WO2018068859A1

WO2018068859A1 - Base station and method for allocating pilot sequences

Info

Publication number: WO2018068859A1
Application number: PCT/EP2016/074629
Authority: WO
Inventors: Samer Bazzi; Wen Xu
Original assignee: Huawei Technologies Duesseldorf Gmbh
Priority date: 2016-10-13
Filing date: 2016-10-13
Publication date: 2018-04-19
Also published as: CN109845164A

Abstract

The present invention provides a base station (BS) 100 for allocating pilot sequences to at least one user equipment (UE) 101. The BS 100 is configured to select, based on channel statistics of the at least one UE 101, a number of pilot sequences from a set 102 of pilot sequences available to the BS 100 and the at least one UE 101. Then, the BS 100 is configured to transmit an index 103 of each selected pilot sequence to the at least one UE 101. The present invention provides also a UE 101, which is correspondingly configured to receive, from the BS 100, a number of indices 103 corresponding to pilot sequences from the set 102 of pilot sequences available to the UE 101 and the BS 100. Further, the UE 101 is configured to select the pilot sequences from the set 102 of pilot sequences, which correspond to the received indices 103, and perform channel estimation based on the selected pilot sequences.

Description

BASE STATION AND METHOD FOR ALLOCATING PILOT SEQUENCES

TECHNICAL FIELD The present invention relates to a base station (BS), a user equipment (UE), a system thereof, and a method for allocating pilot sequences. In particular, the present invention focuses on a dynamic allocation of pilot sequences to one or a plurality of UEs in a communication system or network. The present invention is particularly applicable in multi-user (MU) multiple input multiple output (MIMO) systems.

BACKGROUND

One of the main challenges in such MU MIMO systems is acquiring accurate downlink (DL) channel state information (CSI) at the BS, in order to perform precoding and support multiple users on the same time-frequency resources. Conventionally, this is performed by sending predefined signals - called pilot or training sequences, or reference signals - that are used for channel estimation.

Most cellular systems in West-Europe and USA are frequency-division-duplex (FDD) based. In such systems, the BS has to send pilot sequences to the UEs. The UEs then estimate the DL CSI, and feed it back to the BS. With an increased number of BS antennas (e.g. in massive MIMO systems), the training overhead increases drastically, thus reducing the number of resources that can be used for data. 'Z. Jiang et al., "Achievable rates of FDD massive MIMO systems with spatial channel correlation", IEEE. Trans. Wir. Commun, vol. 14, no. 5, pp. 2868-2881, May 2015' deals with a pilot sequence design in the MU case. In the presented scheme, a BS is configured to find sequences that maximize a sum conditional mutual information (SCMI) metric based on spatial covariance matrices of UEs. However, a big disadvantage of this scheme in a practical system is the necessity of the BS to signal the complete sequences (i.e. every element of each sequence), whenever the set of UEs changes. The sequences found in this scheme cannot be simply stored at the UEs, because the found sequences change dynamically and drastically depending on the number of scheduled UEs and their spatial correlation. This means, signaling the complete sequences is in fact necessary in this scheme. The scheme therefore results in a tremendous overhead, making it not fit for a practical system, such as LTE, which has strict signaling requirements and dynamically schedules UEs on different time-frequency resources. 'J. Choi et al., "Downlink training techniques for FDD massive MIMO systems: open-loop and closed-loop training with memory" IEEE J. Sel. Topics Signal Process., vol. 8, no. 5, pp. 802-814, Oct. 2014, discloses pilot sequences that are designed for a single-user case. The presented scheme does not apply to the MU case, because DL pilot sequences are shared by users. Additionally, the scheme is highly suboptimal when generalized to the MU case, as shown by numerical results.

As another disadvantage, conventional systems and schemes do not address a MU case, in which the UEs are equipped with iterative filters (e.g. a Kalman filter). Iterative filters can help improve channel estimation quality, when the channel temporal correlation is known at the UEs.

SUMMARY

In view of the above-mentioned problems and disadvantages, the present invention aims at improving pilot sequence allocation, particularly in MU MIMO systems. Thereby, the object of the present invention is to reduce an overhead caused by this allocation, and thus to increase the number of resources that can be used for data. Based on this object, the present invention intends to provide a solution fit for systems such as LTE. The present invention also desires to provide a dynamic and efficient solution for the pilot sequence allocation. Specifically, an efficient channel estimation in massive MIMO FDD systems with limited training overhead is desired. Another goal of the present invention is addressing a MU case with UEs equipped with iterative or sequential filters.

The object of the present invention is achieved by the solution provided in the enclosed independent claims. Advantageous implementations of the present invention are further defined in the dependent claims. A first aspect of the present invention provides a base station (BS) for allocating pilot sequences to at least one user equipment (UE), the BS being configured to: select, based on channel statistics of the at least one UE, a number of pilot sequences from a set of pilot sequences available to the BS and the at least one UE, and transmit an index of each selected pilot sequence to the at least one UE.

By letting the pilot sequences, which are selected by the BS, be part of a set of pilot sequences known to both the BS and the at least one UE, potentially even to a multitude of UEs, the pilot sequence signaling overhead is significantly reduced compared to known schemes and systems. This is, because once the BS chooses the pilot sequences from the set, it only has to signal the corresponding indices to the at least one UE. The solution of the first aspect is thus fit for practical systems, such as LTE, which have strict requirements for a low signaling overhead. Finding the pilot sequences based on the UE channel statistics achieves an optimum selection of the sequences, which is itself a challenging task. Once the at least one UE receives the indices, it knows which pilot sequences are chosen by the BS, and can use them for channel estimation.

In a first implementation form of the BS according to the first aspect, the BS is configured to select the pilot sequences based on a metric for minimizing a channel estimation error or maximizing a conditional mutual information at the at least one UE.

With this selection criterion, the best pilot sequences for an efficient channel estimation can be selected. In a second implementation form of the of the BS according to the first aspect as such or according to the first implementation form of the first aspect, the metric is designed for directly minimizing a Channel Estimation Sum (CES) Mean Square Error (MSE) or a weighted CES MSE, or for indirectly minimizing the CES MSE by maximizing a sum conditional mutual information (SCMI).

These metrics allow an optimum selection of the pilot sequences for a most efficient channel estimation. In a third implementation form of the BS according to the second implementation form of the first aspect, the BS is configured to: determine the CES MSE or the SCMI for each possible combination of pilot sequences from the set of pilot sequences, and select that combination, which yields the smallest CES MSE or the largest SCMI as the desired pilot sequences.

This approach is particularly advantageous for small pilot sequence set sizes.

In a fourth implementation form of the BS according to the second or third implementation form of the first aspect, the BS is configured to: find the optimal pilot sequences, which minimize the CES MSE or maximize the SCMI, wherein the optimal pilot sequences are not restricted to being from the set of pilot sequences, and

find the pilot sequences from the set of pilot sequences, which provide a best basis for a subspace spanned by the optimal pilot sequences.

This approach is particularly advantageous for large pilot sequence set sizes.

In a fifth implementation form of the BS according to any of the second to fourth implementation form of the first aspect, for selecting the pilot sequences, the BS is configured to: find the pilot sequences, which minimize the CES MSE or maximize the SCMI, by treating the finding procedure as a linear programming problem.

This approach is particularly advantageous for large pilot sequence set sizes. In a sixth implementation form of the BS according to the first aspect as such or according to any previous implementation form of the first aspect, if a covariance matrix of the at least one UE, or the at least one UE, or a set of UEs, changes, the BS is configured to: re- select at least one of the pilot sequences, and transmit an index of each re-selected pilot sequence to the at least one UE.

Thereby, the pilot sequences can be dynamically adapted to achieve best channel estimation results, even under changing conditions. For instance, the covariance matrix of the at least one UE may change in the order of seconds to tens of seconds, since it depends on the scattering environment close to the UE. A set of served UEs may change due to scheduling and network traffic.

In a seventh implementation form of the BS according to the first aspect as such or according to any previous implementation form of the first aspect, the BS is configured to: dynamically select the pilot sequences, and dynamically transmit an index of each selected pilot sequence to the at least one UE.

Thereby, the pilot sequences can be updated as needed to improve channel estimation.

In an eighth implementation form of the of the BS according to the first aspect as such or according to any previous implementation form of the first aspect, for selecting the pilot sequences in case that the at least one UE is equipped with an iterative or sequential filter, the base station is configured to: periodically update the pilot sequences after each predefined time period, preferably for each fading block, and transmit an index of each periodically updated pilot sequence to the at least one UE.

Thus, when users use iterative filters, the signaling of the pilot sequence indices is periodic. Accordingly, a solution is provided for finding the pilot sequences from the set of pilot sequences, in the case users use iterative filters. The MSE function has a different structure in such an iterative filter case, and thus a solution for this case cannot be simply inferred from a solution in a scenario where a non-iterative filter is used. The problem was not addressed before in the prior art, which only focuses on single-user scenarios. In a ninth implementation form of the BS according to the first aspect as such or according to any previous implementation form of the first aspect, the BS is configured to: transmit indices of pilot sequences to the at least one UE on a UE-specific control channel.

A second aspect of the present invention provides a UE for a communication system, the UE being configured to: receive, from a base station, BS, a number of indices corresponding to pilot sequences from a set of pilot sequences available to the at least one UE and the BS, select the pilot sequences from the set of pilot sequences, which correspond to the received indices, calculate a filter based on the selected pilot sequences, and perform channel estimation based on the calculated filter. The same advantages as for the first aspect are achieved, that is, a signaling overhead is significantly reduced. Further, the channel estimation quality at the UE is substantially improved compared to the case where pilot optimization is not performed, i.e. when the pilots are fixed as is the case in, for example, LTE.

In a first implementation form of the UE according to the second aspect, the UE is configured to: periodically receive a number of indices from the BS, and calculate an iterative or sequential filter of a given iteration based on the pilot sequences corresponding to the last received indices, and perform channel estimation based on the iterative or sequential filter.

Thereby, the channel estimation at the UE in a case of iterative or sequential filters is improved. A third aspect of the present invention provides a system of at least one BS according to the first aspect as such or according to any implementation form of the first aspect, and at least one UE according to the second aspect as such or according to the first implementation form of the second aspect. The system achieves all the advantages of the BS of the first aspect and its implementation forms, and the UE of the second aspect and its implementation form.

A fourth aspect of the present invention provides a method for allocating pilot sequences to at least one user equipment, UE, the method comprising: selecting, based on channel statistics of the at least one UE, a number of pilot sequences from a set of pilot sequences available to a base station and the at least one UE, and transmitting an index of each selected pilot sequence to the at least one UE.

In a first implementation form of the method according to the fourth aspect, the method comprises: selecting the pilot sequences based on a metric for minimizing a channel estimation error or maximizing a conditional mutual information at the at least one UE. a second implementation form of the of the method according to the fourth aspect as ;h or according to the first implementation form of the fourth aspect, the metric is designed for directly minimizing a Channel Estimation Sum (CES) Mean Square Error (MSE) or a weighted CES MSE, or for indirectly minimizing the CES MSE by maximizing a sum conditional mutual information (SCMI). In a third implementation form of the method according to the second implementation form of the fourth aspect, the method comprises: determining the CES MSE or the SCMI for each possible combination of pilot sequences from the set of pilot sequences, and selecting that combination, which yields the smallest CES MSE or the largest SCMI as the desired pilot sequences.

In a fourth implementation form of the method according to the second or third implementation form of the fourth aspect, the method comprises: finding the optimal pilot sequences, which minimize the CES MSE or maximize the SCMI, wherein the optimal pilot sequences are not restricted to being from the set of pilot sequences, and finding the pilot sequences from the set of pilot sequences, which provide a best basis for a subspace spanned by the optimal pilot sequences.

In a fifth implementation form of the method according to any of the second to fourth implementation form of the fourth aspect, for selecting the pilot sequences, the method comprises: finding the pilot sequences, which minimize the CES MSE or maximize the SCMI, by treating the finding procedure as a linear programming problem.

In a sixth implementation form of the method according to the fourth aspect as such or according to any previous implementation form of the fourth aspect, if a covariance matrix of the at least one UE, or the at least one UE, or a set of UEs, changes, the method comprises: re-selecting at least one of the pilot sequences, and transmitting an index of each re-selected pilot sequence to the at least one UE.

In a seventh implementation form of the method according to the fourth aspect as such or according to any previous implementation form of the first aspect, the method comprises: dynamically selecting the pilot sequences, and dynamically transmitting an index of each selected pilot sequence to the at least one UE. In an eighth implementation form of the method according to the fourth aspect as such or according to any previous implementation form of the fourth aspect, for selecting the pilot sequences in case that the at least one UE is equipped with an iterative or sequential filter, the method comprises: periodically updating the pilot sequences after each predefined time period, preferably for each fading block, and transmitting an index of each periodically updated pilot sequence to the at least one UE.

In a ninth implementation form of the method according to the fourth aspect as such or according to any previous implementation form of the fourth aspect, the method comprises: transmitting indices of pilot sequences to the at least one UE on a UE-specific control channel.

With the method of the fourth aspect and its implementation forms, all advantages and effects described above with respect to the BS of the first aspect and its implementation forms are achieved.

It has to be noted that all devices, elements, units and means described in the present application could be implemented in the software or hardware elements or any kind of combination thereof. All steps which are performed by the various entities described in the present application as well as the functionalities described to be performed by the various entities are intended to mean that the respective entity is adapted to or configured to perform the respective steps and functionalities.

Even if, in the following description of specific embodiments, a specific functionality or step to be performed by external entities is not reflected in the description of a specific detailed element of that entity which performs that specific step or functionality, it should be clear for a skilled person that these methods and functionalities can be implemented in respective software or hardware elements, or any kind of combination thereof. BRIEF DESCRIPTION OF DRAWINGS

The above described aspects and implementation forms of the present invention will be explained in the following description of specific embodiments in relation to the enclosed drawings, in which: Fig. 1 shows a BS according to an embodiment of the present invention, and also shows an UE according to an embodiment of the present invention. The BS and the UE form a system according to an embodiment of the present invention. Fig. 2 shows a method according to an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

Fig. 1 illustrates a BS 100 and a UE 101 according to embodiments of the present invention. Together, the BS 100 and UE 101 form a system according to an embodiment of the present invention, wherein such a system can, however, also include more than one BS 100 and/or more than one UE 101.

The BS 100 is configured to allocate pilot sequences to the UE 101 or to more than one UE 101. To this end, the BS 100 is configured to select, based on channel statistics of the UE 101, a number of pilot sequences from a set 102 of pilot sequences, which is available to both the BS 100 and the UE 101. Further, the BS 100 is configured to transmit an index 103 of each selected pilot sequence to the UE 101. Accordingly, the UE 101 is configured to receive a number of indices 103 corresponding to pilot sequences from the set 102 of pilot sequences from the BS 100. With the received indices 103, the UE 101 is configured to select those pilot sequences from the set 102 of pilot sequences, which correspond to the received indices 103, and to perform channel estimation based on these selected pilot sequences.

Fig. 2 illustrates similarly a method 200 for allocating pilot sequences to at least one UE 101 according to an embodiment of the present invention. In a first step 201 of the method 200, a number of pilot sequences are selected form a set 102 of pilot sequences available to a BS 100 and the at least one UE 101. In a second step 201 of the method 200, an index 103 of each selected pilot sequence is transmitted to the UE 101. The steps 201 and 202 can be carried out by the BS 100, as described with respect to Fig. 1. However, it is also possible that a separate entity, for instance a pilot signal allocation apparatus, a relay node, or a dedicated UE selected from the UEs of a communication system or network, is responsible for carrying out these method steps. In the following, more details of the above-described embodiments are explained. These details are applicable to the method 200 of Fig. 2, as well as the BS 100 and UE 101 of Fig. 1, respectively. Generally, the present invention focuses on a constrained pilot sequence selection problem. In other words, as described above, it is assumed that T pilot sequences (T standing for the above-described number) are selected, preferably by the BS 100, from a set 102 of pilot sequences (in the following also referred to a set S of pilot sequences, |S| standing for the number of pilot sequences included in the set 102, i.e. the cardinality of the set 102) that is known to both the BS 100 and at least one UE 101.

Once the BS 100 chooses the pilot sequences, it signals only their indices 103 to the at least one UE 101. This results in a huge overhead reduction compared to conventional approaches.

The pilot sequences can be chosen based on different metrics, e.g. a metric minimizing the CES MSE, or some other metrics that indirectly minimize the CES MSE such as a metric designed for SCMI maximization. Based on such metrics, different approaches for choosing the pilot sequences are possible.

A first approach is a brute-force solution. For instance, the BS 100 may go through all possible pilot sequences combinations taken from the set S of pilot sequences, and may choose the combination that minimizes the CES MSE or maximizes the SCMI. This approach is particularly feasible, when there are not too many combinations, e.g. when the size of the set 102, i.e. |S|, is small.

A second approach is performed in two steps. In a first step, pilot sequences are preferably found, which minimize the CES MSE or maximize the SCMI without constraining these pilot sequences to be from the set S (i.e. optimum pilot sequences are found). In a second step, those pilot sequences from the set S are found, which provide the best basis for the subspace spanned by the optimum pilot sequences found in the first step. This approach is preferable for large sizes of the set 102. A third approach bases on linear programming. That is, CES MSE minimization or SCMI maximization problem may be posed as a linear programming problem, in order to find the desired pilot sequences from the set S. Any of these approaches returns the chosen pilot sequences {si, s₂, . . . , ST} . The indices 103 of these pilot sequences {ii, . .. ,ίτ} are then transmitted to the at least one UE 101. Note that every pilot sequence can be indexed with ceil (log2(\S\)) bits, where ceil(x) denotes the smallest integer greater than or equal to x. Once the at least one UE 101 receive the indices 103, it knows which pilot sequences are chosen and used by the BS 100, and can use them for its respective estimation filter (e.g., MMSE filter). In practice, the indices 103 can be sent on a UE-specific control channel (e.g., PDCCH in LTE).

The BS 100 is preferably able to re-select the pilot sequences, and send the indices 103 of the re-selected pilot sequences to the at least one UE 101 within its cell. The BS 100 carries out this re-selection preferably, whenever at least one covariance matrix of at least one served UE 101 changes significantly, or whenever the set of served UEs 101 changes.

The covariance matrices of served UEs 101 change in the order of seconds to tens of seconds, as they depend on the scattering environment close to the UEs 101 , while the set of served UEs 101 changes due to scheduling and network traffic. Due to these points, the signaling of the sequence indices 103 is preferably dynamic.

The dynamic signaling of the pilot sequence indices {ίι,. .. ,ίτ} on a common control channel has to be specified, and hence is specific for channel estimation. It is noted that in systems such as LTE, the pilot sequence (e.g. cell specific reference signals) allocation in the DL is static/predefined.

It is noted that knowledge of the spatial covariance matrices of the at least one UE 101 at the BS 100 is assumed.

Next, an exemplary mathematical description is provided for the solution above-mentioned second approach. In particular, a system containing a BS 100 with M antennas and K single antenna UEs 101 is considered. The channel of UE k is denoted by hk e C^M, and has a zero mean and spatial covariance matrix Rk. The BS 100 sends pilot sequences for a duration of T time slots, i.e. T pilot sequences are sent. The pilot sequence in the 1^th time slot is si e C^M. The pilot sequences are collected in the matrix S = [SI, . . . ,ST] e C^{M X T}. The k* UE 101 receives the pilot sequences transmitted over the channel: yk = S^H hk + nk where nk is the additive noise at the k* UE 101 with power σ². The k* UE 101 performs MMSE estimation, and forms a channel estimate: iik = Rk S (S^H Rk S + σ² IT)^"1 yk. The CES MSE, a function of S, reads:

MSE(S) =∑k tr (Rk - Rk S (S^H Rk S + σ² IT)^"1 S^h Rk) ( 1 ) where tr(.) denotes the trace of a matrix. Now given a set S known to both the BS 100 and the at least one UE 101 , the set S containing N > T sequences, i.e., S = {vi, . . . ,VN} , T pilot sequences that minimize MSE(S) are to be selected from S. This selection is carried out in two steps in this second approach. The first step is to find an unconstrained solution for the selection, i.e. a solution {ai , . . . ,aT} that does not necessarily lie in S. That is, pilot sequences selected in the first step are not required to be included in the set S of pilot sequences. The second step then finds the T pilot sequences from the set S that best approximate the solution of the first step {ai, . . . ,aT} .

Next, a way of sequence optimization is described. The cost function MSE(S) is non- convex in S, and there exists no closed-form solution for its minimizer. Therefore, it is natural to consider iterative techniques, e.g. descent methods, instead. Furthermore, when dealing with matrix variables, it is useful to investigate, whether the cost function depends on the individual entries of its matrix argument, or only on the subspace spanned by the columns of the matrix argument. The latter case leads to a reduction of the problem space, and efficient gradient-based algorithms exist for handling such problems. In fact, simple manipulations yield:

MSE(S) = MSE(S Q) (2) where Q e ⁽C^{T x T} is a unitary matrix (i.e. Q Q^H = Q^H Q = I_T). Thus, the MSE cost function is invariant to unitary rotations, and is a function of the subspace spanned by the columns of S. This important observation combined with the forced orthogonality constraint S^H S = IT leads to a solution of the minimizer of MSE(S) that can be obtained using an iterative steepest descent method on the Grassmanian manifold.

The iterative steepest descent returns the sequences ai,... ,ΆΎ, collected in the matrix S_opt = [ai , . . . ,aT] . To find the T pilot sequences sai, .. . ,SdT from S that best approximate {ai , . . . ,aT} , it is noted that the CES MSE when using S_opt is not a function of the individual entries of Sopt, but rather a function of the subspace spanned by its columns, or in others words its range, denoted ran(S_opt). Therefore, it is proposed to choose the T pilot sequences that provide the best basis for ran(S_opt). This is inspired by conventional matching pursuit techniques, and is a generalization of such techniques that enables subspace matching. The idea is specifically to find, at each step, the vector that best lies in the subspace consisting of the intersection of ran(S_opt) and the orthogonal complement of the subspace spanned by already chosen vectors. In other words, at each step is attempted to "cover" the residual (remaining) subspace that is still not covered by previously chosen vectors. To accomplish this step, a few quantities need to be defined. Let P_opt be the orthogonal projector onto ran(S_opt), which reads:

Additionally, let the pilot sequences chosen after t steps be stacked in the matrix St = [sai, .. . ,Sdt]. Then, the projector onto the orthogonal complement of ran(St) reads:

Pcomp.t = I - St (St^H St)^"1 St^H Finally, the projector onto the intersection of ran(S_opt) and orthogonal complement of ran (St) can be calculated as a function of P_opt and P_Com_P,t as:

Pintersect,t ⁼ 2 Pcomp,t (Pcomp.t

Popt

Where ()^† denotes the Moore -Penrose pseudoinverse. The following exemplary algorithm can be used for finding the desired sequences.

Initialization:

Pmtersect,0 = Popt ; So <T 0; T <T 0

Steps t = 1 to T

Sdt = arg max _s e S - T | | Pintersect,t-1 s| |₂

T <r {r, Sdt}

Calculate i comp,t based on St

Calculate l intersectt based On i comp.t and opt

End

Note that a SCMI maximizing unconstrained solution (denoted as Semi) can be alternatively used instead of S_opt when the above algorithm is run, because the CMI function is also invariant to unitary rotations of its matrix argument. What is needed is then to replace P_opt with Pcmi Semi (Scmi^H Semi)^"1 Scmi^H. The rest follows in a similar manner.

Next, a combination with iterative filtering is described. In case the UEs 101 apply iterative/sequential filtering, such as Kalman filtering, the pilot sequences are preferably selected by the BS 100 on a fading block slot basis, in order to minimize the MSE. A prerequisite for this is knowing the spatio-temporal user correlation at the BS 100. Here, a first-order Gauss-Markov process is adapted to describe the temporal correlations of the channel of the k^th UE 101 as follows: hk [1] = Rk^½ gi, gi has independent NC(0,1) elements (NC(0, 1) denotes a circularly symmetric Gaussian variable with mean zero and variance 1) hk [n] = η hk [n-1] + sqrt(l - η²) Rk^½ g_n , n > 1 where hk [n] is the channel of UE k in the n fading block, η is the temporal correlation coefficient, and g_n is vector with independent NC(0,1) elements that is uncorrelated with hk[n - 1] and gi forall n>l . The channels of UE k at all fading blocks have the spatial covariance Rk.

In this case, the Kalman filter used at the η^Λ fading block by the k^th user can be written as

K_k[n] = Mk[n/n-l] S[n] (S[n]^H M_k [n/n-1] S[n] + α²1)^Λ where Mk [n/n-1] and S[n] denote the minimum prediction MSE matrix and the pilot sequence used by the BS 100 at the nth fading block. Mk [n/n-1] reads:

M_k [n/n-1] = η² Mk [n-l/n-1] + (1 - η²) Rk which is a function of Mk [n-l/n-1], the minimum MSE matrix of the (η-1)^Λ fading block:

Mk [n-l/n-1] = (I - K_k [n-1] S[n-1]^H) Mk [n-l/n-2].

In the multi-user case, it can be shown that the MSE at the η^Λ fading block summed over all users reads:

MSE [n] =∑ktr (M_k[n/n-l] - Mk[n/n-l] S[n] (S[n]^H M_k[n/n-l] S[n] + σ²!)^"1 S[n]^H M_k[n/n- 1]) (3) Due to the recurs ive/sequential structure of Kalman filters, the MSE at different fading blocks may be different. Further, the choice of the pilot sequences at a given fading block affects not only the MSE at the given block, but also the MSE of all following blocks. For instance, the choice of S[n] affects Kk[n] and therefore Mk [n n], Mk [n+l/n], Kk[n+1], MSE[n+l] and so on. A given choice of S[n] that minimizes MSE [n] might be suboptimal for the MSE in following blocks n+l,n+2,.. This observation makes finding globally optimal pilot sequences very challenging, if not intractable.

Therefore, the present invention follows an approach similar to an approach described in 'S. Noh et al., "Pilot beam pattern design for channel estimation in massive MIMO systems" IEEE J. Sel. Topics Signal Process., vol. 8, no. 5, pp. 787-801, Oct. 2014' and design the pilot sequences in a greedy way. Namely, the variable S[n] is optimized to minimize MSE [n] assuming that S[l] is fixed for 1 < n. In this case, MSE [n] is a function of S[n] only. Further, looking at the above formula (3), it can be observed that it is similar to the formula (1), once the spatial covariance Rk of user k is replaced by the minimum prediction MSE matrix Mk[n/n-l]. Therefore, the above conclusions hold here as well, and pilot sequence design with user alman filtering occurs similarly to the above-given description, namely:

Firstly, an unconstrained solution S[n] minimizing MSE [n], assuming that S[l] is fixed for 1 < n, can be obtained by performing an iterative steepest descent method on the Grassmanian manifold.

Secondly, to find the solution from the set S approximating S[n], P_optis replaced with P_opt[n] = S[n] (S[n]^H Sfn]) ¹ S[n]^H in the second algorithm.

In contrast to the above without Kalman filter, the pilot sequences here are additionally a function of time (fading block index) and are designed for each fading block.

It is assumed that the pilot sequences are updated for each fading block, which may cause a somewhat larger overhead. A simple alternative, however, is to update the pilot sequences and send their indices 103 every pth fading block, where p equals, e.g., 2 or 5. As shown numerically, this heuristic solution only comes with a minor increase in the estimation MSE, and still significantly outperforms randomly chosen pilot sequences. Whether signaling new pilot indices 103 at each slot is beneficial or not depends on the data amount that can be transmitted instead. As a simple example, assume Kalman filtering can reduce the required T to achieve a given MSE from T=8 to T=6. Further, let K=8 users receiving 16- QAM symbols. Then, there are additional (8-6)*K*4 bits = 64 sent data bits, but an overhead of 6*6 = 36 bits for signaling the pilot sequence indices 103 (assuming a set of 64 sequences). The end result is 64 - 36 = 28 additional data bits per slot. Thus, signaling pilot indices 103 at each slot is still beneficial.

Notably, for the present invention, it is assumed that the covariance matrices Ri,...,Rk are spatial covariance matrices, when the BS 100 is equipped with M antennas, and the system model targets a specific frequency sub-band. Alternatively, the system model could target M sub-bands when the BS 100 is equipped with a single antenna. In that case, the co variance corresponds to a frequency co variance. Finally, the covariance could correspond to a joint frequency-spatial correlation (multiple BS antennas and multiple sub- band system model). The present invention applies to any of these combinations.

Further notably, in the present invention, a preamble pilot format is assumed for simplicity. The present invention also holds for a scattered pilot format, with a slight adaptation of the MSE function. Finally, for simplicity, the present invention assumes a block-fading model, wherein the channel remains constant for a number of time slots. It should, however, be clear for a skilled person that the present invention is also applicable, when block-fading does not hold, i.e. when the channel changes, for instance, on a time slot (called symbol slot in LTE) basis.

The present invention has been described in conjunction with various embodiments as examples as well as implementations. However, other variations can be understood and effected by those persons skilled in the art and practicing the claimed invention, from the studies of the drawings, this disclosure and the independent claims. In the claims as well as in the description the word "comprising" does not exclude other elements or steps and the indefinite article "a" or "an" does not exclude a plurality. A single element or other unit may fulfill the functions of several entities or items recited in the claims. The mere fact that certain measures are recited in the mutual different dependent claims does not indicate that a combination of these measures cannot be used in an advantageous implementation.

Claims

1. Base station, BS, (100) for allocating pilot sequences to at least one user equipment, UE, (101) the BS (100) being configured to:

select, based on channel statistics of the at least one UE (101), a number of pilot sequences from a set (102) of pilot sequences available to the BS (100) and the at least one UE (101), and

transmit an index (101) of each selected pilot sequence to the at least one UE (101).

2. BS (100) according to claim 1 being configured to:

select the pilot sequences based on a metric for minimizing a channel estimation error or maximizing a conditional mutual information at the at least one UE.

3. BS (100) according to claim 1 or 2, wherein:

the metric is designed for directly minimizing a Channel Estimation Sum, CES,

Mean Square Error, MSE, or a weighted CES MSE, or for indirectly minimizing the CES MSE by maximizing a sum conditional mutual information, SCMI.

4. BS (100) according to claim 3, wherein, for selecting the pilot sequences, the BS (100) is configured to:

determine the CES MSE or the SCMI for each possible combination of pilot sequences from the set (102) of pilot sequences, and

select that combination, which yields the smallest CES MSE or the largest SCMI as the desired pilot sequences.

5. BS (100) according to claim 3 or 4, wherein, for selecting the pilot sequences, the BS (IOO) is configured to:

find the optimal pilot sequences, which minimize the CES MSE or maximize the SCMI, wherein the optimal pilot sequences are not restricted to being from the set (102) of pilot sequences, and

find the pilot sequences from the set (102) of pilot sequences, which provide a best basis for a subspace spanned by the optimal pilot sequences.

6. BS (100) station according to one of claims 3 to 5, wherein, for selecting the pilot sequences, the BS (100) is configured to:

find the pilot sequences, which minimize the CES MSE or maximize the SCMI, by treating the finding procedure as a linear programming problem.

7. BS (100) according to one of claims 1 to 6 being configured to, if a covariance matrix of the at least one UE (101), or the at least one UE (101), or a set of UEs (101), changes:

re-select at least one of the pilot sequences, and transmit an index (103) of each re- selected pilot sequence to the at least one UE (101).

8. BS (100) according to one of claims 1 to 7 being configured to:

dynamically select the pilot sequences, and dynamically transmit an index (103) of each selected pilot sequence to the at least one UE (101).

9. BS (100) according to one of claims 1 to 8, wherein, for selecting the pilot sequences in case that the at least one UE (101) is equipped with an iterative or sequential filter, the BS (100) is configured to:

periodically update the pilot sequences after each predefined time period, preferably for each fading block, and

transmit an index (103) of each periodically updated pilot sequence to the at least one UE (101).

10. BS (100) according to one of claims 1 to 9 being configured to:

transmit indices (103) of pilot sequences to the at least one UE (101) on a UE- specific control channel.

11. User Equipment, UE, (101) for a communication system, the UE (101) being configured to:

receive, from a base station, BS, (100) a number of indices (103) corresponding to pilot sequences from a set (102) of pilot sequences available to the at least one UE (101) and the BS (100),

select the pilot sequences from the set (102) of pilot sequences, which correspond to the received indices (103), calculate a filter based on the selected pilot sequences, and

perform channel estimation based on the calculated filter.

12. UE (101) according to claim 1 1 being configured to:

periodically receive a number of indices (103) from the BS (100), and

calculate an iterative or sequential filter of a given iteration based on the pilot sequences corresponding to the last received indices (103), and

perform channel estimation based on the iterative or sequential filter.

13. System of at least one base station, BS, (100) according to one of claims 1 to 10, and at least one user equipment, UE, (101) according to claim 1 1 or 12.

14. Method (200) for allocating pilot sequences to at least one user equipment, UE, (101) the method comprising:

selecting (201), based on channel statistics of the at least one UE (101), a number of pilot sequences from a set (102) of pilot sequences available to a base station (100) and the at least one UE (101), and

transmitting (202) an index (103) of each selected pilot sequence to the at least one UE (lOl).