WO2015149812A1

WO2015149812A1 - Pilot decontamination through pilot sequence hopping in massive mimo systems

Info

Publication number: WO2015149812A1
Application number: PCT/DK2015/050075
Authority: WO
Inventors: Elisabeth De Carvalho; Jesper Hemming SØRENSEN
Original assignee: Aalborg Universitet
Priority date: 2014-04-01
Filing date: 2015-03-31
Publication date: 2015-10-08

Abstract

The invention relates to a system for determining channel coefficients of channels in a wireless cellular network. The wireless cellular network comprises a plurality of cells wherein each cell comprises a base station configured to communicate with users within the cell and wherein a communication path between one of the users and one of the base stations define one of the channels. The system comprises a pilot generation unit configured to assign pilot sequences randomly among the users and a pilot processing unit configured to filter the pilot sequences received from a user of interest so that the channel coefficient of the channel of the user of interest is determined. The pilot sequences received from the user of interest are contaminated by other non-orthogonal or identical pilot sequences from other users of the cell of interest or other cells. The filter is configured so that the contamination caused by the other non-orthogonal or identical pilot sequences from the other users is reduced.

Description

PILOT DECONTAMINATION THROUGH PILOT SEQUENCE HOPPING IN MASSIVE MIMO SYSTEMS

FIELD OF THE INVENTION

The invention relates to wireless cellular networks, particularly to methods for estimating channel coefficients.

BACKGROUND OF THE INVENTION

Knowledge of the channel in a wireless cellular network between a base station and a mobile phone is required in order to enable communication between the base and the user's mobile phone. The channel, e.g. a channel coefficient, describes how a transmitted signal is influenced by the environment during transmission from the base station to the user or vice versa. The channel may be estimated by use of pilot signals transmitted from the user to the base station. The pilot signal received by the base station is influenced by the channel and, therefore, contains information about the channel. Since pilot signals are transmitted from many users located in one or more cells, the pilot signal of interest may be contaminated by pilot signals transmitted from other users.

Accordingly, there is a need for determining channel coefficients in cases where the received pilot signal is contaminated by other pilot signals.

SUMMARY OF THE INVENTION

It is an object of the present invention to improve the quality of data

transmissions in wireless cellular networks.

Particularly, it is an object to improve methods for determining channel

coefficients in wireless cellular networks.

A first aspect of the invention relates to a system for determining channel coefficients of channels in a wireless cellular network, wherein the wireless cellular network comprises a plurality of cells, wherein each cell comprises a base station configured to communicate with users within the cell, and wherein a communication path between one of the users and an antenna of one of the base stations define one of the channels, the system comprises:

- a pilot generation unit configured to assign pilot sequences to the users, wherein the pilot sequences are assigned randomly among the users,

- a pilot processing unit configured to filter the pilot sequences received from a user of interest, for one or more users in a cell of interest, over a period of time including at least two pilot periods so that the channel coefficient of the channel of the user of interest is determined, wherein the pilot sequences received from a user of interest are contaminated by other non-orthogonal, identical or

corresponding pilot sequences from other users of the cell of interest or other cells, wherein the filter is configured to that the contamination caused by the other non-orthogonal, identical pilot or corresponding sequences from the other users is reduced.

The pilot generation unit and the pilot processing unit may be units of the base station. Each base station of different cells may have their own independent pilot generation and the pilot processing units.

A user may be a cell phone or other user equipment.

A pilot period, or a time slot as also referred to in the detailed description, may define a period wherein the pilot sequences are assigned and transmitted.

Normally, only one pilot sequence is transmitted during a pilot period, but it is also possible to re-transmit the same pilot sequence multiple times.

A channel coefficient is a complex scalar which describes how the pilot sequence is affected by the channel, i.e. the physical transmission path between the user and an antenna of the base station. The channel coefficient is required for enabling correct determination of information transmitted from a user to a base station. That is, when the channel coefficient is known the channel's impact on the received information can be compensated. As an example, the random assignment of pilot sequences to users in a given cell may be performed according to the steps: 1) The pilot processing unit generates random seed values for each user in a given cell in a first pilot period, 2) The seed values are transmitted to the users, 3) The user has stored information describing relations between seed values and pilot sequences. The user generates a pilot sequence on basis of the received seed value. In is noted that the base stations, e.g. the pilot processing unit is able to generate the same pilot sequences on basis of the different seed values. As explained in the detailed description, the random assignment of pilot sequences to users may be referred to as pilot hopping wherein random shuffling of the pilot sequences is applied within a cell.

The pilot sequences received by a base station of interest can be referred to as a contaminated pilot signal. The contaminated signal includes effects from the channel on the transmitted pilot sequence from the user of interest, i.e. effects from e.g. buildings on the transmitted pilot sequences, and effects from the channels on the transmitted pilot sequences from other users. Furthermore, the contaminated signal includes interfering signal components caused by other non- orthogonal, identical or corresponding pilot sequences from other users of the cell of interest or other cells.

If C_n^kl is the set of all pairs i,j, which identify all UEs applying the same pilot sequence in the n'th time slot as the k'th user in the i'th cell, then the

contaminated signal can be expressed by

wherein the first term expresses how pilot sequences χ_η^ΛΙ 0 transmitted by the user of interest are affected by channel coefficients h_n k0, the second sum term expresses how other non-orthogonal pilot sequences x_n^ transmitted by other users are affected by channel coefficients h_n ij, where in the last term

represents noise. Thus, the sum term describes how the signal received by the user of interest is contaminated. Accordingly, the filter is configured to filter the contaminated pilot signal so that the contamination (expressed by the sum term) caused by the other non- orthogonal, identical pilot or corresponding sequences from the other users is reduced.

The filtering of the pilot signals exploits the fact that the autocorrelation of the channel coefficient of the user of interest is high at relative low velocities,. Thus, the filter is configured so that contaminating signals of other users of other cells are filtered out or reduced.

The filter may be configured so that the contaminating pilot signals, are filtered out, i.e. averaged out, or reduced. Thus, the filtering may be seen as an averaging process which averages out the contaminating pilot sequences or signals.

In general, any filter with an impulse response, such that the information about the current channel, which is available in past and present pilot signals, is combined to achieve an estimate, which is better than what can be achieved by only applying the present pilot signal, can be used for filtering received pilot sequences.

For simplicity of implementation, a linear filter is preferred. Moreover, since the channel varies, an adaptive filter is preferred. Hence, the Kalman filter is a good candidate. If the channel has limited variation, a properly designed non-adaptive filter can be used, achieving suboptimal but acceptable performance.

When applying the Kalman filter in the scenario targeted by embodiments of the invention, the statistics of the varying channel may themselves vary (if the users accelerate, i.e. their velocity changes). To accommodate this, a modification of the Kalman filter is applied, such that the underlying model of the Kalman filter is adaptive.

Accordingly, the modified Kalman filter described in the detailed description may be used for filtering received pilot signal. The parameters in the modified Kalman filter are described as follows: e_n = The a priori estimation error,

R_n = (no interpretation),

nabla_n = Partial derivative, with respect to a_n, of the mean squared error a_n = autoregressive model coefficient,

k_n = Kalman gain (how much weight is put on the a priori error, the lower the value the more we trust the autoregressive model and ignore the error, and vice versa),

h_n = The channel estimate (output of filter),

m_n = Partial derivative, with respect to a_n, of the Kalman gain,

q_n = Partial derivative, with respect to a_n, of the channel estimate,

p_n+l = Estimate error covaria nee,

s_n+l = Partial derivative, with respect to a_n, of the estimate error covariance. In an embodiment, the pilot sequences assigned to at least some of the users in a first cell are orthogonal, and wherein the pilot sequences assigned to at least some of the users in a second cell are non-orthogonal with the pilot sequences assigned to at least some of the users in a first cell. In principle, the random assignment of pilot sequences to users can be seen as a process wherein pilot sequences are randomly selected from a set of pilot sequences. Thus, effectively, the pilot sequences are selected from the same set of sequences for each cell. Therefore, the pilot sequences assigned to at least some of the users in the second cell are non-orthogonal with the pilot sequences assigned to at least some of the users in the first cell. Since, the filtering is performed across multiple pilot periods, contamination from a given user in the second cell is averaged out due to the decorrelation of contaminating signals (due to the random assignment of pilot sequences for each pilot period), even when a contaminating pilot sequence may be non-orthogonal with the pilot signal of interest for a given pilot period.

In an embodiment, each one of the users, such as user equipment or cell phones, is configured to transmit the assigned pilot sequence during the present pilot period to the base station. In an embodiment, a first pilot generation unit is configured to assign the random pilot sequences to the users of a first cell, and a second pilot generation unit is configured to assign the random pilot sequences to the users of a second cell independently of the first pilot generation unit. Accordingly, each cell may be configured with their own pilot generation unit (and pilot processing unit) which functions independently of each other. Advantageously, the assignment of pilot sequences to different cells are non-coordinated, so that non-coordinated pilot decontamination through pilot sequence hopping is achievable. In an embodiment the pilot generation unit is configured to assign a first set of the random pilot sequences to the users in a first pilot period, and configured to assign a second set of the random pilot sequences to the users in a subsequent second pilot period, wherein the first and second set contains the same pilot sequences, but where the pilot sequences of each of the sets are assigned randomly among the users. Accordingly, the assignment of pilot sequences may be performed merely by random shuffling of the pilots applied within each cell. The assignment of pilot sequences in the second pilot period, is independent of the assignment of pilot sequences in the previous first pilot period. The described assignment of pilot sequences in different pilot periods applies also to the embodiment wherein a first pilot generation unit is configured to assign the random pilot sequences to the users of a first cell, and a second pilot generation unit is configured to assign the random pilot sequences to the users of a second cell independently of the first pilot generation unit.

In an embodiment, the filter is configured to exploit that contaminating signals are decorrelated (across pilot periods) due to the random assignment, so that the influence (contamination) of other channel coefficients of other (orthogonal or non-orthogonal) pilot sequences transmitted by other users of the other cells on the channel coefficient of one of the users of the cell are filtered out, substantially filtered out or at least reduced. In order words, the filter may be seen to average out the contamination over multiple pilot periods.

In an embodiment the filter is configured so that the determination of the channel coefficient is based on one or more previously determined channel coefficients. In an embodiment the filter is configured so that the determination of the channel coefficient is based on a prediction error between the received pilot sequences and a prediction of the received pilot sequences, wherein the prediction is based on one or more previously determined channel coefficients, a channel model and the assigned pilot sequences.

In a related embodiment the filter is configured so that the channel model is updated over time based on a gradient of a mean value of the prediction error, wherein the gradient is determined as the derivative mean value of the prediction error with respect to the channel model. For example, the prediction error may be determined as a squared prediction error.

In an embodiment the filter is configured to filter the contaminated signal y_n k0 received by the base station of interest,

by use of a Kalman filter model, yn = Cn bn + dn, for determining the channel coefficients h_n k0 of the channel of the user of interest, wherein

Cn represent the transmitted pilot sequences, χ_η^ΛΙ 0 bn represent the channel coefficients h_n k0, and wherein n is an index of individual periods or time slots, yn represents vector values of the contaminated pilot signal received by the base station, dn is measurement noise and contaminating signals from users in other cells applying the same pilot sequence as the user of interest = Sum(h_n kl x_n kl) +z_n k0, and wherein the evolution of the system state xn follows the model, xn = An xn-1 + vn, wherein An is a state transition matrix an vn is process noise, and wherein the Kalman filter is processed so that estimates of the one or more channel coefficients xn are determined.

A second aspect relates to a method as defined in the claims. A third aspect of the invention relates to a computer program configured for enabling a processor running the program to carrying out of a method according to claim. The computer program may be stored on a non-volatile storage medium, e.g. a cd, a dvd, a solid state memory, a computer or server, e.g. a server comprised by the Internet or other network.

Other embodiments are described in the claims.

The various aspects of the invention may be combined and coupled in any way possible within the scope of the invention. These and other aspects, features and/or advantages of the invention will be apparent from and elucidated with reference to the embodiments described hereinafter.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the invention will be described, by way of example only, with reference to the drawings, in which

Fig. 1 shows a cellular system 100 with three cells 101. Cell 0 is of interest and the neighboring cells will potentially cause interference,

Fig. 2 shows an example of a transmission schedule with two time slots,

Fig. 3 shows an example of a random pilot schedule for the UE of interest and potential contaminators in a neighboring cell. Boxes 301 represent pilots, which are orthogonal to the pilot from the UE of interest. Highlighted boxes 302 represent contamination and x_i denotes a pilot sequence,

Fig. 4 shows an overview of simulation parameters,

Fig. 5 shows MSE as a function of the autoregressive model coefficient and the user mobility,

Fig. 6 shows a comparison between the proposed scheme and conventional solutions with respect to means squared error as a function of mobility,

Fig. 7 shows a comparison between the proposed scheme and conventional solutions with respect to means squared error as a function of the signal-to- interference ratio,

Fig. 8 shows a comparison between the proposed scheme for first and higher order models and conventional solutions with respect to means squared error as a function of mobility, and Fig. 9 shows a system for determining channel coefficients of channels in a wireless cellular network.

DESCRIPTION OF EMBODIMENTS

The invention relates to wireless cellular networks applying massive multiple-input multiple-output (MIMO) technology. In such a system, the base station in a given cell is equipped with a very large number (hundreds or even thousands) of antennas and serves multiple users. Estimation of the channel from the base station to each user is performed at the base station using an uplink pilot sequence. Such a channel estimation procedure suffers from pilot contamination. Orthogonal pilot sequences are used in a given cell but, due to the shortage of orthogonal sequences, the same pilot sequences must be reused in neighboring cells, causing pilot contamination. The solution presented according to the embodiments suppresses pilot contamination, without the need for coordination among cells. Pilot sequence hopping is performed at each transmission slot, which provides a randomization of the pilot contamination. Using a modified Kalman filter, it is shown that such randomized contamination can be significantly suppressed. Comparisons with conventional estimation methods show that the mean squared error can be lowered as much as an order of magnitude at low mobility.

Multiple-input multiple-output (MIMO) technology is finding its way into practical systems, like LTE and its successor LTE-Advanced. It is a key component for these systems' ability to improve the spectral efficiency. The success of MIMO

technology has motivated research in extending the idea of MIMO to cases with hundreds, or even thousands of antennas, at transmitting and/or receiving side. This is often termed massive MIMO. In mobile communication systems, like LTE, the more realistic scenario is to have a massive amount of antennas only at the base station (BS), due to the physical limitations at the user equipment (UE). It has been shown that such a system, in theory, can eliminate entirely the effect of small-scale fading and thermal noise, when the number of BS antennas goes to infinity. The only remaining impairment is inter-cell interference, caused by imperfect channel state information (CSI), which is a result of non-orthogonality of training pilots used to gather the CSI. This is often referred to as pilot contamination. It is considered as one of the major challenges in massive MIMO systems.

Mitigation of pilot contamination has been the focus of several works recently. These fall into two categories; one with coordination among cells and one without. The first category utilizes that the desired and interfering signals can be

distinguished in the channel covariance matrices, as long as the angle-of-arrival spreads of desired and interfering signals do not overlap. A pilot coordination scheme is proposed to help satisfying this condition. It has also been shown that coordination among base stations to share downlink messages can be utilized. Each BS then performs linear combinations of messages intended for users applying the same pilot sequence. This is shown to eliminate interference when the number of base station antennas goes to infinity. The category without coordination also includes notable contributions. A multi-cell precoding technique is used in with the objective of not only minimizing the mean squared error of the signals of interest within the cell, but also minimizing the interference imposed to other cells. It has also been shown that channel estimates can be found as eigenvectors of the covariance matrix of the received signal when the number of base station antennas grows large and the system has favorable propagation. Another work is based on examining the eigenvalue distribution of the received signal to identify an interference free subspace on which the signal is projected. It is shown that an interference free subspace can be identified when certain conditions are fulfilled concerning the number of base station antennas, user equipment antennas, channel coherence time and the signal-to-interference ratio.

The major contribution of the embodiments of the present invention is a pilot decontamination, which does not require inter-cell coordination, and is able to exploit past pilot signals. It is based on pilot sequence hopping performed within each cell. Pilot sequence hopping means that every user chooses a new pilot sequence in each transmission slot. Consider a user of interest and the effect of the inter-cell pilot contamination when pilot sequence hopping is applied. At each transmission slot, the pilot signal of the user is contaminated by a different set of interfering users. Hence channel estimation at each transmission slot is affected by a d ifferent set of interfering channels. If channel estimation is carried out based solely on the pilot sequence of the current slot, then pilot sequence hopping does not bring a ny gain . The key in our solution is a cha nnel estimation that incorporates m ultiple time slots so that it can benefit from random ization of the pilot conta mination .

Consider the sim ple exa mple, where the cha nnel of the UE of interest is time- invariant. Its estimation is performed across m ultiple time slots. Specifically, the resulting cha nnel estimate is the average of the estimates across the time slots. In the averaging process, the conta mination signal is averaged out. Note that, if the contam ination sig na l rema ins constant across the time slots, i .e. there is no hopping, this averag ing brings no benefit (except an averaging of the receive noise) . When the channel is time-variant a nd correlated across time slots, it remains possible to exploit the information about the channel across time slots by an appropriate filtering a nd benefit from contam ination ra ndom ization . In this description, channel estimation across multiple time slots is performed using a mod ified version of the Ka lma n filter, which is ca pable of tracking the channel a nd the channel correlation . The level of contam ination suppression depends on the channel correlation between slots of the UE of interest as well as the

conta minators. In LTE, channel correlation between time slots is large even at medium-high speeds, making the proposed solution very efficient. System Model

In this description we denote sca la rs in lower case, vectors in bold lower case and matrices in bold upper case. A superscript T denotes the transpose a nd a superscript H denotes the conjugate transpose. Fig . 1 shows a cellula r system 100 consisting of L cells 101 with K users UE in each cell . A massive MIMO scenario is considered, where the base station BS has M antennas 103 and the UE has a sing le antenna . We restrict our attention to the channel estimation performed in a sing le cell, which we term the "cell of interest" and assign the index "0". The channel between the BS in the cell of interest and the k'th user in the I'th cell is denoted h^(kl) = [h^klXl) h^(kl)(2) ... h^(k\)(M)], where the individual channel coefficients are complex scalars. Note that for l>0, Η^Λ(Ι Ι) refers to a channel between the BS of interest and a UE connected to a different base station. We furthermore restrict our attention to the estimation of a single channel coefficient, hence a channel is denoted as the complex scalar h^kl). The work easily extends to vector estimations, in which case spatial correlation can be exploited for improved performance. A rich scattering

environment is assumed, such that h^kl) can be modeled using Clarke's model, hence (eq. 1) :

here N_s is the number of scatterers, f_d is the maximum Doppier shift, a_m and cp_m is the angle of arrival and initial phase, respectively, of the wave from the m'th scatterer. Both a_m and cp_m are i.i.d. in the interval [-n, n) and f_d=v/c f_c, where v is the speed of the UE, c is the speed of light and f_c is the carrier frequency.

In a massive MIMO system, collection of channel state information (CSI) is performed using uplink pilot training, i.e. by transmitting pilot sequences from the user UE to the base station BS. The CSI achieved this way is utilized in both downlink and uplink transmissions based on the channel reciprocity assumption. We define a pilot training period followed by an uplink and a downlink

transmission period as a time slot. See Fig. 2 for an example of a transmission schedule with two time slots. During the n'th pilot training period, the k'th user in the I'th cell transmits a pilot sequence x (kl)_n = [x (kl)_n(l), x (kl)_n(2) ... x (kl)_n(T)] T, where τ is the pilot sequence length. Ideally, all pilot sequences in the entire system are orthogonal, in order to avoid interference. However, this would require pilot sequences of at least length L · K, which in most practical systems is not feasible. Instead, orthogonality within each cell only is ensured, i.e. T =K, thereby dealing with the potentially strongest sources of interference. As a result, all cells use the same set of pilots, potentially causing interference from neighboring cells. This is referred to as pilot contamination. We define the contaminating set, C_n (kl)$, as the set of all pairs (i,j), which identify all UEs applying the same pilot sequence in the n'th time slot as the k'th user in the I'th cell. Hence, χ^Λ( )_η = χ^Λ(^)_η for all (i,j) ε C_.n^kl). The pilot signal received by the BS of interest, concerning the k'th user in the n'th time slot can be expressed as (eq. 2):

_V ) ^ . fcO kO , _hij ij , fcO

J n ^l'n -^n ' / _j ^,l ri- n > ^Λ where

ζ^Λ(Ι 0)_η(2) ... ζ^Λ(Ι 0)_η(τ)]^ΛΤ and ζ^Λ(Ι 0)_ηϋ) are circularly symmetric Gaussian random variables with zero mean and unit variance for all j. Here, only signals leading to contamination are included in the sum term, since any h (ij)_n χ^Λ( )_η for all (i,j) ί ( _η^Λ(Ι Ι) are removed when correlating with the applied pilot sequence. Hence, all contributions from the sum term are undesirable and will contaminate the CSI. Without loss of generality, we focus on the channel estimation for a single user in a single cell. Hence, in the remainder of the paper, we omit the superscript k for ease of notation.

Pilot Decontamination

The solution to pilot contamination proposed in this work consists of two components:

1) Pilot sequence hopping: This component refers to random shuffling of the pilots applied within a cell. This shuffle occurs between every time slot. The purpose of this component is to decorrelate the contaminating signals. When pilots are shuffled, the set of contaminating users will be replaced by a new set, whose channel coefficients are uncorrelated with those of the previous set.

2) Kalman filtering: The autocorrelation of the channel coefficient of the user of interest is high at low mobility. This means that information about the value of the current channel coefficient exists not only in the most recent pilot signal, but also in past pilot signals. This can be extracted using a filter. For this purpose a Kalman filter is desirable due to its recursive structure, which provides low complexity, yet optimal performance. Additionally, since the contaminating signals have been decorrelated, the Kalman filter will suppress the impact of these signals, leading to pilot decontamination.

Pilot sequence hopping is a technique where the UEs randomly switch to a new pilot sequence in between time slots. This must be coordinated with the BS, which in practice can be realized by letting the BS send a seed for a pseudorandom number generator to each UE. Random pilot sequence hopping is illustrated in Fig. 3 in the case of τ=Κ=5. Note how the identity of the contaminator changes between time slots, as opposed to a fixed pilot sequence schedule, where the contaminator remains the same UE. Consequently, the undesirable part of the pilot signal, i.e. the sum term in eq. 2, varies rapidly between time slots compared to the variation caused by the mobility of a single contaminator in a fixed schedule. In fact, the impact of pilot sequence hopping, from a

contamination perspective, can be viewed as a dramatic increase of the mobility of the contaminator. This in turn leads to a lowered autocorrelation, or

decorrelation, in the contaminating signal, which is the motivation behind performing pilot sequence hopping.

The level of decorrelation is related to the time between two instances, where the same user acts as a contaminator. We refer to this as the collision distance, and we denote it t_c, see Fig. 3. Note that in the case of a fixed pilot schedule, t_c= l. The goal of pilot sequence hopping is to maximize t_c, either in an expected sense or maxmin sense, i.e. maximization of the minimum value. The latter can be pursued through a minimal level of coordination of pilot sequence schedules among neighboring cells. However, this work is strictly restricted to a framework with no inter-cell coordination, hence, we focus on the expected value of t_c. If pilot sequence hopping is performed at random and τ=Κ, then t_c follows a geometric distribution, such that (eq. 3)

P(t ^·- (! ) ( 1 -- />r V d = l, 2, . . . .

where P(t_c=d) is the probability that the collision distance is d and p is the probability of a given UE being the next contaminator. The expected value of t E [t_c], is then found as (eq. 4)

oc Hence, the expected collision distance increases with the number of users/pilots per cell, which follows intuition.

Example: To help the understanding of the benefit from pilot sequence hopping, consider the ideal case of a constant channel between BS and UE of interest and a single contaminating neighboring cell. Noise is disregarded in this example, since attention is on decontamination. Moreover, we assume an infinite amount of orthogonal pilot sequences and an infinite amount of users per cell, such that T=K=∞ and E [t_c] =∞, which means contaminating signals in all time slots are independent. For simplicity, we assume χ_η^ΛΗ x_n = 1, such that the estimate in time slot n is (eq. 5)

h_n = h + h!_n

where h_n' is the channel of the contaminator in time slot n. Now consider a new estimator, h_n, which is the average of all estimates until time slot n. Hence, we have (eq. 6)

In this case, the error in the estimate is solely composed of the average of the contaminating signals, which are independent and have variance σ_ο^Λ2. Hence, the variance of the estimation error is σ_ο^Λ2/η$. If pilot sequence hopping had not been performed, the variance of the estimation error had remained σ_ο^Λ2, since h_n' would be constant. Note that the MSE goes towards zero for n→∞, when pilot sequence hopping is performed. This is a result of the fact that a pilot signal in the infinite past carries as much information about the current channel as the most recent pilot signal, in the ideal example of a constant channel. Note also that for finite τ (and K) and thereby finite E [t_c], the variance of the estimation error is lower bounded by σ_ο^Λ2/Κ, since only a maximum of K independent estimates can be achieved. In a more practical example with a time-varying channel, the amount of information carried in a pilot signal decays over time. It is, however, still possible to extract such information using appropriate filtering techniques. For this purpose we have chosen a modified version of the Kalman filter, which is described next. A conventional Kalman filter can be used to track the state, b_n, of a system based on observations, y_n, where (eq. 7)

Y_n = C_nb_n + d_n.

C_n is the measurement matrix of the system and d_n is measurement noise. Moreover, the evolution of the system state must follow (eq. 8) b_n = A_nb_n-i + v_n where A_n is the state transition matrix and v_n is the process noise. In a conventional application of the Kalman filter, A_n is assumed constant and known.

The problem of estimating a time-varying channel based on pilot signals, also termed channel tracking, can be solved using the Kalman filter. The observations as expressed in eq. 2 follow the linear model in eq. 7, where the observation matrix is the transmitted pilot sequence and the tracked state is the channel coefficient. The evolution of the channel coefficient as expressed by Clarke's model does not follow the model in eq. 8. However, it can be transformed into an autoregressive (AR) model with a finite number of coefficients, which follows the form of eq. 8. If the instantaneous velocity of the user of interest, and thereby the autocorrelation function, are known, the AR coefficients can be found using the Yule-Walker equations. However, this cannot be assumed in our case, hence the AR coefficients must be tracked along with the channel state. For this purpose, we must modify the conventional Kalman filter to include an AR model tracker. A first order AR model is applied, since experiments tell us this adequately captures the autocorrelation of the system. Therefore, only a single AR coefficient, a_n, must be tracked. First we state the conventional Kalman filter in our context, where the AR coefficient is assumed known. For all n (eqs. 9-13) :

p_n+-i = «;; ( !. - k,,x, .. )/„. - (1 - On)^*1 σ^Λ2_η and σ^Λ2_ο are noise power and total contamination power (average over time), respectively, which are both assumed known, Ι_τ is the τ^χτ identity matrix and h_n is the estimate of h_n.

For the tracking of the AR coefficient, an approach similar to the one in "K.-Y. Han, S.-W. Lee, J.-S. Lim and K.-M. Sung, Channel estimation for OFDM with fast fading channels by modified Kalman filter, Consumer Electronics, IEEE

Transactions on, 2004, May, vol. 50, p. 443-449" is taken. In this publication the inclusion of an AR coefficient tracker is presented for a Kalman predictor, i.e. a filter with the purpose of predicting the channel, h_n, based on all observations until y_(n-l). In the embodiments of this invention, this approach is extended to take all observations until y_n into account.

The approach is based on calculating the partial derivative (i.e. the gradient Vn) with respect to a_n of the cost function, the mean squared error (MSE), and using this to adjust a_n in the direction of decreasing MSE. The partial derivative of the MSE is (eq. 14) :

here q_n = (3h_n)/(3a_n) and is found by differentiating eq. 12 with respect to _n, such that (eq. 14) q_n = (1 - k,,x_n) (a_ng_n„i - h _{ ) + m.,_; e n Here, m_n = (3k_n)(3a_n), which is found by differentiating eq. 11 with respect to a_n, hence (eq. 16) ni_n ^™ (1 — k_nx_n).s_nx_n R_n

Finally, we introduced s_n = (3p_n)/(3a_n), which is a differentiation of eq. 13 with respect to a_n, giving us (eq. 17)

⁵' +^{1 ~ a} fi ^~~ ^w^x )^n (l ^~~ ^n^n ^~~ 2 _rik X ^. Using Vn, we can adjust a_n as follows (eq. 18)

where μ is a parameter adjusting the convergence speed and the brackets denote truncations. The inner truncation involving v is to avoid dramatic adjustments in situations with a high slope and the outer truncation is to obey 0≤ a_n≤ 1. The need for v will be explained below.

We can now state the modified Kalman filtering algorithm including an AR coefficient tracker (eq. 19) :

For all n:

e = Yn ^~ X^.„.<½-l^n-l_?

a_n— [α._η._ι— #[ _n]i¾

k„ ^ ρ_ηχξη^~ι.

h_n ----- Q,_n h_n—i ~f li _?i€?._ri ,

ϊ^β«— ( ί· k/j -ri - ff-Xji. >

¾ = (1 - k. x_n)(a_n¾f_n_i + _i)

Pn+i = «_« ·^™ k_nx„)i½ + (1. - a_n)²,

Sn+i = <*_«.{! - k_n.x« _n(l -

The model in eq.19 is based on a first order AR model and, therefore, the estimation of the channel coefficient h_n is only dependent on the previous estimated channel coefficient h_n-l. By using an AR model and a Kalman model of first or higher order, the channel coefficient h_n is dependent on one or more previously estimated channel coefficients. According to this embodiment, the autoregressive (AR) model has order d+1 and, therefore, expresses the current and d previous channel coefficients as a function of the d+1 previous channel coefficients. Hence, the present and d previous channel coefficients are defined as h_n = [h_n ... h_(n-d)] T. The process equation for the Kalman filter is expressed as (eq.20):

Α

where I_d is the dxd identity matrix, 0_dxl is a dxl vector of zeros and ν_η^Λρ=[ν_η^Λρ(1) ... v_n p(d + l)] T is the process noise, which is zero mean circularly symmetric Gaussian with covariance matrix Q_n I_d+1, where (eq.21):

rf+1

3 = 1 The corresponding measurement equation for the Kalman filter is expressed based on eq. 2 as follows (eq. 22)

where v_n m is the measurement noise, which is zero mean circularly symmetric Gaussian with covariance matrix σ^Λ2_οΙ_τ + o 2_cX_nX_n H. Here, σ^Λ2_ο and a^2_c are noise power and total contamination power (average over time), respectively, which are both assumed known.

Again, since A_n cannot be assumed constant the varying elements, a^^j, j = l,...,d+ l, must be tracked along with the channel coefficients. Therefore, the conventional Kalman filter is modified to include an AR model tracker. First the conventional Kalman filter is formulated similarly to eqs. 9- 13 as the following eqs. 23-28 :

For all n :

, k_n A_rih_n—_\ + K_rie_{n <}

I_T is the TXT identity matrix and h_n is the estimate of the channel coefficient h n.

For the tracking of the AR coefficients, an approach similar to the one in eqs. 14- 19 is taken. In eqs. 14- 19 the inclusion of a first order AR coefficient tracker is presented for a Kalman predictor, i.e. a filter with the purpose of predicting the channel, h_n, based on all observations (i.e. measurements y) until y_n- l. In this embodiment this approach is extended to higher order AR models taking all observations until y_n into account.

The gradient Vn with respect to A_n of the cost function, the mean squared error (MSE). The gradient is then used adjust A_n in the direction of decreasing MSE. The gradient of the MSE is (eq. 29) :

OA,-,

j) ^'

Using Vn, A_n can be adjusted as follows (eq. 30) :

where μ and v are defined in eq. 18.

The modified Kalman filtering algorithm of order d+1 including an AR coefficient tracker can now be stated as (eq. 31) :

For all n :

X V h -i)

The matrix A_n used for determining the prediction error e_n in eq. 23 and the scalar coefficient a_n used for determining the prediction error e_n in eq. 9 is referred to as the channel model for determining the prediction error.

Numerical Results

The proposed scheme (Estimator) has been simulated and compared to the scheme from "K.-Y. Han ,S.-W. Lee, J.-S. Lim and K.-M. Sung, Channel estimation for OFDM with fast fading channels by modified Kalman filter, Consumer

Electronics, IEEE Transactions on, 2004, May, vol. 50, p. 443-449" (Predictor) and the conventional solutions of least squares (LS) estimation and minimum mean squared error (MMSE) estimation based on a single time slot. The expressions for the LS and MMSE estimators are given in eq. 32 and eq. 33 respectively. An overview of the parameters, which are common for all simulations, is given in Fig. 4. The choice of μ is based on experiments showing that this is a good

compromise between convergence speed and robustness towards variance.

Throughout all simulations, we assume that all users have equal and constant mobility. Moreover, we assume that contaminating signals have zero

autocorrelation between time slots, which is justified by the choice of K=96, such that E [t_c]=96, cf. eq. 4. Equations 32 and 33:

h_n ^'

y_n Initially, results are shown for the conventional Kalman filter expressed in equations 9 through 13. MSE as a function of the user mobility, v, and the AR coefficient, a_n, is shown in Fig. 5. From this figure, it is evident how important it is to have an accurate AR model, which suits the current mobility of the UE of interest. This stresses the need for the modification of the Kalman filter, as proposed above. Moreover, it is seen that the derivative of the MSE with respect to a_n may attain very high values at low a_n. This can cause undesirably high variance in the estimate of the optimal a_n, which motivates the use of a derivative cap, v. Fig. 6 shows a comparison of the simulated estimators with respect to MSE as a function of user mobility when σ_^2=0.6. For both the predictor and the scheme proposed in this work, results where the optimal value of a_n is assumed to be known, have been included. This highlights the performance of the tracker. It is evident that the tracker provides a very good estimate of the optimal AR coefficient. Moreover, it is seen that the proposed scheme outperforms LS and MMSE and performs as well as the predictor at low mobility. At high mobility, the proposed scheme outperforms LS and the predictor, while matching the performance of MMSE. A different perspective is given in Fig. 7. Here the MSE is plotted as a function of the signal-to-interference ratio (SIR), at typical mobility levels as defined by 3GPP. This figure shows how the proposed scheme is able to suppress even very strong contamination at typical mobility. Fig. 8 shows a comparison of the proposed estimator - configured as a first order, second order or third order Kalman filter according to eq. 19 - with the LS estimator and the MMSE estimator, with respect to MSE as a function of the speed of the UE using a mobility model where the user is assumed to move with a constant speed (abscissa of the coordinate system in Fig. 8). Accordingly, the first, second and third order Kalman filters are configured with AR models of first, second or third order, respectively. The results show that a significant

performance improvement is achieved at medium and high levels of mobility when increasing the AR model order from one to two. Further increasing to a third order model yields a more mixed result. At medium mobility, a significant gain is achieved, whereas at higher mobility the performances of the second and third order models are quite close and take turns in being the better. At low mobility, no gain is achieved when increasing the order of the AR model. Compared to the conventional methods of LS and MMSE, the proposed scheme offers a

performance in an entirely different league. The gain decreases as speed increases, but only at unusually high speeds is the gain insignificant.

Fig. 9 shows the system 900 for determining channel coefficients h^kl of channels in the wireless cellular network 100. The system 900 comprises a pilot generation unit 901 configured to assign pilot sequences Xn to the users UE and a pilot processing unit 902 configured to filter the pilot sequences received from a user of interest UE. The pilot generation unit 901 may be configured to randomly assign pilot sequences to the users as described in the summary and in the embodiments described above. Accordingly, the pilot generation unit 901 may be configured as a processing means to generate the seed values and to transmit the seed values or generate an input to a transmitter unit of the base station BS to invoke the transmission of the seed values via the antenna 103. Whether, the pilot sequences are generated by transmission of seed values, or by other methods, the process is referred to as an assignment of pilot sequences to the users by use of the pilot generation unit 901 or different pilot generation units. The pilot processing unit 902 may be configured to filter the pilot sequences received from a user of interest, i.e. received by a given base station of interest, according to the Kalman filter examples. Pilot sequences received from a user of interest refer to the pilot sequences transmitted by the user of interest being contaminated by pilot sequences from other users in the cell of interest and/or other cells and received by a base station.

However, the pilot processing unit 902 could be configured to filter the pilot sequences using other methods than Kalman filters. For example, the pilot processing unit 902 could be configured with a filter bank containing a plurality of filters for filtering the pilot sequences (yn⁰) received from a user of interest. Each of the filters are configured with filter parameters to provide the best estimation of channel coefficients h^kl for a given range of velocities of the user of interest. Accordingly, the pilot processing unit 902 is configured to select one of the filters dependent on the actual velocity of the user of interest. The filter may be configured according to known methods, e.g. as causal FIR filter.

The velocity may be estimated by known methods. Specifically, the velocity may be determined based on a calculation of the autocorrelation of the channel estimates since there is relationship between the velocity and the autocorrelation.

Accordingly, the pilot processing unit 902 may be configured according to the modified Kalman filters defined in eq. 19 or eq. 31, the filter bank or other methods. The pilot sequences received by a base station from a user of interest, for one or more users in a cell of interest, over a period of time including at least two pilot periods are used for determining channel coefficient of the channel of the user of interest. For the modified Kalman filter in eq. 19, the channel coefficient is determined over a period of time including the previous pilot period and the present pilot period, i.e. the channel coefficient is determined based on the previously estimated channel coefficient h_n-l and the presently received pilot sequence ^°. For the modified Kalman filter in eq. 31, the channel coefficient is determined over a period of time including the one or more previous pilot periods and the present pilot period, i.e. the channel coefficient is

determined based on one or more previously estimated channel coefficient h_n-l and at least the presently received pilot sequence y^°. Due to the randomly assigned pilot sequences x ^tne P''^ot sequences become de-correlated over time. The filter of the pilot processing unit 902 utilizes this de- correlation so that the contamination caused by the other non-orthogonal or identical pilot sequences from the other users can be reduced.

Thus, in general the filter is configured to exploit that the contamination from contaminating non-orthogonal or identical pilot sequences pilots are decorrelated over time (i.e. over subsequent pilot periods), so that the influence of other channel coefficients of other pilot sequences transmitted by other users (of the cell of interest and/or of other cells) on the channel coefficient of the user of interest are filtered out, substantially filtered out or at least reduced.

Orthogonal pilot sequences x ¹ may be assigned randomly to at least some of the users in a first cell (Cell 0), and pilot sequences may be assigned randomly to at least some of the users in a second cell (Cell 1) so that pilot sequences assigned to the second cell are non-orthogonal with the pilot sequences assigned to at least some of the users in a first cell. Accordingly, the same set of pilot sequences may be assigned randomly among users in the first cell as well as in the second cell. In other words, a first set of the random pilot sequences may be assigned to the users in one or more cells in a first pilot period, and a second set of the random pilot sequences may be assigned to the users in one or more cells in a subsequent second pilot period, where the first and second set contains the same pilot sequences, but assigned randomly among the users for each pilot period.

The same pilot generation unit 901 may assign pilot sequences to users in different cells.

Alternatively, a first pilot generation unit may be configured to assign pilot sequences randomly among the users of a first cell, and a second pilot generation unit may configured to assign pilot sequences randomly among the users of a second cell independently of the first pilot generation unit. The pilot sequences assigned by the first and second pilot generation unit may be selected from the same group of pilot sequences. The users, such as user equipment or cell phones, located in one or more cells 101, transmits the assigned pilot sequence during the present pilot period. The assigned pilot sequence are received by one or more antennas 103 of the base station in a cell, e.g . the first cell (Cell 0).

The implementation of the filter of the pilot processing unit 902 as a Kalman filter may imply that the filter is configured so that the determination of the channel coefficient is based on one or more previously determined or estimated channel coefficients. The previous channel coefficients are determined by the filter based on previous pilot sequences received from a user of interest during previous pilot periods. Since the mobility, i.e. velocity or changes in velocity, of the user of interest is relatively low (below 300 km/h) the present channel coefficient is sufficiently correlated with previous actual channel coefficients so that the estimation of the present channel coefficient may be improved by including one or preferably two or more previously determined or estimated channel coefficients in the estimation.

Furthermore, the implementation of the filter of the pilot processing unit 902 as a Kalman filter may imply that the filter is configured so that the determination of the channel coefficient is based on a prediction error between the received pilot sequences y_n feO

and a prediction of the received pilot sequences based on one or more previously determined channel coefficients h_n-l, the channel model An and the assigned pilot kl

sequences X_n . Accordingly, for a single user the prediction error is determined as the difference between the received pilot sequence yn from the user of interest and the prediction of the received pilot sequence from the user of interest. The channel model An may refer to the scalar a_n of the Kalman model in eq. 19 or the matrix A_n of the Kalman model in eq. 23.

Advantageously, the filter of the Kalman model may be configured so that the channel model An is updated over time based on a gradient of a mean value of the prediction error, wherein the gradient is determined as the derivative mean value of the prediction error with respect to the channel model An.

The pilot generation unit 901 and pilot processing unit 902 may be implemented as computer software on a computer, possibly different computers, wherein the software contains computer program coded instructions capable of instructing the computer(s) to carry out the functions defined in the software. Alternatively, part or all of the functions of the pilot generation unit 901 and pilot processing unit 902 may be implemented as hardware in an electronic circuit or in firmware.

Conclusion

A solution to pilot contamination in channel estimation, which is a major challenge in massive MIMO systems has been presented. It is based on a combination of a pilot sequence hopping scheme and a modified Kalman filter. The pilot sequence hopping scheme involves random shuffling of the assigned pilot sequences within a cell, which ensures decorrelation in the time dimension of the contaminating signals. This is essential, since it enables subsequent filtering to suppress the contamination. For this filtering, the Kalman filter has been chosen, due to its ability to track a time-varying state. However, a conventional Kalman filter is not able to adapt to changes in the underlying model, which is necessary when users have unknown and varying levels of mobility. For this problem we have presented a modified Kalman filter, which can adapt the underlying model based on a minimization of the mean squared error. Numerical evaluations show that the proposed solution can suppress a significant portion of the contamination at low and moderate levels of mobility. Even at high mobility, i.e. car speeds of 100 to 130 km/h, the proposed solution can provide a noticeable gain over conventional estimation methods. Embodiments of invention can be implemented by means of electronic hardware, software, firmware or any combination of these. Software implemented

embodiments or features thereof may be arranged to run on one or more data processors and/or digital signal processors. Software is understood as a computer program which may be stored/distributed on a suitable computer-readable medium, such as an optical storage medium or a solid-state medium supplied together with or as part of other hardware, but may also be distributed in other forms, such as via the Internet or other wired or wireless telecommunication systems. Accordingly, the computer-readable medium may be a non-transitory medium. The individual elements of an embodiment of the invention may be physically, functionally and logically implemented in any suitable way such as in a single unit, in a plurality of units or as part of separate functional units. The invention may be implemented in a single unit, or be both physically and functionally distributed between different units and processors. A unit may constitute a control system or subunits thereof.

Although the present invention has been described in connection with the specified embodiments, it should not be construed as being in any way limited to the presented examples. The scope of the present invention is to be interpreted in the light of the accompanying claim set. In the context of the claims, the terms "comprising" or "comprises" do not exclude other possible elements or steps. Also, the mentioning of references such as "a" or "an" etc. should not be construed as excluding a plurality. The use of reference signs in the claims with respect to elements indicated in the figures shall also not be construed as limiting the scope of the invention. Furthermore, individual features mentioned in different claims, may possibly be advantageously combined, and the mentioning of these features in different claims does not exclude that a combination of features is not possible and advantageous.

Claims

CLAIMS kl

1. A system (100) for determining channel coefficients (h ) of channels in a wireless cellular network, wherein the wireless cellular network comprises a plurality of cells (101), wherein each cell comprises a base station (BS) configured to communicate with users (UE) within the cell, and wherein a communication path between one of the users and one of the base stations define one of the channels, the system comprises:

- a pilot generation unit (901) configured to assign pilot sequences ( ^) ^{t0 tne} users, wherein the pilot sequences are assigned randomly among the users, and

- a pilot processing unit (902) configured to filter the pilot sequences ( n⁰) received from a user of interest, for one or more users in a cell of interest, over a period of time including at least two pilot periods, so that the channel coefficient of the channel of the user of interest is determined, wherein the pilot sequences received from the user of interest are contaminated by other non-orthogonal or identical pilot sequences from other users of the cell of interest or other cells, wherein the filter is configured so that the contamination caused by the other non-orthogonal or identical pilot sequences from the other users is reduced.

2. A system according to claim 1, wherein the pilot sequences assigned to at least some of the users in a first cell are orthogonal, and wherein the pilot sequences assigned to at least some of the users in a second cell are non-orthogonal with the pilot sequences assigned to at least some of the users in a first cell.

3. A system according to any of the preceding claims, wherein each one of the users, such as user equipment or cell phones, is configured to transmit the assigned pilot sequence during the present pilot period to the base station.

4. A system according to any of the preceding claims, wherein a first pilot generation unit is configured to assign the random pilot sequences to the users of a first cell, and wherein a second pilot generation unit is configured to assign the random pilot sequences to the users of a second cell independently of the first pilot generation unit.

5. A system according to any of the preceding claims, wherein the pilot generation unit is configured to assign a first set of the random pilot sequences to the users in a first pilot period, and configured to assign a second set of the random pilot sequences to the users in a subsequent second pilot period, wherein the first and second set contains the same pilot sequences, but where the pilot sequences of each of the sets are assigned randomly among the users.

6. A system according to any of the preceding claims, wherein the filter is configured to exploit that the contamination from contaminating non-orthogonal or identical pilot sequences pilots is decorrelated, so that the influence of other channel coefficients of other pilot sequences transmitted by other users of the other cells on the channel coefficient of one of the users of the cell are filtered out, substantially filtered out or at least reduced.

7. A system according to any of the preceding claims, wherein the filter is configured so that the determination of the channel coefficient is based on one or more previously determined channel coefficients.

8. A system according to any of the preceding claims, wherein the filter is configured so that the determination of the channel coefficient is based on a prediction error (en) between the received pilot sequences (y_n ) and a prediction of the received pilot sequences, wherein the prediction is based on one or more previously determined channel coefficients (h_n-l), a channel model (a_n, A_n) and the assigned pilot sequences ( ^) -

9. A system according to claim 8, wherein the filter is configured so that the channel model (An) is updated over time based on a gradient of a mean value of the prediction error, wherein the gradient is determined as the derivative mean value of the prediction error with respect to the channel model.

10. A system according to any of the preceding claims, wherein the filter is configured to filter the contaminated signal y_n k0 received by the base station of interest,

by use of a Kalman filter model, yn = Cn bn + dn, for determining the channel coefficients h n ^ kO of the channel of the user of interest, wherein Cn represent the transmitted pilot sequences, χ_η^ΛΙ 0 bn represent the channel coefficients h_n k0, and wherein n is an index of individual periods or time slots, yn represents vector values of the contaminated pilot signal received by the base station, dn is measurement noise and contaminating signals (Sum(h_n kl x_n^-k\) +z_n k0) from users in other cells applying the same pilot sequence as the user of interest, and wherein the evolution of the system state xn follows the model, xn = An xn- 1 + vn, wherein An is a state transition matrix an vn is process noise, and wherein the Kalman filter is processed so that estimates of the one or more channel coefficients xn are determined.

11. A system according to claim 10, wherein the Kalman filter is configured to track the channel coefficients xn and the state transition matrix An according to

and a modified Kalman filter method specified in the detailed description.

12. A system according to claim 10 or 11, wherein a solution to the Kalman filter model is given by,

^::- y,i — X-u. d n ··· .[ " /; ··· 1 -

H

R_n - ·· ΧηΡ,,χ, '! ! · π~ Ι- + σ₍ ²χ,

V„ -

n =

m_n = - ( 1 k_nx }-s_nx_n J¾_rt ,

Qn = = (1 - k_nx ) (a_n<¾_i + Λ

^6> +i — ^a ( ^ ^~~ k _ix_n)-s_ri.(l — x_n k_ft )— 2 _nk_n.x p_n .

13. A method for determining channel coefficients of channels in a wireless cellular network, wherein the wireless cellular network comprises a plurality of cells, wherein each cell comprises a base station configured to communicate with users within the cell, and wherein a communication path between one of the users and one of the base stations define one of the channels, the method comprises:

- in a first pilot period and for a first cell, assigning pilot sequences to the users, wherein the pilot sequences are assigned randomly among the users so that the contaminating pilot signals are decorrelated, - in the first pilot period and for the first cell, transmitting the assigned pilot sequences from the users to the base station,

- in the first pilot period and for the first cell, receiving the transmitted pilot sequences,

- in the first pilot period and for the first cell, filtering the received pilot sequences from users of the first cell and other cells, for one or more of the users in the first cell, including at least one pilot period from a previous pilot period, so that the channel coefficients are determined for each of the channels of the users, wherein the filter is configured so that the contaminating pilot signals of other users of other cells are filtered out or reduced.

14. A method according to claim 10, wherein the method further comprises

- in the first pilot period and for a second cell, assigning pilot sequences to the users, wherein the pilot sequences are assigned randomly among the users so that the contaminating pilot signals are decorrelated, wherein the assigning of pilot sequences to users of the first cell is performed independently of the assigning of pilot sequences to users of the second cell,

- in the first pilot period and for the second cell, transmitting the assigned pilot sequences from the users to the base station, - in the first pilot period and for the second cell, receiving the transmitted pilot sequences,

- in the first pilot period and for the second cell, filtering the received pilot sequences from users of the first cell and other cells, for one or more of the users in the first cell, including at least one pilot period from a previous pilot period, so that the channel coefficients are determined for each of the channels of the users, wherein the filter is configured so that the contaminating pilot signals of other users of other cells are filtered out or reduced.

15. A method according to claim 13 or 14, wherein the method further comprises

- performing the steps of claim 13 and/or of claim 14 in a subsequent second pilot period, independently of the steps performed during the first pilot period.

16. A computer program configured for enabling a processor running the program to carrying out of a method according to claim 13.