlink, special and uplink slots, respectively, at a slot index t. The uplink OFDM symbols towards the end of a special slot carry SRS of various multiplexed users across the entire bandwidth. As an example, 30 kHz subcarrier spacing is used, which means a slot is 0.5 ms in duration and SRS periodicity is five slots or 2.5 ms. Referring to the DSUUU slot pattern shown in FIG. 2 (which is repeated three times in FIG. 2), in order to prepare for the reception of uplink Slot U.sub.t+1 after the special slot S.sub.t-5, the DU computes the channel estimates of all users across the entire bandwidth. The DU then decides which N.sub.U users need to be paired for transmission in the same time-frequency resource, and then computes the combining matrix to receive these N.sub.U users over a selected RB in Slot U,+i. This combining matrix is sent to the RU before the reception of U,+i. As shown in FIG. 2, the sequence of first seven slots, collectively referenced as 201, is used for full band channel sounding in special slots. Also shown in FIG. 2 is a second sequence of UUU slots, collectively referenced as 202, which slots are used for computing channel estimates, user paring and combining matrix based on scheduled users who are scheduled for reception in U,+i and transfer combining matrix to the RU before U.sub.t+1.

[0029] In FIG. 3, three physical sites are shown, ABCDEF, CKLMND and IJAFGH. Each physical site is comprised of three sectors, e.g., as shown by the physical site ABCDEF in FIG. 3, which has three sectors OABC, OCDE and OEFA. Each sector is considered to be a cell, so “sector” and “cell” will be used interchangeably. The base station (RUs and DU) for the physical site ABCDEF resides at the location indicated as O in FIG. 3. The DU receives signals from three RUs, each corresponding to a sector/cell within the physical site ABCDEF. Signals of users in sector/cell OABC (referred to as desired users) received at the base station at O have interference from users in other sectors/cells (OCDE and OEFA) of the same physical site, which interference is called intra-site interference. The desired user also experiences interference from users in sectors/cells of other physical cell sites (CKLMND and IJAFGH), which interference is called inter-site interference. Because the DU of a physical site has access to scheduling information of users in all the sectors/cites belonging to the same physical site, the DU at O can estimate the channels of the desired users and intra-site interferers, but the DU can't estimate the channels of inter-site interferers. Intra-site and inter-site interferers are collectively abbreviated as ICI (Inter-cell interference). The desired user at the center of a cell will have negligible ICI, which can be neglected, while the desired user at the cell edge will experience significant ICI. In the present disclosure, the case of absence of ICI (e.g., for cell-center desired user) is first analyzed, and then the case of presence of ICI (e.g., for cell-edge desired user) is analyzed.

[0030] Brief explanation of notations is provided here. The quantity E {x}denotes the expectation of x. The quantity I represents an Identity matrix of appropriate dimension. The estimate of x is denoted by {circumflex over (x)}. Matrices and vectors will be represented by bold uppercase and lowercase, respectively, while scalars are denoted by normal fonts. Matlab notation is used to access parts of matrices/vectors. The (a,b).sup.th element of a matrix X is denoted by X(a,b). The p element of a vector x is denoted by x(p). The quantity [xJ denotes a floor operation on x, i.e., it denotes the greatest integer less than x. As an example, [4.19]=4. The quantity x*is the conjugate of x.

SYSTEM MODEL IN THE ABSENCE OF ICI

[0031] For this scenario, we are concerned with demodulating OFDM data symbols in uplink Slot U.sub.tm+i which is i slots away from nearest special slot St that contains the SRS. Let the received signal in a given OFDM data symbol in uplink Slot U.sub.tm+iacross the N.sub.R antennas on a given subcarrier s in a given Resource block (RB) rbe denoted by the N.sub.R ×1 vector y (for the sake of simplicity, we do not parametrize y, H, x and n by the OFDM data symbol index and Parameters s, r, and t.sub.m+i),

y=Hx+n  (1)

where H is a N.sub.R ×N.sub.U channel matrix of desired users, x is N.sub.U x 1 vector of desired users, n is additive white Gaussian noise (AWGN) whose covariance matrix is C=E{nnH}=ag. The N.sub.R ×N.sub.U channel matrix, H.sub.DMRS, is the average of all H across subcarriers corresponding to the given RB rand the first demodulation reference symbol (DMRS) in an uplink Slot U.sub.tm+i. Let the N.sub.R ×N.sub.U channel matrix corresponding to a given Subcarrier s in the given RB r in an SRS symbol in special Slot S.sub.tm−5(SRS periodicity is five slots) be denoted by Hi. The quantity H.sub.SRS denotes the average of all Hiacross subcarriers in the given RB r. The estimate of channel matrix H for all subcarriers in the given RB rand all OFDM data symbols in uplink Slot U.sub.tm+iis either HDMRS.sup.2 or H.sub.SRS.

[0032] Two points should be noted regarding the above-described system model in the absence of ICI. First, in 5G N.sub.R, an RB is a set of 12 subcarriers. In the present disclosure, an RB is a set of 12 subcarriers in any OFDM symbol (as per Section 4.4.4.1 in 3GPP TS 38.211, “Physical Channels and Modulation,” 3GPP, V15.8.0, Dec 2019). The RBs in any OFDM symbol are indexed from r=0, . . . , 49, as we use 50 RBs across the channel bandwidth in the present disclosure. Second, channel estimates for OFDM data symbols in any subcarrier can be interpolated from channel estimates of all DMRS in the slot for that subcarrier. However, for the sake of simplicity, channel estimates of all OFDM symbols in the slot can be based on the channel estimate derived in the first DMRS only.

[0033] The O-RAN fronthaul Split 7.2 and Split 7.3 receivers are defined as follows: [0034] Split 7.3: An estimate of {circumflex over (x)} is computed as {circumflex over (x)}=(H.sup.H.sub.DMRSH.sub.DMRS+σ.sup.2I).sup.−1 H.sup.H.sub.DMRSY [0035] Split 7.2: An M xN.sub.R combining matrix W.sub.RU is used by RU to compress y. [0036] What we get at the DU is

y=Hx+n  (2)

where y=W.sub.RUy, H=W.sub.RUH and n=W.sub.RUn. We use one combining matrix for all subcarriers in an RB across the OFDM data symbols in Uplink slot U.sub.tm+i. At the DU, the effective channel estimate used for all subcarriers in the given RB r across OFDM data symbols in uplink Slot U.sub.tm+iis 1=W.sub.RUH.sub.DMRS and the covariance matrix seen by DU is C =E{nn.sup.H}=σ.sup.2W.sub.RUW.sub.RU.sup.H . The DU receives y and computes an estimate of x as {circumflex over (x)} =W.sub.DUy where the minimum mean square error (MMSE) solution for W.sub.DU is given as:

W.sub.DU=(HDMRSHC−1HDMRS+I)−1HDMRSHC−1.  (3a)

or the alternate form

W.sub.DU=H.sub.DMRS.sup.H(H.sub.DMRSH.sub.DMRS.sup.H+C).sup.−1  (3b)

Note that if WRu=HiiktRs (conjugate combining matrix or CCM), we have

W.sub.DU==(H.sup.H.sub.DMRS H.sub.DMRS+σ.sup.2I).sup.−1  (4)

which translates to estimating x as

{circumflex over (x)}=W.sub.DUW.sub.RUy==(H.sup.H.sub.DMRS H.sub.DMRS+σ.sup.2I).sup.−1 H.sup.H.sub.DMRSy  (5)

which is the MMSE of estimate x based on y. One can select W.sub.RU=(H.sup.HDMRS H.sub.DMRS+σ.sup.2 I).sup.−1 H.sup.H.sub.DMRS, called as MMSE combining matrix or MMSE-CM. In this case, no processing is required in DU and W.sub.DU=I.

[0037] In this section, signal-to-interference-plus-noise ratio (SINR) computation will be discussed. If an estimate of {circumflex over (x)} is computed as {circumflex over (x)}=Wy={tilde over (H)}x+ñ, where {tilde over (H)} =WH and if ñ=Wn, the SINR of the ith user is given as

[00001]$\begin{array}{cc}{\mathrm{SINR}}_i=\frac{{.Math.\tilde{H}\left(i,i\right).Math.}^2}{\underset{j=1,j\ne i}{\overset{N_U}{.Math.}}{.Math.\tilde{H}\left(i,j\right).Math.}^2+{\sigma }^2\underset{j=1}{\overset{N_U}{.Math.}}{.Math.W\left(i,j\right).Math.}^2}& \left(6\right)\end{array}$

Furthermore, we define the spectral mean of a set of SNRs as follows. Suppose there are N.sub.USINRs, i.e., SINR.sub.1, . . . ,SINR.sub.Nu, the spectral mean (SM) SINR of these SINRs is given by

[00002]$\begin{array}{cc}{\mathrm{SINR}}_{\mathrm{SM}}=\sqrt[N_U]{\left(1+{\mathrm{SINR}}_1\right).Math.\left(1+{\mathrm{SINR}}_{N_U}\right)}-1.Math.& \left(7\right)\end{array}$

[0038] The SINRsM of a set of N.sub.U SNRs is the SINR which will give the same spectral efficiency (as the sum of spectral efficiencies of the corresponding N.sub.U SINRs) if each of the Nu SINRs is replaced by SINRsM.

[0039] The above-noted MMSE equation (5) is implementable in the Split 7.3 architecture as the uplink Slot U,is decoded after being received over air and the Split 7.3 architecture can compute H.sub.DMRS. While the CCM and MMSE-CM methods also reduce to the MMSE solution, CCM and MMSE-CM can't be implemented in Split 7.2. This is because the combining matrix W.sub.RU that needs to be sent to RU before the uplink Slot U.+, can't be based on H.sub.DMRS as DU is yet to have access to it (one needs uplink Slot U.+, to compute it). As an alternative, approximations of CCM and MMSE-CM methods can be used in the context of Split 7.2. The approximations of the two methods are obtained by replacing H.sup.HDMRS with H.sup.HSRSin WR.sub.U and are given by the following: CCM approximation to Split 7.2: The combining matrix is W.sub.RU=H!n The quantity W.sub.DU is as per above-noted equation (3).

[0040] MMS1E-CM approximation to Split 7.2: The combining matrix is W.sub.RU=(H.sup.HS.sub.RS HS.sub.RS+c.sup.2I ) H.sup.HsRs. The quantity W.sub.DU is the Identity matrix I.

[0041] Note that the approximations of CCM and MMSE-CM to Split 7.2 will incur a loss of performance relative to Split 7.3 (which uses MMSE method) at high speeds. At high speeds, there is a significant difference between HsRS and H.sub.DMRS as they are channel estimates of channels that are 5+i slots apart (Sm-s and Um+,, respectively). This is called channel aging effect and depends on Doppler spreadfo. The Doppler spread depends on speed of the UE v and carrier frequency fcasfv=fc(v/c), in which c is the speed of light. Accordingly, at high speeds Split 7.2 CCM and MMSE methods will have a loss of performance compared to Split 7.3. Split 7.3 can be treated as the upper bound for Split 7.2. At low speeds, Split 7.2 tends to be the same as Split 7.3 or the MMSE method as the channel aging is very minimal. One of the goals of the method according to the present disclosure is how to design the combining matrices such that the gap between a Split 7.2 and 7.3 is reduced.

[0042] An example embodiment of the method according to the present disclosure uses linear channel prediction (LCP) to address this loss of performance of Split 7.2 relative to Split 7.3 due to channel aging. The combining matrix has to be sent to RU before the reception of uplink Slot U.sub.tm+i ,+,. The DU can use SRS channel estimates of Slots Sm-s and the ones before that to build the combining matrix. Note that the DU can't use SRS slot Sm, due to latency requirements and the SRS slot being close to uplink slot Um+,. The LCP method in the DU uses channel estimates of SRS in Slots S.sub.M,-s and ones before that to predict an estimate of H.sub.DMRS (that corresponds to Um.,) as H.sub.DMRS and uses this in CCM-LCP (Split 7.2) and MMSECM-LCP (Split 7.2) methods as W.sub.RU=H.sub.DMRS and W.sub.RU=(H.sub.DMRSHD.sub.MRS+Q.sup.ZI)-iH.sub.DMRS, respectively. The quantity WD.sub.U is as per above-noted equation (3) for CCM-LCP (Split 7.2) and the Identity matrix I for MMSE-CM-LCP (Split 7.2).

[0043] LCP methods for Split 7.2 in the absence of ICI will be discussed below. LCP is generally used to predict future values of a channel based on present and past values. The LCP equation can be written as S.sub.up.sub.u=d.sub.u(will be defined later). LCP operates in two modes. First, in learning/training mode, we populate the input matrix S. and desired vector d.sub.u. Once populated we determine the LCP coefficient vector p.sub.u. Next is the prediction mode, where we populate the input Matrix S. based on present and past values and use the already-learnt LCP coefficient vector .sub.pu to compute/predict vector of future channel values d.sub.u. There are two methods of LCP for Split 7.2 that will be discussed below.

[0044] LCP Method 1: This method uses channel estimates of only SRS symbols to learn the LCP coefficients. Define θ.sub.i.t.r.a as the channel estimate of User i in RB r, antenna a and channel corresponding to SRS symbol in a special Slot S.sub.t. Likewise, ω.sub.i.t.r.a as the channel estimate of User i in RB r, antenna a and channel corresponding to the first DMRS symbol in an uplink Slot U.sub.t. The quantities θ.sub.i.t.r.a and ω.sub.i.t.r.a can be considered as the average of the channel values of all subcarriers in a RB. We now discuss the learning/training mode for User u at Special slot S,. We now build an input matrix S.sub.r.t.u as

[00003]$\begin{array}{cc}{S}_{r,t,u,}=\left[\begin{array}{cccc}{\theta }_{u,t-5-5\left(o_t-1\right),r,1}& .Math.& {\theta }_{u,t-10,r,1}& {\theta }_{u,t-5,r,1}\\ {\theta }_{u,t-5-5\left(o_t-1\right),}r,2& & {\theta }_{u,t-10,r,2}& {\theta }_{u,t-5,r,2}\\ .Math.& .Math.& .Math.& .Math.\\ {\theta }_{u,t-5-5\left(o_t-1\right),r,N_R}& .Math.& {\theta }_{u,t-10,r,N_R}& {\theta }_{u,t-5,r,N_r}\end{array}\right]& \left(8\right)\end{array}$

and desired/predicted vector d.sub.r,t,u as

[00004]$\begin{array}{cc}{d}_{r,t,u}=\left[\begin{array}{c}{\theta }_{u,t,r,1}\\ {\theta }_{u,t,r,2}\\ .Math.\\ {\theta }_{u,t,r,N_R}\end{array}\right].& \left(9\right)\end{array}$

[0045] The preliminary LCP equation is S.sub.r,t,up.sub.u=d.sub.r.t.u. This corresponds to using past values in RB rto predict future values in same RB r. In the preliminary LCP equation, one can use values in RBs r - o.sub.f, . . . ,r, . . . ,r+of to predict future values in RB r where of is the frequency-domain prediction order (either side of RB.sub.r). The equation would then be [srr−oj,i,a. . . Sr.sub.,t,u.sup.T . . . S.sub.r+o,j,t,a.sup.T].sup.Tp.sub.a=d.sub.r,t,a. Frequency-domain prediction order needs to be employed if there is correlation across RBs in frequency domain and this will generally exist for low delay spreads which result in frequency-selectivity across larger number of RBs in frequency domain. However, for the sake of simplicity, we consider of =0 in the present disclosure. Note that each row of the input matrix S.sub.r,t,u has o.sub.t channel estimates and we say that order of prediction is o.sub.t. Each row of S.sub.r,t,u corresponds to an unique antenna and RB r. One can stack S.sub.r,t,u and d.sub.r,t,u for various time instants t=t.sub.1, . . . ,t.sub.n as

[00005]$\begin{array}{cc}{S}_{r,u}=\left[\begin{array}{c}{S}_{r,t_1,u}\\ .Math.\\ S_{r,t_u,u}\end{array}\right],d_{r,u}=\left[\begin{array}{c}{d}_{r,t_1,u}\\ .Math.\\ d_{r,t_u,u}\end{array}\right]& \left(10\right)\end{array}$

Furthermore, we can stack the various S.sub.r,u and d.sub.r,u for RBs r.sub.1, . . . ,r.sub.A as

[00006]$\begin{array}{cc}{S}_u=\left[\begin{array}{c}{S}_{r_1,u}\\ .Math.\\ S_{r_A,u}\end{array}\right],d_u=\left[\begin{array}{c}{d}_{r_1,u}\\ .Math.\\ d_{r_A,u}\end{array}\right].& \left(11\right)\end{array}$

We now have the relation

S.sub.up.sub.u=d.sub.u  (12)

which is the LCP equation used for training User u (determining LCP coefficient vector p.sub.u using SRS in slots across time and RBs). The estimate of p.sub.u is obtained as p.sub.u =(S.sub.u.sup.HS.sub.u).sup.−1 S.sub.u.sup.Hd.sub.u.

[0046] Once the estimate of LCP coefficient vector pu is determined, we can use it in the prediction mode. Let it be required to decode an uplink Slot U.sub.tm+i in RB r where i=1,2,3. As shown in FIG. 2, we are dealing with the slot pattern DSUUU with SRS periodicity of five slots. The nearest special slot to U.sub.tm+i containing an SRS symbol is S.sub.tm. Further let us assume t.sub.m>t.sub.n where t.sub.n is the last special slot containing SRS used in the learning phase. We compute an estimate of d.sub.r,tm,u as

{circumflex over (d)}.sub.r,t.sub.m.sub.,u=S.sub.r,t.sub.m.sub.,u{circumflex over (P)}.sub.u  (13)

[0047] The elements of {circumflex over (d)}.sub.r,t.sub.m.sub.,u will denote channel estimates of User u in SRS of Slot S.sub.tm for various antennas. We use this channel estimate as the channel estimate of the DMRS in any of the next three uplink slots U.sub.tm+i ,+,,i=1,2,3. While this would be ok for the uplink slot U.sub.tm+1 immediately after the special slot Sm, (referred to as first uplink slot after special slot or FUS), there would be considerable loss of performance for the third uplink slot U.sub.tm+3 after the special slot S.sub.tm (TUS). The LCP Method 2 discussed below addresses this issue of LCP Method 1. An estimate of H.sub.DMRS that corresponds to uplink slots U.sub.tm+i,i =1,2,3 and RB r is given as

Ĥ.sub.DMRS(p, q)={circumflex over (ω)}.sub.q,t.sub.m.sub.+i,r,p ≈{circumflex over (d)}.sub.r,t.sub.m.sub.,q(p)  (14)

which can then be used in combining matrix of CCM-LCP (Split 7.2) or MMSE-CM-LCP (Split 7.2). Note that though H.sub.DMRS corresponds to uplink Slot U.sub.tm+i ,+,,i=1,2,3, the calculation can be done any time after special Slot Sm-s and can be sent to RU well ahead of reception of uplink Slot U.sub.tm+i,i=1,2,3. If H.sub.DMRS ≈H.sub.DMRS then we can expect Split 7.2 to perform as well as Split 7.3 (which is what we will see later in this disclosure).

[0048] LCP Method 2: As described above, LCP Method 1 only predicts the channel of a user in SRS symbol of a special slot closest to the uplink slot. While this is ok for FUS, there is loss of performance for TUS. LCP Method 2 addresses this issue by reconstructing the channel between two SRS symbols and using the reconstructed channel to build the desired vector d,r..u. In order to perfectly reconstruct the channel between two SRS symbols/special slots, the channel should be sampled at a frequency greater than the Nyquist sampling frequency, which is.sup.2fD. Consequently, the distance between two special slots should be less than 2AD which is the Nyquist sampling period, which means reconstruction is possible up to a speed of v=61.7 km/hr atfc=3.5 GHz carrier frequency.

[0049] Let it be required to reconstruct the channel (or the channel estimate) ω.sub.u,t+i,r,a uplink Slot U.sub.t+i,i=1,2,3 where the nearest special slot preceding it is S,. As per Whittaker-Shanon interpolation and Nyquist-Shannon sampling theorem

[00007]$\begin{array}{cc}{\hat{\omega }}_{u,t+i,r,a}=\underset{n=-\infty }{\overset{\infty }{.Math.}}{\theta }_{u,t+5n,r,a}\mathrm{sinc}\left(\frac{d_i-{\mathrm{nT}}_{\mathrm{SRS}}}{T_{\mathrm{SRS}}}\right)& \left(15\right)\end{array}$

where d.sub.1 is the time between the starts of the SRS symbol in Special slot S.sub.t and first DMRS in uplink Slot U.sub.t+i, T.sub.SRS=25 ms is the SRS periodicity. Note that to compute the estimate of {circumflex over (ω)}.sub.u,t+i,r,a, infinite past and future values of θ.sub.u,t+5n,r,a are needed, but we approximate the above summation by using only B.sub.1 past and B.sub.2 future values. It should be noted that the Nyquist-Shannon sampling theorem is for reconstruction in the time domain, but since time-domain to frequency-domain is a linear transformation, the reconstruction can be applied in frequency-domain as well.

[0050] We now discuss the learning/training mode, which can be done only at or after Special slot S.sub.t+5B2. The desired/predicted vector d.sub.r,t,+i,u is constructed as

[00008]$\begin{array}{cc}{\overline{d}}_{r,t+i,u}=\left[\begin{array}{c}{\hat{\omega }}_{u,t+i,r,1}\\ {\hat{\omega }}_{u,t+i,r,2}\\ .Math.\\ {\hat{\omega }}_{u,t+i,r,N_R}\end{array}\right].& \left(16\right)\end{array}$

[0051] The preliminary LCP equation is Sr,tu,pu=d.sub.r,t+i,u. We retain the same definitions for S.sub.r,t,u,S.sub.r,u,S.sub.u. as discussed above in connection with LCP Method 1, and we i) stack the various d.sub.r,t+i,u for time instants t=t.sub.1,t.sub.2, . . . ,t.sub.n, to arrive at d.sub.r,u and ii) then stack the various d.sub.r,u for RBs r.sub.1, . . . ,r.sub.A to arrive at d.sub.u as

[00009]$\begin{array}{cc}\begin{array}{cc}{\stackrel{\_}{d}}_{r,u}=\left[\begin{array}{c}{\overline{d}}_{r,t_1+i,u}\\ .Math.\\ {\overline{d}}_{r,t_n+i,u}\end{array}\right]& {\stackrel{\_}{d}}_u=\left[\begin{array}{c}{\overline{d}}_{r_1,u}\\ .Math.\\ {\overline{d}}_{r_A,u}\end{array}\right]\end{array}& \left(17\right)\end{array}$

We now have the relation

S.sub.up.sub.u=d.sub.u  (18)

which is the LCP equation used for training User u (determining LCP coefficient vector p.sub.u).

[0052] The estimate of p.sub.u is obtained as {circumflex over (p)}.sub.u=(S.sub.u.sup.HS.sub.u ).sup.−1 S.sub.u.sup.H{circumflex over (d)}.sub.u . Once LCP coefficient vector p.sub.u is determined, we can use it in the prediction mode. Let it be required to decode an uplink Slot U.sub.tm+i, in RB r where i=1,2,3. As shown in FIG. 2, the slot pattern DSUUU with SRS periodicity of five slots is used. The nearest special slot to U,+, containing an SRS symbol is S.sub.tm . Furthermore, it is assumed t.sub.m>t.sub.n+B.sub.2 where t.sub.n is the last special slot containing SRS used in the learning phase. This will allow for the channel reconstruction at uplink Slot U.sub.tn+i and also learning p.sub.u using S.sub.u, {circumflex over (d)}.sub.u at time instants t.sub.1, . . . ,t.sub.n. We compute an estimate of {circumflex over (d)}.sub.r,t.sub.m+iu as

{circumflex over (d)}.sub.r,t.sub.m+i.sub.,u=S.sub.r,t.sub.m.sub.,u{circumflex over (P)}u  (19)

The elements of {circumflex over (d)}r,t.sub.m+i,u, are the channel estimates of User u in DMRS of uplink Slot U.sub.tm+i,i=1,2,3, for various antennas. An estimate of H.sub.DMRS that corresponds to first DMRS in uplink slots U.sub.tm+i ,+,,i=1,2,3 and RB r is given as

Ĥ.sub.DMRS(p,q)=ŵ.sub.q,,t.sub.m+i.sub.,r,p=d.sub.r,tm+i,q(p)  (20)

which can then be used in combining matrix of CCM-LCP (Split 7.2) or MMSE-CM-LCP (Split 7.2). Note that though H.sub.DMRS corresponds to uplink Slot U.sub.tm+i,i=1,2,3, the calculation can be done any time after special Slot S,M-s and can be sent to RU well ahead of reception of uplink Slot U.sub.tm+i,i=1,2,3.

[0053] In the following section, example system models and LCP methods for Split 7.2 in the presence of ICI are discussed (along with MMSE receiver for Split 7.3). The channel of the ith desired user in a Subcarrier s in Resource block (RB) r, Slot I and Antenna a is denoted by .sub.hi,t,s,a. If Slot t is a special slot, h.sub.i,t,s,a corresponds to the SRS OFDM symbol and if it is an uplink slot, it corresponds to the first DMRS of the slot. Similar to the above-noted equation (1), let the received signal in a given OFDM data symbol in uplink Slot U.sub.tm+i, across the N.sub.R antennas on a given subcarrier s in a given Resource block (RB) r be denoted by the N.sub.R ×1 vector y (for the sake of simplicity, we do not parametrize y, H, x, G, xi, J, x.sub.2 and n by the OFDM data symbol index and parameters s, r, t.sub.m+i)

y=Hx+Gx.sub.1+Jx.sub.2+n  (21)

where H is a N.sub.R ×N.sub.U channel matrix of Nudesired users, x is N.sub.U x.sub.1 vector of desired users, G is a N.sub.R ×N.sub.U1 channel matrix of Nui intra-site interfering users, x.sub.1 is N.sub.U1 ×1 vector of intra-site interfering users, J is a N.sub.R ×N.sub.U2 channel matrix of N.sub.U2 inter-site interfering users, x.sub.2 is N.sub.U2 ×1 vector of inter-site interfering users, and Ĩ, defined in equation (22) below,

Ĩ=GX.sub.1+JX.sub.2+n  (22)

is the total interference. Likewise, let the N.sub.R ×N.sub.U1 channel matrix of intra-site interferers corresponding to a given Subcarrier s in the given RB r in a SRS symbol in special Slot S.sub.tm-5 (SRS periodicity is five slots) be denoted by G.sub.1. The DU receives signals from RUs of all three sectors/cells in a physical site, so it has access to intra-site channels G but not to inter-site channels J. The quantities G.sub.DMRS and G.sub.SRS correspond to channel matrix G and G.sub.1 of intra-site interferers the same way as H.sub.DMRS and H.sub.SRS correspond to channel matrix H and H.sub.1 as discussed above in connection with LCP methods for Split 7.2 in the absence of ICI.

[0054] In this section, MMSE receiver for Split 7.3 is discussed. The interference covariance matrix (ICV) C.sub.7.3 is given as

[00010]$\begin{array}{cc}{C}_{7.3}=E\left\{\text{?}\right\}=\frac{1}{12}\underset{\text{?}}{.Math.}\left(y-\mathrm{Hx}\right){\left(y-\mathrm{Hx}\right)}^H={\sigma }^{2}I+\frac{1}{12}\underset{\text{?}}{.Math.}\left({\mathrm{GG}}^H+{\mathrm{JJ}}^H\right)& \left(23\right)\end{array}$$\text{?}\text{indicates text missing or illegible when filed}$

where the expectation operator is implemented by averaging (y−Hx(y−Hx).sup.H over the 12 subcarriers in RB r of the first DMRS in uplink Slot U.sub.tm+i. The quantity x denotes the data vector of desired users corresponding to any Subcarrier s in a RB r and any OFDM data symbol in uplink Slot U.sub.tm+1. An estimate of x is given as

x=H.sub.DMRSC.sub.73.sup.−1H.sub.DMRS+I).sup.−1H.sub.DMRS.sup.HC.sub.7.3.sup.−1y  (24a)

or alternatively,

{circumflex over (x)} =H.sub.DMRS.sup.H(H.sub.DMRSH.sub.DMRS.sup.H+C.sub.7.3).sup.−1 y  (24b)

[0055] In this section, receivers for Split 7.2 are discussed. At the DU, for calculation of W.sub.DU as per equation (3), we need to update C which is equal to W.sub.RUC.sub.7.3W.sub.RU .sup.H and which is calculated by averaging (Y- Hx)(Y-Hx).sup.H over the 12 subcarriers in the RB corresponding to first DMRS in received uplink slot at DU. In the above section discussing the LCP methods for Split 7.2 in the absence of ICI, we defined θ.sub.i,t,r,a as the channel estimate of desired User i in RB r, antenna a and channel corresponding to SRS symbol in a special Slot S.sub.t. Likewise, we define δ.sub.i,t,r,a as the channel estimate of intra-site interfering User i in RB r, antenna a and channel corresponding to SRS symbol in a special Slot S.sub.t. The quantities θ.sub.i,t,r,a and δ.sub.i,t,r,a are considered as the average of the channel values of all subcarriers in a RB. Just as we computed Ĥ.sub.DMRS corresponding to uplink Slot U.sub.tm+i, in equations (14) and (20) (using LCP Methods 1 and 2 and θ.sub.i,t,r,a), we similarly compute an estimate Ĝ.sub.DMRScorresponding to uplink Slot U.sub.tm+i , using δ.sub.i,t,r,a . An estimate of ICM for Split 7.2 is then given by

Ĉ.sub.7.2=Ĝ.sub.DMRS.sup.H+σ.sup.2 I  (25)

which is just an approximation to ICV (ICVA) as we use average channel value per RB to compute ICV. A more accurate way of computing the ICV would be to use all channel values per subcarrier in the computation which is done as follows. The channel of the ith intra-site interfering user in a Subcarrier s in Resource block (RB) r, Slot i and Antenna a is denoted by g.sub.i,t,s,a(note that the average of g.sub.i,t,s,a for all subcarriers s in RB r is δ.sub.i,t,r,a). If Slot t is a special slot, g.sub.i,t,s,acorresponds to the SRS OFDM symbol and if it is an uplink slot, it corresponds to the first DMRS of the slot. Using LCP method 1, we get an estimate of the channel in Special slot Sim as ĝ.sub.i,tm,s,awhich is a linear combination of gi,tm-5,s,a, . . . ,gi,tm-5-5*(ot-1),s,a based on the channel predictor coefficients for the ith intra-site interfering user. This estimate is used as the estimate of the channel in the first DMRS of Uplink slot U.sub.tm+i, i.e., ĝ.sub.j,tm+i,s,a=ĝ.sub.,j,tm,s,a..

[0056] Let us concatenate across all antennas as

[00011]$\begin{array}{cc}{\hat{g}}_{i,t_m,s}=\left[\begin{array}{c}{\hat{g}}_{i,t_m,s,1}\\ .Math.\\ {\hat{g}}_{i,t_m,s,N_R}\end{array}\right]& \left(26\right)\end{array}$

[0057] The estimate of ICV based on the predicted intra-site interfering channels in the SRS symbol of Special slot S.sub.tm is given as

[00012]$\begin{array}{cc}{\hat{C}}_{7.2}={\sigma }^{2}I+\frac{1}{12}\underset{i=\text{?}}{\overset{N_{u_{\text{?}}}}{.Math.}}\underset{\text{?}}{\overset{}{.Math.}}{\hat{g}}_{i,t_m,s}{\hat{g}}_{i,t_{m,s}}^H& \left(27\right)\end{array}$$\text{?}\text{indicates text missing or illegible when filed}$

[0058] Using LCP method 2, we get an estimate of the channel in uplink Slot U.sub.tm+i as ĝ.sub.j,tm+i,s,a which is a linear combination of g.sub.j,tm−5,s,a, . . . ,g.sub.j,tm−5−5.Math.(ot−1),s,a based on the channel predictor coefficients for thejth intra-site interfering user. Let us concatenate ĝ.sub.j,tm+i,s,a across all antennas as

[00013]$\begin{array}{cc}{\hat{g}}_{j,t_m+1,s}=\left[\begin{array}{c}{\hat{g}}_{j,t_m+i,s,1}\\ .Math.\\ {\hat{g}}_{j,t_m+i,s,N_U}\end{array}\right]& \left(28\right)\end{array}$

[0059] The estimate of ICV based on the predicted intra-site interfering channels in the first DMRS in Uplink slot U.sub.tm+1 is given as

[00014]$\begin{array}{cc}{\hat{C}}_{7.2}={\sigma }^{2}I+\frac{1}{12}\underset{j=\text{?}}{\overset{N_{u_{\text{?}}}}{.Math.}}\underset{\text{?}}{\overset{}{.Math.}}{\hat{g}}_{j,t_m+i,s}{\hat{g}}_{j,t_{\text{?}}}^H& \left(29\right)\end{array}$$\text{?}\text{indicates text missing or illegible when filed}$

An estimate of ICV based on SRS symbol in Special slot S,,,,-s is given as

[00015]$\begin{array}{cc}{\hat{C}}_{7.2}={\sigma }^{2}I+\frac{1}{12}\underset{i=1}{\overset{N_{u_{\text{?}}}}{.Math.}}\underset{s\in r}{\overset{}{.Math.}}{g}_{i,t_m-5,s}{g}_{i,t_m-5,s}^H& \left(30\right)\end{array}$$\mathrm{where}$$\begin{array}{cc}{g}_{i,t_m-5,i}=\left[\begin{array}{c}{g}_{i,t_m-5,s,\text{?}}\\ .Math.\\ {\hat{g}}_{i,t_m-5,s,N_R}\end{array}\right]& \left(31\right)\end{array}$$\text{?}\text{indicates text missing or illegible when filed}$

[0060] The various combining matrices for Split 7.2 are given as follows: [0061] 1) MMSE-CM (7.2): The combining matrix W.sub.RU=(HsasC iHs.sub.Rs+I).sup.−1H.sub.SRS.sup.HĈ.sub.7.2.sup.−1, where Ĉ.sub.7.2is based on equation (30) and W.sub.DU=I. or W.sub.DU as per equation (3). Alternatively, W.sub.RU=H.sub.SRS.sup.H(H.sub.SRSH.sub.SRS.sup.H+Ĉ.sub.7.2).sup.−1 [0062] 2) CCM (7.2): The combining matrix W.sub.RU=H.sub.SRS.sup.HĈ.sub.7.2.sup.−1, where Ĉ.sub.7.2 is based on equation (30) and W.sub.DU is based on equation (3). [0063] 3) MMSE-CM-LCP (7.2): The combining matrix W.sub.RU=(Ĥ.sub.SRS.sup.HĈ.sub.7.2.sup.−1Ĥ.sub.DMRS+I).sup.−1Ĥ.sub.DMRS.sup.HC.sub.7.2.sup.−1, where Ĥ.sub.DMRS .sup.H and Ĉ.sub.7.2 are based on equation (14) and equation (27), respectively, for LCP Method 1. For LCP method 2, Ĥ.sub.DMRS .sup.H and C.sub.7.2 are based on equation (20) and equation (29), respectively. Furthermore, W.sub.DU=I. or W.sub.DU as per equation (3). Alternatively, W.sub.RU=Ĥ.sub.DMRS.sup.H(Ĥ.sub.DMRSĤ.sub.DMRS.sup.H+Ĉ.sub.7.2).sup.−1 [0064] 4) CCM-LCP (7.2): The combining matrix W.sub.RU=H.sub.SRS.sup.HĈ.sub.7.2.sup.−1, where Ĥ.sub.DMRs and C.sub.7.2 are based on equation (14) and equation (27), respectively, for LCP Method 1. For LCP method 2, Ĥ.sub.DMRS.sup.H and Ĉ.sub.7.2 are based on equation (20) and equation (29), respectively. Furthermore, W.sub.DU is computed as per equation (3).

[0065] Some points to be noted regarding the ICV for Split 7.2 and Split 7.3 include the following: [0066] 1) The ICV for Split 7.3 in (23) depends on both the intra-site interfering channels (G) and the inter-site interfering channels (J). In functional Split 7.2, the DU has access to only intra-site interferers and not inter-site interferers. Consequently, the ICV for Split 7.2 (using equations (27), (29) and (30)) have contributions from only intra-site interferers but not inter-site interferers. As will be seen in the following sections, the performance of Split 7.2 (with linear channel prediction) can equal the performance of Split 7.3 only in the absence of inter-site interference. When inter-site interference is present, the performance of Split 7.2 consistently falls short of the performance of Split 7.3.

[0067] 2) Note that ICV for Split 7.3 implicitly uses interfering channels at all subcarriers s in a RB r (23). It is for this reason that we have to use linear channel prediction at all subcarriers of intra-site users, as per equations (27), (29) and (30). It might appear that complexity of implementing training and prediction of channels of all intra-site interferers at all subcarriers of a RB is quite costly. However, as will be seen in the following sections, the linear channel predictor coefficients are substantially the same across RBs and slots. Therefore, we need not train the LCP coefficients for all subcarriers in an RB. Instead, we can just train the LCP for some subcarriers, and once trained, the same coefficients can be used in prediction across many RBs.

[0068] 3) For Split 7.2, we compute the ICV based on LCP-estimated channel of intra-site interferers across all subcarriers in an RB, which needs to be done to match the performance of Split 7.3. The channel at all subcarriers can be calculated by taking the FFT of the received signal divided by the reference signal across subcarriers, separating the various FFT bins of users, and then taking the IFFT of the separated FFT bins.

[0069] 4) Low complexity implementation of ICV for Split 7.2 is as per equation (25), which implements an approximate ICV (ICVA) based on an average channel across an RB of intra-site interferers.

[0070] In this section, some example applications of LCP in the context of Split 7.2 are discussed, as well as some low-complexity implementation alternatives of the techniques discussed above.

[0071] Downlink Precoding:

[0072] The first example application is downlink precoding. Consider a TDD system with uplink and downlink channel reciprocity. In downlink MU-MIMO, precoding is often employed at the base station (transmitter) to reduce interference in the downlink among many users. As an example, consider a pattern of slots DDDSUDDDSU and Downlink slot Dm., where the nearest Special slot is S.sub.t.. The input-output equation at any OFDM data symbol in this slot D,.,, subcarrier s and RB r is given by

y=HPx+n  (32)

where x is N.sub.D ×1 vector of downlink data to ND users, P is ND xND precoder a t transmitter of base station, H is the ND xND channel matrix from base station to all ND UEs, n is AWGN, y is N.sub.D ×1 vector of received signals at NDusers stacked on top of one another. If we select the precoding matrix as P=H.sup.H(HH).sup.−1, then the above equation reduces to y=x+n, which essentially means no inter-user interference in the downlink among the UEs. However, the base station (e.g., RU) needs to know the channel H in Downlink slot Dm+,. The DU has channel estimates at the SRSs of special slots S.sub.tm,S.sub.tm−5, . . . , and using these estimates across users and antennas for the given Subcarrier s in the RB r and LCP Method 2, the DU can predict H and send the precoder P to RU well ahead of the transmission of Downlink slot D.sub.tm+i. Note that LCP Method 1 may not work well if the Downlink Slot D.sub.tm+i is quite away from SRS in Special slot S.sub.tm(especially for i =2,3, . . . ), in which case it becomes necessary to use LCP Method 2.

[0073] Low-Complexity Implementations: [0074] 1) Adaptive Filters: The LCP coefficient vector p.sub.t(as discussed above in the section discussing LCP methods for Split 7.2 in the absence of ICI) is learnt via computing an inverse of a o.sub.t ×o.sub.t matrix. An alternative is to use adaptive filters to learn p. (which does not involve any o.sub.t×o.sub.t matrix inversion). Adaptive filters, e.g., normalized least mean square (NLMS), affine projection (AP) and recursive least squares (RLS) can be used. While the RLS converges quickly compared to NLMS, it is computationally expensive. AP converges as good as RLS at a complexity of NLMS. Adaptive filters can be used across antennas for learning as discussed above in connection with LCP methods for Split 7.2 in the absence of ICI. Learning via adaptive filters needs to be careful as the filter coefficients can diverge in deep fades. Generally, a step-size controller can be employed, which freezes learning in deep fades, employs bigger step size initially so that the filter converges quickly, and in steady state employs a smaller step size so that steady-state error is small.

[0075] 2) Kalman Filters: Kalman filters are used to study channel estimation. A Kalman filter inherently has a LCP coefficient vector to govern the state equation. As will be seen in the sections below, performance of Split 7.2 is substantially the same as Split 7.3 when LCP prediction order o.sub.t=7 (though lower orders such as o.sub.t=3 also result in good performances). A Kalman filter performs prediction and correction based on noisy observations, while an LCP does only prediction. A Kalman filter with low order o.sub.t=1,2 as part of its state equation may achieve performances substantially the same as LCP of order o.sub.t=7. In that case, the complexity comparisons between the Kalman filter with o.sub.t=1,2 and LCP with o.sub.t=7 need to be consider.

[0076] 3) Fractional Delay Filters: In LCP Method 2, we used Whittaker-Shannon to reconstruct the channel between two SRSs in special slots. This used both future and past SRSs for reconstruction. The number of SRS symbols used on either side of reconstruction can be reduced if one uses fractional delay infinite impulse response (IIR) filters.

[0077] 4) ICV Updates: The error in the estimate of ICV depends on the prediction order ot. If the prediction order is less (e.g., for complexity reasons), the estimate of ICV has more error, but this error can be accounted for by using the prediction error variance during training of all users. We now describe how it is done. Assume training at Uplink slot U.sub.tm+i , (this is where the channel is reconstructed in LCP Method 2) and nearest SRS in Special slot is S.sub.tm. The actual channel of the jth intra-site interferer in Subcarrier s belonging to RB r and Antenna a is denoted, as before, by g.sub.j,tm+i,s,a. For the sake of simplicity, let us assume a low prediction order o.sub.t=2. The estimated channel of the jth intra-site interferer in Subcarrier s belonging to RB r and Antenna a is denoted by ĝ.sub.j,tm+i,s,a. Note that ĝ.sub.j,tm+i,s,a is a linear combination of g.sub.j,tm−5,s,a and g.sub.j,tm−10,s,a (SRS periodicity is five slots) and error in prediction is denoted as e.sub.j,m+s,a=g.sub.j,tm +i,s,a−ĝ.sub.j,tm+i,s,a. Just like equation (28), we concatenate all g.sub.j,tm+i,s,a across antennas to give the vector g.sub.j,tm+i,s. Similarly, we concatenate e.sub.j,tm+i,s,a into e.sub.j,tm+i,s and ĝ.sub.j,tm+i,s,a into ĝ.sub.j,tm+i,s. We have

gj,tm+.sub.i,s=ĝ.sub.j,tm+i,s +e.sub.j,tm+i,s  (33)

From the definition of LCP, error is orthogonal to input data, i.e., E{e,.sub.j,tm+i,s,aĝ.sub.j,tm+i,s,a*}=0. Furthermore, the channel across antennas is uncorrelated, implying E{e,.sub.j,tm+i,s,aĝ.sub.j,tm+i,s,a*}=0, a≠b. From this and equation (33), it follows

E{g,.sub.j,tm+i,sg.sub.j,tm+i,s.sup.H}=E{g,.sub.j,tm+i,sg.sub.j,tm+i,s.sup.H}+σ.sub.i.sup.2I  (34)

where E{e.sub.j,tm+i,s,ae.sub.j,tm+i,s,a.sup.H}=σ.sub.i.sup.2. An estimate of σ.sub.1.sup.2 is computed as

[00016]$\begin{array}{cc}{\hat{\sigma }}_i^2=\frac{1}{12N_R}\underset{s\in r}{.Math.}{e}_{j,t_m+i,s}^H{e}_{j,t_m+i,s}=\frac{1}{12N_R}\underset{s\in r}{.Math.}{\left(g_{j,t_m+i,s}-{\hat{g}}_{j,t_m+i,s}\right)}^H\left(g_{j,t_m+i,s}-{\hat{g}}_{j,t_m+i,s}\right)& \left(35\right)\end{array}$

which is computable as we are in training mode and have access to both g.sub.j,m+i,s, ĝ.sub.j,m+i,s. The ICV for Split 7.2 based on ĝ.sub.j,m+i,s is given by equation (29) while the ICV for Split 7.2 based on actual channel value g.sub.j,m+i,s is

[00017]$\begin{array}{cc}{\hat{C}}_{7.2}={\sigma }^{2}I+\frac{1}{12}\underset{j=1}{\overset{N_{u_{\text{?}}}}{.Math.}}\underset{s\in r}{\overset{}{.Math.}}{g}_{j,t_m+i,s}{g}_{j,t_m+i,s}^H.& \left(36\right)\end{array}$$\text{?}\text{indicates text missing or illegible when filed}$

[0078] So, it follows from equation (34) that the updated version of equation (29) is

[00018]$\begin{array}{cc}{\hat{C}}_{7.2}={\sigma }^{2}I+\frac{1}{12}\underset{j=1}{\overset{N_{u_{\text{?}}}}{.Math.}}\underset{s\in r}{\overset{}{.Math.}}{g}_{j,t_m+i,s}{g}_{j,t_m+i,s}^H+\underset{j}{\overset{N_{u_{\text{?}}}}{.Math.}}{\sigma }_i^{2}I.& \left(37\right)\end{array}$$\text{?}\text{indicates text missing or illegible when filed}$

[0079] 5) LCP Coefficients: LCP coefficient vector p. depends on the channeP-.sup.38,E variation across time. This in turn is dependent on delays, scattering, angle of arrival at base station, speed etc. To a large extent, it can be dependent on speed of the UE. In that case, we can find speed of the UE by computing power spectral density of SRS symbols and then using a look-up table to determine the LCP coefficient of a given order. We then do not have to spend resources in learning, and we can just use the coefficients directly in prediction.

[0080] 6) Training in FFT Domain: Due to frequency selectivity, channel across subcarriers varies slowly. If we take a 12-point FFT of the channel in an RB, it can be accurately represented by a few FFT bins only, e.g., FFT bins 1, 2, 3, 11, and 12 (bin index starts at 1). If frequency-selectivity is less, it can even be represented by FFT bins 1, 2, and 12, for example. Now if we take the IFFT of these FFT bins (other bins being zero), the channel across subcarriers in the RB can be represented quite accurately with around 5% error. In general, for multi-RB, we can take FFT of all subcarriers across the RBs, and use only very few FFT bins. To get subcarrier-by-subcarrier channel and separate the multi-users, we need to get into FFT domain, so we can learn on the selected reduced FFT bins and then reconstruct the channels at subcarriers over the RBs.

[0081] SRS Channel Estimation: In an example method, we take FFT of raw channel across subcarriers, drop some FFT bins which correspond to noise and retain only the low-pass FFT bins corresponding to the channel, and then generate IFFT. This is called denoising, which works because the channel varies as a low-pass signal across subcarriers. We can extend this to two dimensions for SRS, i.e., time and frequency. The channel across various SRS also varies slowly (depends on Doppler and a low-pass signal). So, if we take a 2D-FFT of raw SRS channel (received signal divided by reference sequence), we can separate the various users in 2D-FFT domain, remove the noise 2D-FFT bins, and then generate IFFT to obtain SRS channel estimations across various SRS OFDM symbols/RBs for each user.

[0082] Delay-Doppler-based Channel Prediction and SRS Capacity Improvement:

[0083] Delay-Doppler-based channel prediction is implemented when we have modeled all the multipath channel taps along with delays. These channel taps can be tracked and predicted like the channel prediction described in the present disclosure. The key aspect is at any time a set of frequency subcarriers can be converted into time-domain multipath channel taps (the channel taps of many users derived from the same subcarriers can be separated.). These channel taps are computed for every SRS symbol and learning/prediction can happen for each channel tap. The Doppler associated with each channel tap can vary, but we can assume the Doppler to be constant for a few taps and learning can happen for selected few channel taps only, and the prediction be used on all channel taps (based on learning of some selected taps). Once the future channel taps are predicted/estimated, we can reconstruct/predict the channel in any RB. In present disclosure, we use full-band scheduling. However, with the proposed usage of linear prediction in time domain of channel taps, sub-band scheduling can be employed as one can estimate/update the channel taps in time domain from any sub-band. This will increase the SRS capacity, but is computationally expensive.

SIMULATION RESULTS

[0084] The channel model used in these simulations corresponds to CDL-B (see, e.g., 3GPP TR 38.901, “Study on Channel Model for Frequencies from 0.5 to 100 GHz,” 3GPP, V14.3.0, Dec. 2017). Furthermore, we assume that v=30 km/hr,fc=3.5 GHz, N.sub.R =64, N.sub.U=4, delay spread (ds) is 1000 ns. The delay spread corresponds to the highest value in Table 7.7.3-1 in 3GPP TR 38.901, “Study on Channel Model for Frequencies from 0.5 to 100 GHz,” 3GPP, V14.3.0, Dec. 2017. This means the frequency-selectivity is the highest and the variation of HDMRsw.r.t H in equation (1) is the largest. Furthermore, we assume perfect channel estimation, i.e., we have perfect knowledge of Hi, H in equation (1). We assume a 4×8×2 panel of antennas with four in vertical direction, eight in horizontal direction and two cross polarized antennas in each location. We consider the DSUUU pattern, 30 kHz subcarrier spacing, where each slot is 0.5 ms in duration and TsRs=25 ms (SRS periodicity of five slots).

[0085] FIG. 4 illustrates the effect of using predictions of both LCP methods vs. not using the LCP methods, which FIG. 4 uses plots of the normalized error square (y-axis labeled as NES) vs. prediction order o.sub.t (on the x-axis). Assume we are detecting an uplink Slot U.sub.tm+i ,, and the nearest preceding special slot is Srm. The prediction error is defined as the difference in the actual channel ω.sub.u,tm+i,r,a value and predicted value. The predicted values are p.sub.u,tm+i,r,a=ω.sub.u,tm+i,r,a and p.sub.u,tm+i,r,a=θ.sub.u,tm,r,a, for LCP Method 1 and 2, respectively. The SRS error is defined as the difference in the actual channel value and value of the channel at S.sub.tm−5. The normalized prediction error square (NPES) is defined as the ratio of expectation of the square of the absolute value of the prediction error to the expectation of the square of the absolute channel value. The expectation is with respect to users (all users have same speed and hence we assume the same random process statistically), antennas, RBs and across time slots. The normalized SRS error square (NSES) is defined as the ratio of expectation of the square of the absolute value of the SRS error to the expectation of the square of the absolute channel value. The resulting equations for NPES and NSES are as follows:

[00019]$\begin{array}{c}\mathrm{NPES}=\frac{\underset{\text{?}}{.Math.}\underset{\text{?}}{.Math.}\underset{\text{?}}{.Math.}\underset{\text{?}}{.Math.}{.Math.\text{?}.Math.}^2}{\underset{\text{?}}{.Math.}\underset{\text{?}}{.Math.}\underset{\text{?}}{.Math.}\underset{\text{?}}{.Math.}{.Math.\text{?}.Math.}^2}\\ \mathrm{NSES}=\frac{\underset{\text{?}}{.Math.}\underset{\text{?}}{.Math.}\underset{\text{?}}{.Math.}\underset{\text{?}}{.Math.}{.Math.\text{?}.Math.}^2}{\underset{\text{?}}{.Math.}\underset{\text{?}}{.Math.}\underset{\text{?}}{.Math.}\underset{\text{?}}{.Math.}{.Math.\text{?}.Math.}^2}\end{array}.$$\text{?}\text{indicates text missing or illegible when filed}$

[0086] Note that, but for the LCP methods, we will have to use the channel estimate of the of the SRS at Sm,-s. As shown in FIG. 4, the NSES is quite high compared to NPES, and it is evident the LCP methods improve the performance by reducing the NPES relative to the NSES. NPES for LCP method 2 is worse than that of LCP method 1 as there is reconstruction error associated with the learning.

[0087] FIG. 5 depicts the normalized reconstruction error using Whittaker-Shanon interpolation and Nyquist-Shannon sampling theorem, e.g., for LCP Method 2. We consider 771 OFDM symbols or 56 slots (0.0275 s). Beginning from the first OFDM symbol, every 70th OFDM symbol is an SRS symbol that is known. Using only the channel estimates (perfect) of the SRS symbols the channel estimates of all the OFDM symbols are reconstructed using Whittaker-Shanon interpolation and Nyquist-Shannon sampling theorem. The channel estimates are denoted by x(n,i,a),n=0, . . . ,771, where i is the iteration index, a is the antenna index and n is the OFDM symbol index. For the sake of simplicity, we assume only one user. The reconstructed channel estimates are denoted by x∧(n,i,a),n=0, . . . ,771. The normalized reconstruction error square is defined as |x∧(n,i,a)−x(n,i,a)|.sup.2 ETF X(n. i., a?-TT a).sup.2

[00020]$\begin{array}{cc}\mathrm{NRES}\left(n\right)=\frac{\underset{\alpha }{.Math.}\underset{i}{.Math.}{.Math.\hat{x}\left(n,i,a\right)-x\left(n,i,a\right).Math.}^2}{\underset{i}{.Math.}{.Math.x\left(n,i,a\right).Math.}^2}.& \left(39\right)\end{array}$

The channel estimate at the middle is as small as 0.5%. Each iteration is over an RB (one channel estimate per RB) and 56 slots. A time-frequency observation of 50 RBs and 105 slots was used. A sliding window of 56 slots was used as we move from one iteration to another in the time domain.

[0088] FIGS. 6 and 8 depict performance comparisons of various methods discussed in the present disclosure. The simulation corresponds to 2000 iterations. The dataset for each iteration is from one RB over 13 special slots (SRS symbols) followed by three uplink slots (the three uplink slots are just after the 13th special slot). The datasets for iterations first vary over a channel bandwidth of 50 RBs while the time domain slots are held constant and then a sliding window that slides by five slots (SRS periodicity) is used to move in the time domain to get the next 50 datasets for iterations over the channel bandwidth of 50 RBs. We use prediction order o.sub.t=7. In any dataset (iteration) that requires learning, the first eight special slots (SRS) are used for training. Learning is over only one RB and one time instant, i.e., r.sub.1=r.sub.A, t.sub.1 =t.sub.n . For every 400 iterations, we use LCP coefficients learnt in the first of the 400 iterations. This is ideal from a complexity and scheduling viewpoint as we can learn in one RB and time slot and use it to predict in another RB and time slot. At the time of learning, we do not know where (in which RB) the user will be scheduled in future. In each dataset, the channel estimates of the first 12 SRS symbols in the RB is used to reconstruct the channel estimate of all OFDM symbols between the first SRS symbol and 12th SRS symbol (a region of 56 slots or 770 OFDM symbols). The prediction in any dataset (iteration) uses channel estimates of SRS symbols from special slots six to 12, to predict the channel estimate in the SRS symbol of the 13th special slot (LP Method 1) or the channel estimate of the first DMRS of any of the three uplink slots following the 13th special slot (LP method 2). Mathematically, the dataset for the kth iteration is taken from RB r=k mod 50 and Slots

[00021]$S_{t+5.Math.\frac{k}{50}.Math.},S_{t+5.Math.\frac{k}{50}.Math.+5},.Math.,S_{t+5.Math.\frac{k}{50}.Math.+55},S_{t+5.Math.\frac{k}{50}.Math.+60},$$U_{t+5.Math.\frac{k}{50}.Math.+61},U_{t+5.Math.\frac{k}{50}.Math.+62},U_{t+5.Math.\frac{k}{50}.Math.+63}.$

[0089] In FIG. 6, which corresponds to only FUS, we can see that the MMSE-CM 7.2 method has the worst performance as it is entirely based on a 2.5 ms (or five slots) old SRS value. The CCM 7.2 method has improved performance compared to MMSE-CM 7.2 method as it is partly based on an old SRS channel estimate (only W.sub.Ru part is based on the 2.5 ms (or five slots) old SRS value, while the W.sub.DU part is based on the effective channel matrix H DMRS corresponding to the first DMRS of the uplink slot being decoded). Both methods, however, have a big performance gap relative to the Split 7.3 method. The LCP Method 1 for prediction order of seven exactly matches the performance of Split 7.3 method (i.e., the upper bound) for FUS, thereby overcoming the channel aging and fronthaul constraints. This matching of the upper bound of Split 7.3 method via LCP is one of the goals of the present disclosure. FIG. 6 also shows LCP Method 1 performances for prediction orders o.sub.t=2, 4, and these are close to the upper bound of the Split 7.3 method, and much better than MMSE-CM 7.2 and CCM 7.2, thereby emphasizing the importance of the LCP methods.

[0090] FIG. 8 illustrates the comparisons between LCP Methods 1 and 2 for FUS and TUS. As discussed previously, LCP Method 1 (Split 7.2) works well for FUS and attains the same upper bound performance of Split 7.3 method. However, LCP method 1 will exhibit loss of performance for TUS, while LCP Method 2 attains the same performance as Split 7.3 method, as shown in FIG. 8.

[0091] Ideally, one can learn the LCP coefficients across time, RBs and antennas as given in equation (12). The channel is a random process characterized by Doppler spread f.sub.D which is dependent on the speed of the UE v and carrier frequency fc. The channels at various RBs and antennas can be considered to be realizations of the same random process. Doppler spread which is dependent on speed and carrier frequency is expected to change little across the RBs, as change in frequency from RB to RB is very little compared to carrier frequency. Consequently, we assume that LCP coefficients are constant across RBs, antennas and time, as shown in FIG. 7.

[0092] For O-RAN massive MIMO systems, there is a loss of performance of Split 7.2 relative to Split 7.3 for mobility use cases in the uplink when conventional methods are used. The two example linear channel prediction methods provided in the present disclosure overcome this loss of performance of Split 7.2 and help the Split 7.2 systems achieve substantially the same performance as Split 7.3 systems. Results for four uplink users at speeds of 30 km/hr at a carrier frequency of 3.5 GHz showed that Split 7.2 achieved the same performance as Split 7.3 systems, as illustrated in FIG. 7. FIG. 7 additionally illustrates that LCP Method 2 overcomes the limitations of LCP Method 1 for TUS.

[0093] In summary, several example embodiments of the method according to the present disclosure are listed below:

[0094] 1) Learning and predicting channel at each subcarrier in a future SRS symbol from present and past channel values at subcarriers of past and present SRS symbols for each user (desired and intra-site) using LP Method 1.

[0095] 2) Learning and predicting average of channels across subcarriers in a RB for a future SRS symbol from present and past such average values corresponding to past and present SRS symbols for each user (desired and intra) using LP Method 1.

[0096] 3) Learning and predicting channel at each subcarrier in a future PUSCH symbol from present and past channel values at subcarriers of past and present SRS symbols for each user (desired and intra) using LP Method 2.

[0097] 4) Learning and predicting average of channels across subcarriers in a RB for a future PUSCH symbol from present and past such average values corresponding to past and present SRS symbols for each user (desired and intra) using LP Method 2.

[0098] 5) Using the Method of 1) above to compute ICV.

[0099] 6) Using the Method of 2) above to compute ICV.

[0100] 7) Using the Method of 3) above to compute ICV.

[0101] 8) Using the Method of 4) above to compute ICV.

[0102] 9) Using Method of 2) above to compute desired Channel matrix.

[0103] 10) Using Method of 4) above to compute desired Channel matrix.

[0104] 11) Using any of Methods 5)-8) for ICV in conjunction with any of Methods 9)-10) for channel matrix of desired users to decode desired users as per equation (24).

[0105] 12) For determining LCP coefficients of any user, learning can be done at only one subcarrier and this can be used for prediction across RBs and time domain slots.

[0106] 13) Use of LCP methods for downlink precoding for MU-MIMO.

[0107] 14) The use of adaptive filters to determine LCP coefficients.

[0108] 15) The use of Kalman filters to determine LCP coefficients.

[0109] 16) The use of fractional delay IIR filters for reconstruction in LP Method 2.

[0110] 17) The use of Nyquist sampling for reconstruction in LP Method 2.

[0111] 18) Updating ICV corresponding to a lower prediction order to a more accurate version.

[0112] 19) Determining speed of users and using a LUT to determine LCP coefficients.

[0113] 20) Taking FFT of raw channel estimates across subcarriers, and using linear prediction only on a subset of FFT bins, predicting those FFT bins and in turn reconstructing predicted channels across subcarriers for many RBs and multiple users.

[0114] 21) Going from frequency-domain to time domain and computing multipath tap channel values. Using LCP on the time domain taps and predicting future time domain taps, thereby being in a position to compute the channel for any RB in a future time domain slot. Using this to improve SRS capacity via sub-band scheduling.

[0115] 22) Using 2D-FFT for SRS channel estimation.

[0116] 23) A method of linear channel prediction (LCP) in an Open Radio Access Network (O-RAN) massive Multiple Input Multiple Output (MIMO) system, comprising: predicting a channel corresponding to a sounding reference signal (SRS) symbol closest to a target uplink (UL) slot to be decoded, wherein said predicting is performed based on at least one previous SRS symbol; and using the predicted channel as a combining matrix to be applied in a radio unit (RU) for decoding the target UL slot.

[0117] 24) A method of linear channel prediction (LCP) in an Open Radio Access Network (O-RAN) massive Multiple Input Multiple Output (MIMO) system, comprising: i) reconstructing a channel between the two periodic SRS symbols using past and future SRS symbols; ii) training for predicting a channel between two periodic SRS symbols; and iii) using the predicted channel corresponding to the UL slot located between the slots containing the two periodic SRS symbols and decoding the UL slot using a combining matrix based on the predicted channel.

Definitions

[0118] 3GPP 3rd Generation Partnership Project [0119] 5G N.sub.R TDD 5G New Radio Time-Division Duplex. [0120] AWGN Additive White Gaussian Noise [0121] ADC Analog to Digital Converter [0122] BS Base Station [0123] CE Channel Estimation [0124] CP Cyclic Prefix [0125] CSF Current Subframe [0126] CSI Channel State Information [0127] DL Downlink [0128] DMRS Demodulation Reference Signals [0129] DU Distributed Unit [0130] eNB eNodeB [0131] FEC Forward Error Correction [0132] FFT Fast Fourier Transform [0133] FH Fronthaul [0134] GSMA Global System for Mobile Communications Association [0135] IFFT Inverse Fast Fourier Transform [0136] IQ In-phase/Quadrature-phase [0137] IRC Interference Rejection Combining [0138] LTE Long-Term Evolution [0139] LCP Linear Channel Prediction [0140] MAC Medium Access Layer [0141] MIMO Multiple Input Multiple Output [0142] mMIMO Massive MIMO [0143] MMSE Minimum Mean Squared Error [0144] MU-MIMO Multi-User MIMO [0145] NG-RAN Next Generation Radio Access Network [0146] OFDM Orthogonal Frequency Division Multiplexing [0147] O-DU Open Distributed Unit [0148] O-RAN Open Radio Access Network [0149] O-RU Open Radio Unit [0150] PUSCH Physical Uplink Shared Channel [0151] RAN Radio Access Network [0152] RB Resource Block [0153] RF Radio Frequency [0154] SF Subframe [0155] SFN System Frame Number [0156] SRS Sounding Reference Signals [0157] SSF Special Subframe [0158] TDD Time division duplex [0159] UE User Equipment [0160] UL Uplink