Patent Description:
The document "<NPL>, discloses base station receiver chains for MIMO uplink according to two architectures: centralized and fully decentralized.

Future wireless communications networks will be expected to support communications routinely and efficiently with a wider range of devices associated with a wider range of data traffic profiles and types than current systems are optimised to support. For example it is expected future wireless communications networks will be expected to efficiently support communications with devices including reduced complexity devices, machine type communication (MTC) devices, high resolution video displays, virtual reality headsets and so on.

In view of the desire to support a wide variety of traffic profiles and system different types of wireless communications techniques are being explored. These include using multiple antennas to form an array which can be used to improve a likelihood of correctly communicating data. One such technique is referred to as Multiple Input Multiple Output (MIMO) in which a plurality of receiver antennas can be used to detect signals carrying the data. However adopting MIMO systems can create technical challenges.

According to example embodiments there is provided a method of receiving data transmitted by a plurality of communications devices, the method comprising receiving at each of a plurality of M antennas reference signals transmitted by each of a plurality of K communications devices, and processing by each of a plurality of antenna modules the reference signals, each of the antenna modules being connected to a corresponding one of the plurality of antennas. The processing by each of the antenna module includes estimating for each of the K detected reference signals received from the K communications devices a sample of a radio channel through which the received signals have passed, generating for each of the K samples of the radio channel a KxK partial matrix forming a part of a signal processing matrix for performing zero forcing equalisation of the received signals, and transmitting via a communications interface the partial matrix KxK from each of the M antenna modules to a central processing unit. The method also includes detecting by the central processing unit the data from the received radio signals using the MxK equalisation matrix formed by combining the KxK partial matrices from each of the M antenna modules.

According to example embodiments the partial matrices are communicated separately from each antenna module, which may be done sequentially in each of a plurality of successive time periods. Accordingly there can be provided a significant reduction of a bandwidth requirement between the antenna modules and the central processing units.

The network <NUM> includes a plurality of base stations <NUM> connected to a core network part <NUM>. Each base station provides a coverage area <NUM> (e.g. a cell) within which data can be communicated to and from communications devices <NUM>. Data is transmitted from the base stations <NUM> to the communications devices <NUM> within their respective coverage areas <NUM> via a radio downlink. Data is transmitted from the communications devices <NUM> to the base stations <NUM> via a radio uplink. The core network part <NUM> routes data to and from the communications devices <NUM> via the respective base stations <NUM> and provides functions such as authentication, mobility management, charging and so on. Communications devices may also be referred to as mobile stations, user equipment (UE), user terminals, mobile radios, terminal devices, and so forth. Base stations, which are an example of network infrastructure equipment / network access nodes, may also be referred to as transceiver stations / nodeBs / e-nodeBs, g-nodeBs (gNB) and so forth. In this regard different terminology is often associated with different generations of wireless telecommunications systems for elements providing broadly comparable functionality. However, example embodiments of the disclosure may be equally implemented in different generations of wireless telecommunications systems such as <NUM> or new radio as explained below, and for simplicity certain terminology may be used regardless of the underlying network architecture. That is to say, the use of a specific term in relation to certain example implementations is not intended to indicate these implementations are limited to a certain generation of network that may be most associated with that particular terminology.

<FIG> is a schematic diagram illustrating a network architecture for a new RAT wireless communications network / system <NUM> based on previously proposed approaches which may also be adapted to provide functionality in accordance with embodiments of the disclosure described herein. The new RAT network <NUM> represented in <FIG> comprises a first communication cell <NUM> and a second communication cell <NUM>. Each communication cell <NUM>, <NUM>, comprises a controlling node (centralised unit) <NUM>, <NUM> in communication with a core network component <NUM> over a respective wired or wireless link <NUM>, <NUM>. The respective controlling nodes <NUM>, <NUM> are also each in communication with a plurality of distributed units (radio access nodes / remote transmission and reception points (TRPs)) <NUM>, <NUM> in their respective cells. Again, these communications may be over respective wired or wireless links. The distributed units <NUM>, <NUM> are responsible for providing the radio access interface for communications devices connected to the network. Each distributed unit <NUM>, <NUM> has a coverage area (radio access footprint) <NUM>, <NUM> where the sum of the coverage areas of the distributed units under the control of a controlling node together define the coverage of the respective communication cells <NUM>, <NUM>. Each distributed unit <NUM>, <NUM> includes transceiver circuitry for transmission and reception of wireless signals and processor circuitry configured to control the respective distributed units <NUM>, <NUM>.

A communications device or UE <NUM> is represented in <FIG> within the coverage area of the first communication cell <NUM>. This communications device <NUM> may thus exchange signalling with the first controlling node <NUM> in the first communication cell via one of the distributed units <NUM> associated with the first communication cell <NUM>. In some cases communications for a given communications device are routed through only one of the distributed units, but it will be appreciated in some other implementations communications associated with a given communications device may be routed through more than one distributed unit, for example in a soft handover scenario and other scenarios.

Thus example embodiments of the disclosure as discussed herein may be implemented in wireless telecommunication systems / networks according to various different architectures, such as the example architectures shown in <FIG> and <FIG>. It will thus be appreciated the specific wireless communications architecture in any given implementation is not of primary significance to the principles described herein. In this regard, example embodiments of the disclosure may be described generally in the context of communications between network infrastructure equipment / access nodes and a communications device, wherein the specific nature of the network infrastructure equipment / access node and the communications device will depend on the network infrastructure for the implementation at hand. For example, in some scenarios the network infrastructure equipment / access node may comprise a base station, such as an LTE-type base station <NUM> as shown in <FIG> which is adapted to provide functionality in accordance with the principles described herein, and in other examples the network infrastructure equipment / access node may comprise a control unit / controlling node <NUM>, <NUM> and / or a TRP <NUM>, <NUM> of the kind shown in <FIG> which is adapted to provide functionality in accordance with the principles described herein.

A better appreciation provided by the example embodiments can be gained from reviewing a proposed wireless access interface according to 3GPP LTE/<NUM> and NR/<NUM> can be found in [<NUM>] and [<NUM>]. However it will be appreciated that the wireless access interface provides physical communications resources including shared channels for both uplink and the downlink which may be accessed by communicating appropriate control signalling as those acquainted with LTE will appreciate. Equally a wireless access interface for the <NUM> Standard as represented in <FIG> may be similarly formed and may use OFDM on the downlink and OFDM or SC-FDMA on the uplink.

A more detailed illustration of a UE <NUM> and an example network infrastructure equipment <NUM>, which may be thought of as a gNB <NUM> or a combination of a controlling node <NUM> and TRP <NUM>, is presented in <FIG>. As shown in <FIG>, the UE <NUM> is shown to transmit uplink data to the infrastructure equipment <NUM> via grant free resources of a wireless access interface as illustrated generally by an arrow <NUM>. As with <FIG> and <FIG>, the infrastructure equipment <NUM> is connected to a core network <NUM> via an interface <NUM> to a controller <NUM> of the infrastructure equipment <NUM>. The infrastructure equipment <NUM> includes a receiver <NUM> connected to an antenna <NUM> and a transmitter <NUM> connected to the antenna <NUM>. Correspondingly, the UE <NUM> includes a controller <NUM> connected to a receiver <NUM> which receives signals from an antenna <NUM> and a transmitter <NUM> also connected to the antenna <NUM>.

The controller <NUM> is configured to control the infrastructure equipment <NUM> and may comprise processor circuitry which may in turn comprise various sub-units / sub-circuits for providing functionality as explained further herein. These sub-units may be implemented as discrete hardware elements or as appropriately configured functions of the processor circuitry. Thus the controller <NUM> may comprise circuitry which is suitably configured / programmed to provide the desired functionality using conventional programming / configuration techniques for equipment in wireless telecommunications systems. The transmitter <NUM> and the receiver <NUM> may comprise signal processing and radio frequency filters, amplifiers and circuitry in accordance with conventional arrangements. The transmitter <NUM>, the receiver <NUM> and the controller <NUM> are schematically shown in <FIG> as separate elements for ease of representation. However, it will be appreciated that the functionality of these elements can be provided in various different ways, for example using one or more suitably programmed programmable computer(s), or one or more suitably configured application-specific integrated circuit(s) / circuitry / chip(s) / chipset(s). As will be appreciated the infrastructure equipment <NUM> will in general comprise various other elements associated with its operating functionality.

Correspondingly, the controller <NUM> of the UE <NUM> is configured to control the transmitter <NUM> and the receiver <NUM> and may comprise processor circuitry which may in turn comprise various sub-units / sub-circuits for providing functionality as explained further herein. These sub-units may be implemented as discrete hardware elements or as appropriately configured functions of the processor circuitry. Thus the controller <NUM> may comprise circuitry which is suitably configured / programmed to provide the desired functionality using conventional programming / configuration techniques for equipment in wireless telecommunications systems. Likewise, the transmitter <NUM> and the receiver <NUM> may comprise signal processing and radio frequency filters, amplifiers and circuitry in accordance with conventional arrangements. The transmitter <NUM>, receiver <NUM> and controller <NUM> are schematically shown in <FIG> as separate elements for ease of representation. However, it will be appreciated that the functionality of these elements can be provided in various different ways, for example using one or more suitably programmed programmable computer(s), or one or more suitably configured application-specific integrated circuit(s) / circuitry / chip(s) / chipset(s). As will be appreciated the communications device <NUM> will in general comprise various other elements associated with its operating functionality, for example a power source, user interface, and so forth, but these are not shown in <FIG> in the interests of simplicity.

As those familiar with radio access technologies will appreciate, Multiple Input Multiple Output (MIMO) systems are known for use in radio communications in order to improve a likelihood of correctly receiving data transmitted from a communications device. There are various forms of MIMO systems which also conclude Single Input Multiple Output (SIMO) and Multiple Input Single Output (MISO) systems. MIMO systems are particularly useful where the signals transmitted are carried by a wireless access interface configured to support Orthogonal Frequency Division Multiple access.

Massive MIMO systems for uplink detection in mobile communications systems represent an arrangement in which a very large number of antennas are used at the receiver in order to create a much more accurate estimate of a transmission channel formed from channel state information (CSI). With massive MIMO systems, the number of antennas may be hundreds or thousands and these are used in combination for received signals in order to build up a much more detailed estimate of a channel impulse response based on the channel state information. According to this arrangement base band data from all antenna modules is routed to a central processing unit in order to be processed. The central processing unit processes that base band data so that channel estimates for each of the antennas can be combined in order to improve a detection process. Typically the detection process requires a training or estimation phase in which channel state information acquired from channel reference symbols or pilot symbols are used to perform a sample of each channel at each antenna which are then combined to generate a highly accurate estimate of the channel. Data is then recovered from received signals in a detection phase by applying the channel estimate to the received signals in order to equalise the signals and recover the data. The detection phase may also be called a payload data phase.

<FIG> provides an example of such a massive MIMO system. As shown in <FIG> each of the UEs shown in <FIG>, <FIG> and <FIG> are transmitting data as uplink signals to a base station or gNB <NUM>. The gNB <NUM> is provided with a plurality of antennas <NUM> which form an antenna array <NUM>. As indicated above, for a massive MIMO scheme the number of antennas in the antenna array may be hundreds or thousands although only six antennas <NUM> are shown which are numbered <NUM> to N. In the following description the number of antennas in the massive antenna array <NUM> is designated M.

Embodiments of the present techniques relate to a massive MIMO scheme in which the formation of a signal processing matrix (Gramian matrix G) for implementing a zero forcing equalisation scheme for a MIMO system is partially decentralised in that the formation of the signal processing matrix is partially formed in signal processing modules associated with each antenna. The signal processing modules are referred to as antenna modules. As explained in [<NUM>], as a result of the large number of antennas which are generating signal processing samples, a conventional arrangement is to transmit each of the samples to a central processing unit where the signal processing matrix for equalisation is formed. The signal processing matrix is known as a Gramian matrix, which is required to perform equalisation according to the channel state estimates for each of the antennas. According to a centralised architecture, the central processing unit within a receiver in the gNB collects all channel state information generated from each of the antenna modules which allows an optimal estimation of the signal processing matrix required to perform equalisation of the received signals. The central processing unit also detects and decodes the samples of the base band signal samples to recover the data. However each of the antenna modules can perform processing of the radio frequency signals, that is radio frequency signal filters and down converters as well as analogue to digital converters and OFDM processing. As indicated above, because of the large number of antennas, the amount of data required to be communicated on an interface between the antenna modules and the central processing unit, requires a significant bandwidth. The bandwidth required is as a function of number of antennas M. In contrast to a centralised architecture, a decentralised system provides for processing the channel state information locally at the antenna modules. However according to this arrangement, the full channel state information is not available.

Embodiments of the present technique can provide an arrangement in which formation of the signal processing matrix required for equalising uplink radio signals is partially decentralised thereby substantially reducing the bandwidth requirements for connecting the antenna modules to the central processing unit. Moreover, each of the plurality of partial matrices is broken up into K columns and transmitted in K time slots from the antenna modules to the central processing unit thereby reducing the bandwidth requirement for communicating signal samples in order to generate the signal processing matrix for equalisation.

<FIG> provides an example embodiment of the present technique. As shown in <FIG>, the antenna array <NUM> comprises a number of antennas N but for illustration purposes only, only four antennas numbered (<NUM>, <NUM>, <NUM> and m) are shown <NUM>, <NUM>, <NUM>, <NUM>. Each of the antennas <NUM>, <NUM>, <NUM>, <NUM> includes an antenna module <NUM>, <NUM>, <NUM>, <NUM>. Each of the antenna modules <NUM>-<NUM> is connected to a central processing unit <NUM>. The connection between the antenna modules <NUM>-<NUM> to the central processing unit <NUM> may be via formed in various ways and is represented generally as a formation point <NUM>. In some examples the formation point <NUM> may be formed as a summation point <NUM>. The corresponding circuitry may be called summation point circuitry. In particular the summation point <NUM> or the summation point circuitry may be formed as a binary tree so that the output from one antenna module is combined with the output from its neighbour and thereafter combination is performed according to a tree structure.

As indicated above, in order to detect and recover data transmitted on an uplink using a massive MIMO system, a training phase is first performed which estimates the channel and thereafter a data detection phase is performed in which the channel is equalised and the data is recovered from the received OFDM symbols carrying the data. In particular, the method may include re-using the same summation point circuitry which has been used during a training phase during a data detection phase. The data detection phase may also be called payload data phase. When operating in the payload data phase values from each of the M antenna modules may be combined using the summation point circuitry and error control decoding and/or Hybrid Automatic Repeat Request based on the combined values may be implemented.

According to example embodiments, a zero forcing equalisation technique is used which requires the formation of Gramian matrix G=HHH. In accordance with example embodiments the Gramian matrix is formed at the central processing unit <NUM> by combining partial versions of the Gramian matrix hm*hmT formed at each of the N antennas modules. Each of the antenna modules generates K samples of the channel from reference symbols or pilot symbols transmitted with the uplink data. In accordance with the present embodiments K is the number of UEs <NUM> shown in <FIG>. For each of the K UEs <NUM>, K signal samples are generated for each of the antennas. Each of the antenna modules <NUM>-<NUM> then forms a KxK matrix hm*hmT which is a matrix with K columns and K samples. The reference symbols or pilots, which may be considered as reference signals, may be discarded at each of the plurality of antenna modules upon said generating of the respective KxK partial matrix, while the KxK partial matrix may be stored for transmission to the central processing unit (<NUM>).

It has been found that transmitting each of the K columns of the K complex samples of the KxK partial matrix sequentially may allow for dispensing with a dedicated circuitry for combining the partial matrix at the central processing unit. Instead, circuitry also used during a payload data phase may be used. This enables to re-use such circuitry in both the payload data phase, as well as the training phase. Typically, each antenna contributes, at the very minimum, with a scalar value to the payload analysed by the central processing unit, which may be responsible for error control decoding, HARQ, etc. These individual antenna contributions are typically summed up before being formally presented to the central processing unit to maintain low interconnection bandwidth.

As shown in <FIG> schematically for one of the antenna modules <NUM> on an interface <NUM>, each of the K columns <NUM> of K samples is transmitted in K timeslots as represented by boxes <NUM> with the columns represented as long boxes <NUM>. As explained above, the formation point <NUM> may be arranged in the form of a binary true, each of the columns is summed with the columns from other sub-matrices generated by the other antenna modules so that at the central processing unit <NUM> the samples are received over the K timeslots which forms during transmission the Gramian equalisation matrix which can then be applied to equalise the data. In particular, the same formation point <NUM> used during a payload data phase may also be used for the transmission of the partial matrices.

In an embodiment, the signal processing matrix may be an estimate of the Gramian equalisation matrix formed by estimates of the KxK partial matrices of the Gramian partial matrices, wherein the estimates of the KxK partial matrices are formed locally at the antenna modules. By using the estimate, a noise contribution can be taken into account. The noise contribution can be described by a noise vector associated with each of the M antenna elements.

Embodiments of the present technique therefore provide an arrangement in which the antenna modules <NUM>-<NUM> are adapted to generate a partial or local signal processing matrix which is then communicated as a sequences of columns over K timeslots to the central processing unit <NUM> which combines the partial matrices into the signal processing or Gramian matrix to perform zero forcing equalisation of the received data signals.

It will further be appreciated that the principles described herein are not applicable only to LTE-based wireless telecommunications systems, but are applicable for any type of wireless telecommunications system that supports a random access procedure comprising an exchange of random access procedure messages between a communications device and a base station.

Further particular and preferred aspects of the present invention are set out in the accompanying independent and dependent claims. It will be appreciated that features of the dependent claims may be combined with features of the independent claims in combinations other than those explicitly set out in the claims.

Thus, the foregoing discussion discloses and describes merely exemplary embodiments of the present invention. As will be understood by those skilled in the art, the present invention may be embodied in other specific forms without departing from the spirit or essential characteristics thereof. Accordingly, the disclosure of the present invention is intended to be illustrative, but not limiting of the scope of the invention, as well as other claims. The disclosure, including any readily discernible variants of the teachings herein, define, in part, the scope of the foregoing claim terminology such that no inventive subject matter is dedicated to the public.

Respective features of the present disclosure are defined by the following numbered paragraphs: Paragraph <NUM>.

Abstract-Algorithms for Massive MIMO uplink detection are typically based on a centralized approach, by which baseband data from all antenna modules need to be routed to a central node in order to be processed. In the case of Massive MIMO, where hundreds or thousands of antennas are expected in the base-station, this architecture leads to a bottleneck, with critical limitations in terms of interconnection bandwidth requirements. Recently, decentralized architectures have been proposed to alleviate this problem, where channel-state-information (CSI) is obtained locally in each antenna node and not shared, in order to reduce bandwidth. On the other hand, it is well known that Massive MIMO performance is very sensitive to the CSI estimate. However, in the literature, ideal CSI is typically assumed in decentralized systems, which is not only far from reality but also limits the generality of the analysis. This paper proposes a decentralized (a term that will be defined in the main body of the paper) architecture with the following main features: (i) the channel matrix is not made available at any single node, (ii) there is no inter-communication among antennas, (iii) the architecture used during the payload data phase, is reused to provide a certain statistic to a processing node, (iv) a non-standard channel estimation problem based on said statistic arises, (v) a matrix inversion is needed (for zero-forcing purposes) at said processing node. A hefty share of the paper is devoted to (iv) above. Index Terms-Massive MIMO, decentralized, detection, zero-forcing, wishart, MMSE, ML, MAP.

Massive MIMO is one of the most relevant technologies in wireless communications [<NUM>]. High spectral efficiency and improved link reliability are among the key features of this technology, making it a key enabler to exploit spatial diversity far beyond traditional MIMO systems by employing a large scale antenna array with hundreds or thousands of elements. This allows for unprecedented spatial resolution and high spectral efficiency, while providing simultaneous service to several users within the same time-frequency resource.

Despite all advantages of Massive MIMO, there are challenges from an implementation point of view. Uplink detection algorithms like zero-forcing (ZF) typically rely on a centralized architecture, where baseband samples and channel state information (CSI) are collected in a central processing node for further matrix inversion and detection. Physical connections are needed between antenna modules and the central node to carry the required data. This approach, that is perfectly valid for a relatively low number of antennas, shows critical limitations when the array size increases, with the interconnection bandwidth as the main bottleneck in the system.

Initial Massive MIMO prototypes [<NUM>] [<NUM>] were the first to face this problem and solutions were proposed, but these were not optimal [<NUM>]. There are recent proposals to address this limitation, such as [<NUM>] and [<NUM>]. In [<NUM>], a partial decentralized (PD) solution is put forth, which is able to achieve exactly the same estimates (and therefore performance) as linear detectors such as maximum ratio combing (MRC), ZF and L-MMSE. In order to achieve this, obtaining CSI is required prior to detection. However, due to scalability reasons, decentralized architectures do not allow to collect all CSI at the same point and that limits the quality of channel estimates.

It is recognized that the full benefits of massive MIMO, such as high spectrum efficiency, heavily rely on accurate CSI estimation [<NUM>]. Non-ideal CSI cannot reach perfect inter-user interference (IUI) cancellation, with negative consequences, especially as the number of users grows. Unfortunately, channel estimation is not typically covered in the decentralized debate and ideal CSI is always assumed to be available.

In this work we argue that much of the centralized vs. non-centralized discussion is unnecessary. In short, our arguments are as follows: The non-centralized discussion seems to be revolving around the training phase in general, and to avoid collecting full CSI at any given node in particular. However, there is also a payload data phase, and during this phase it can be assumed that each antenna contributes, at the very minimum, with a scalar value to a central processing unit (responsible for, e.g., error control decoding, HARQ, etc.). In order to maintain low interconnection bandwidth, these antenna contributions are likely to be summed up before being formally presented to the central processing unit. That said, we observe that there is an easy way to transfer a statistic that is sufficient for demodulation purposes, using the same circuitry used during the payload data phase. Such a method can, according to a separate discussion in the next section, be classified as non-centralized since it <NUM>) does not store the full CSI at any given node, and <NUM>) it does not expand the interconnections between antennas and processing unit beyond what is needed for payload data. At the central processing node, channel estimation and channel inversion remains, but we argue that these are fairly minor tasks compared to other baseband tasks needed at such a node. The main message we try to convey is that, in our view, meeting <NUM>) and <NUM>) is sufficient for a scheme to be classified as non-centralized.

The remainder of the paper is organized as follows. A system model and a review of linear detection methods in Massive MIMO is presented in section II. In III we compare centralized and decentralized systems and motivates the research done in this article. The proposed channel estimation method and the different estimators are presented in IV. Results are presented in V. Finally, section VI presents the conclusions of this publication.

Notation: In this paper, lowercase, bold lowercase and upper bold face letters stand for scalar, column vector and matrix, respectively. The operations (. )H denote transpose, conjugate and conjugate transpose respectively. Vectors are assumed to be columns. <NUM>F̃<NUM> is the hypergeometrical function of matrix argument defined as in [<NUM>], Γ̃m denotes the complex multivariate gamma function. |A|, tr(A) and eig(A) represents the determinant, trace and eigenvalues of matrix A respectively.

For uplink detection, we consider a scenario with K single-antenna users transmitting to a base-station (BS) with an antenna array with M elements through a flat-fading channel. The input-output relation is <MAT> where y is the M × <NUM> received vector, x is the transmitted user data vector (K × <NUM>), H = [h<NUM> h<NUM> • • • hM]T is the channel matrix (M × K), where hm is a K × <NUM> vector representing CSI at antenna m, and n a noise vector (M × <NUM>) with N<NUM> as variance.

We focus only on linear detectors, because they show close to optimal performance in Massive MIMO regime [<NUM>] while exhibiting low complexity.

A linear equalizer provides an estimate of x, x̂, by applying the equalizer filter matrix W to the vector of observations, y, as follows <MAT> where W = [w<NUM> w<NUM> • • • wK]T is a K × M complex matrix. wm is a K x <NUM> equalizer vector local to antenna m.

We consider the conventional linear detectors maximum-ratio combining (MRC) and zero-forcing (ZF), whose equalizer matrix is defined as <MAT> where G = HHH is the Gramian matrix, which can be also expressed as <MAT>, where <MAT> is a K × K partial Gramian matrix with local CSI of each antenna module. It is important to note that matrix W is valid during a Coherence Block (CB) of the channel, representing a frequency-time region where the channel can be considered approximately constant.

MRC provides complete decentralized processing, allowing each antenna node to obtain a local equalization vector from local CSI. ZF, on the other hand, requires the system to collect all CSI from all antennas in a central processing node, for further matrix inversion. It is well known that ZF provides superior performance over MRC due to perfect inter-user interference cancellation capabilities at the cost of an increment of inter-connection bandwidth and processing requirements. However, those extra requirements are despicable when compared to the overall physical layer requirements.

Linear processing in Massive MIMO was presented in the previous section together with two detection methods. These two schemes can be implemented in centralized or decentralized systems.

In centralized architectures, the central unit collects all CSI from all antenna modules, represented by the matrix H, which allows optimal estimation of matrix W. Apart from that, the central unit tasks also includes detection and decoding. Processing in the antenna side comprises RF, ADC and optionally OFDM processing (FFT). The amount of interconnection data-rate between antennas and the central unit depends on M, which is an important limitation in Massive MIMO systems where a large number of antenna elements is expected.

There is nowadays a trend towards decentralized systems in order to allow scalability of the system. Decentralized systems perform antenna processing locally, including CSI acquisition and partial detection. One of the key characteristics of this type of systems is that full CSI is not available at any point. The central node is left for the remaining parts of the per-user processing (symbol de-mapping and decoding).

In both types of architectures, antenna modules need to be connected to the central node. In decentralized systems, this connection is used to transfer partial detection data, of a volume that is independent of M. This existing connection may be used also to transfer additional data which allows to improve the detection performance. This is the case of ZF, where the Gramian matrix is collected in the central node for further inversion. During a channel CB, antenna-nodes transfer two types of data to central node, partial Gramian (Gm) and partial detection data. The former one, available after pilots are received and channel estimation is completed in the antenna modules, and the last one after the reception of each data symbol. As presented in section II-A, a partial Gramian matrix (Gm) consists of K × K complex elements which are assumed to be transmitted by each antenna within one OFDM symbol to avoid buffering, reduce memory requirements and latency. The outcome of the detection process is K complex numbers (one per transmitting user) per subcarrier under MU-MIMO. We also assume to have K subcarriers per CB and per OFDM symbol, which corresponds to a K × K complex elements after detection. As we can observe there is no need to increase the inter-connection data-rate requirements of the existing connection network for the transmission of the partial Gramian matrices. Furthermore, the matrix inversion required in ZF has a complexity that is far below other processing tasks of the central processing node such as decoding, so we regard the computational overhead to be negligible. Once the Gramian matrix G is inverted, it can either be stored and used in the central node during data detection, increasing the memory and computational requirements of this node [<NUM>], or distribute back to the antenna modules so they can compute locally their corresponding vector, which increase traffic and latency [<NUM>]. The selection of a strategy is out of scope for this work and is a decision that depends on the specific application and system requirements. In this paper we propose a channel estimator based on the built Gramian, which delivers an estimate of G. We demonstrate that carrying out channel estimation in a centralized way outperforms its decentralized counterpart.

A first channel estimation is performed per-antenna basis, based on pilots sent by users. Recalling the MIMO equation, <MAT> the goal of the channel estimation phase is to obtain an estimate of H. If users send orthogonal pilots, we can define the K × K matrix P = [p<NUM>, p<NUM>, • • •, pK], where pk is defined as a K × <NUM> vector of the following form <MAT> where pk is a complex-number known by the BS which represents the pilot from k-th user. Based on this definition, the Mx K BS observation matrix Z can be described by <MAT> where Z = [z<NUM>, z<NUM>, • • •, zM]T, zm being the K × <NUM> observation vector at antenna m. N = [n<NUM>, n<NUM>, • • •, nM]T represents the noise term as a M × K matrix , where nm is the K × <NUM> noise vector corresponding to the same antenna. For one of the antennas, equation (<NUM>) boils down to <MAT> and channel estimation is performed locally based on the observation vector zm.

The Least Squares (LS) estimate of H can be obtained as follows <MAT> which can be easily computed in each antenna node by exploiting the fact that P is a diagonal matrix as follows <MAT> where ĥm is obtained locally in each antenna-node. For the simple case that pk = <NUM>, ∀k, then P = I and ĤLS = Z.

Second step in channel estimation is to obtain matrix <MAT>. In order to do that, each antenna can compute the partial term <MAT>, which is a K × K matrix, and therefore <MAT>. This addition can be carried out by exploiting the existing antenna-nodes connections needed for data detection.

In next subsections we obtain the PDF of R and G, and the results will be used to formulate estimators of G, which outperform the one-step channel estimation based solely on the decentralized LS channel estimate derived from (<NUM>).

If Z is an M × K complex matrix whose rows follow a multivariate normal distribution as in, with covariance matrix Σ and (Z) = H, then the distribution of R = ZHZ is noncentral Wishart and is defined as [<NUM>] <MAT> and noted as R|G ~ WK (M, Σ, Σ-<NUM>G). The matrix Σ-<NUM>G is referred to as noncentrality matrix in most literature.

The marginal PDF for matrix G becomes a central Wishart and its expression is as follows <MAT> and noted as G ~ WK (M, C), where C is the covariance matrix of the rows of H.

The marginal PDF of R can be obtained as <MAT>.

Introducing the matrix A such that A-<NUM>Σ-<NUM> = Σ-<NUM> + C-<NUM>, which translates to A = (I + C-<NUM>Σ)-<NUM>, leads to <MAT> where we used the fact that eig(PXPY) = eig(PYPX) holds for any complex matrix P, being X and Y two Hermitian complex matrices, and therefore <NUM>F̃<NUM> (M; PXPY) = <NUM>F̃<NUM> (M; PYPX). In our case P = Σ-<NUM>, X = G and Y = R.

We can obtain a more adequate form for <MAT> as follows <MAT> where the equality C-<NUM> = (A-<NUM> - I) Σ-<NUM> has been used.

By comparing (<NUM>) and (<NUM>) it is possible to observe that the second part of (<NUM>) is actually the integral of a noncentral Wishart PFD and therefore its value must be <NUM>. The final expression for p(R) is a central Wishart as shown below <MAT> which is R ~ WK(M, Σ(I - A)-<NUM>). Additionally, if we take into account that Σ(I - A)-<NUM>) = C + Σ then translates to R ~ WK(M, C + Σ).

Finally, the posterior PDF can be obtained by using Bayes' theorem and the results from (<NUM>), (<NUM>) and (<NUM>) as follows <MAT> where the result from (<NUM>) has been used. PDF in equation (<NUM>) is a noncentral Wishart, G|R~ WK(M, ΣA, AΣ-<NUM>R).

Once we have presented the PDFs involved in this study we can introduce the estimators.

Maximum Likelihood (ML) estimate of G is defined as the matrix ĜML, which maximizes the likelihood as follows <MAT> If R has an eigenvalue decomposition R = UΛUH, then we look for solutions whose form is G = UΩUH, where Ω and Λ are diagonal matrices containing the eigenvalues of G and R respectively.

In the particular case that all pilots have the same power, this is |pk| = |p|, ∀k, then without loosing generality we can set |p| = <NUM>, leading to Σ = N<NUM>I, and (<NUM>) can be expressed as follows <MAT>.

After derivation of the argument of previous expression, the optimality condition can be expressed as <MAT> from where we do not continue in an analytical form.

The Maximum A Posteriori (MAP) estimate is defined as <MAT>.

If Σ = N<NUM>I and C = hpowI then <MAT> I and therefore the MAP estimate can be expressed as follows <MAT> where µ<NUM>, µ<NUM>, • • •, µK are the eigenvalues of G.

The Minimum Mean Square Error (MMSE) estimate is defined as the expectation over the posterior probability. Taking into account that G|R is a noncentral Wishart, that is G|R ~ WK(M, ΣA, AΣ-<NUM>R), the expectation is known as <MAT>.

If C = hpowI and Σ = N<NUM>I then <MAT>, and (<NUM>) can be expressed as follows <MAT>.

When N<NUM> = <NUM> then ĜMMSE = R, which is the true value because in this particular case R = G. On the other hand, when N<NUM> » hpow then ĜMMSE ≈ hpowMI, which is the conditional expectation of G, that is ĜMMSE = (G|R) ≈ (G), which means that R does not give much information about G in that case.

The ZF equalization matrix is made up of two parts (<NUM>). There is an MRC part (ĤH) that is implemented in a decentralized form by the antenna modules, and the second part, (Ĝ-<NUM>), that is performed in a central processing unit. Let's define two equalizers and compare their performance. The first one, ZF based on the MMSE channel estimator from (<NUM>) is defined as <MAT> and the second one, ZF based on LS channel estimation from (<NUM>) <MAT> which only requires a decentralized channel estimation.

In this subsection we compare the channel estimation made by these two approaches by studying the error norm as follows for MMSE <MAT> and for LS <MAT>.

In scenarios with low noise levels, that is N<NUM> « <NUM>, (<NUM>) simplifies to ĜMMSE ≃ R and therefore ∈MMSE ≃ ∈LS. On the other hand, at high noise levels, that is N<NUM> » hpow then ĜMMSE ≈ hpovMI and ∈MMSE saturates unlike ∈LS, that grows proportionality to N<NUM>. <FIG> shows this fact.

Equation (<NUM>) can be rewritten in an equivalent form as a linear combination of user's data <MAT>.

During detection stage, in order to estimate the symbol transmitted by user k, xk, receiver needs to pre-multiply y by the equalization vector wk <MAT>.

The instantaneous SINR for user k is given by the next expression <MAT>.

The total sum-rate follows the next expression <MAT>.

Claim 1:
A method of receiving data transmitted by a plurality of communications devices, the method comprising
receiving at each of a plurality of M antennas reference signals transmitted by each of a plurality of K communications devices,
processing by each of a plurality of antenna modules the reference signals, each of the antenna modules being connected to a corresponding one of the plurality of antennas, the processing by each of the antenna module including
estimating for each of the K detected reference signals received from the K communications devices a sample of a radio channel through which the received signals have passed,
generating for each of the K samples of the radio channel a KxK partial matrix forming a part of a signal processing matrix for performing zero forcing equalisation of the received signals, and
transmitting via a communications interface the partial matrix KxK from each of the M antenna modules to a central processing unit, and
detecting by the central processing unit the data from the received radio signals using the MxK equalisation matrix formed by combining the KxK partial matrices from each of the M antenna modules,
wherein the transmitting the partial matrix KxK from each of the M antenna modules to the central processing unit via the communications interface comprises
transmitting each of the K columns of K complex samples of the KxK partial matrix via the communications interface sequentially.