TRANSFORMING AND COMBINING SIGNALS FROM ANTENNA ARRAY

Abstract

A method of reducing a number of signals that are output for processing by an antenna array and the antenna array are disclosed. The method comprises: receiving signals at a plurality of antenna elements from at least one user equipment; transforming the signals to at least one different domain to generate sparse signals; combining at least some of the signals to form a reduced number of signals; and outputting the reduced number of sparse signals to signal processing circuitry.

Claims

1. A method performed on signals received at a plurality of elements of an antenna array comprising: transforming said signals to at least one different domain to generate sparse signals; combining at least some of said signals to form a reduced number of sparse signals; and outputting said reduced number of sparse signals.

2. A method according to claim 1, comprising a further converting said signals from analogue to digital signals using a plurality of transceivers.

3. A method according to claim 2, wherein said combining and transforming said signals are performed together prior to converting said sparse signals from analogue to digital signals at said plurality of transceivers.

4. A method according to claim 1, wherein said combining and transforming are performed and comprises multiplying said signals by a transformation matrix, said transformation matrix having one dimension equal to said number of antennas and a smaller dimension equal to said reduced number of sparse signals.

5. A method according to claim 1, wherein said combining comprises combining signals from said plurality of antenna elements in a random or semi-random manner such that signals from all or all except one or two of said antenna elements each contribute an amount to said reduced number of sparse signals.

6. A method according to claim 1, further comprising processing said reduced number of sparse signals in conjunction with estimated channel state information to derive signals transmitted by said at least one user equipment.

7. A method according to claim 1, comprising performing said method, for at least one predetermined pilot signal received at said plurality of antenna elements from at least one user equipment; and analysing said reduced number of sparse signals output to said processor and said predetermined pilot signals using a reconstruction algorithm based on compressive sensing techniques to generate said channel state information.

8. A method according to claim 7, comprising periodically generating updated channel state information.

9. A method according to claim 7, wherein said reconstruction algorithm estimates a combined effect of a wireless channel transmitting said signal and a coupling effect between antenna elements on said signal such that said coupling effects are compensated for by said channel state information.

10. A method according to claim 8 wherein said reconstruction algorithm further estimates an effect of imperfections in elements from said plurality of antenna elements up to and including transceivers, such that said imperfections are compensated for by said channel state information.

11. A method according to claim 8, comprising in response to detecting a change in said channel state information amending at least one of said transforming and combining.

12. A computer program which when executed by a computer is operable to control said computer to perform a method according to claim 1.

13. An antenna array comprising: a plurality of antenna elements configured to receive signals from at least one user equipment; a plurality of transceivers; transforming logic operable to transform said signals to at least one different domain to generate sparse signals; combining logic operable to combine at least some of said signals to form a reduced number of sparse signals; and output circuitry operable to output said reduced number of sparse signals.

14. An antenna array according to claim 13, and further comprising signal processing circuitry, said signal processing circuitry being operable to process said reduced number of sparse signals using channel state information to derive signals transmitted by said at least one user equipment.

15. An antenna array according to claim 13, wherein said signal processing circuitry is operable, in response to predetermined pilot signals being received at said plurality of antenna elements, to analyse said reduced number of sparse signals output to said processor and said predetermined pilot signals using a reconstruction algorithm based on compressive sensing techniques to generate said channel state information.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Embodiments of the present invention will now be described further, with reference to the accompanying drawings, in which:

[0050] FIG. 1 illustrates a MIMO and associated processing circuitry according to an embodiment;

[0051] FIG. 2 shows an alternative embodiment to that of FIG. 1;

[0052] FIG. 3A shows a RF transformation matrix operating on a massive MIMO array and connected to a reduced number of transceivers;

[0053] FIG. 3B shows a transformation matrix operating on digital signals output from a massive MIMO array via transceivers;

[0054] FIG. 4 schematically shows the modelling of an antenna array setup in joint angle-delay space that is able to exploit sparsity;

[0055] FIG. 5 shows a flow diagram illustrating steps in a method of generating channel state information for a MIMO according to an embodiment;

[0056] FIG. 6 shows a flow diagram illustrating steps in a method of deriving input signals from reduced sparse output signals at a MIMO according to an embodiment; and

[0057] FIG. 7 shows a flow diagram illustrating steps in a method of periodically updating channel state information for a MIMO according to an embodiment.

DESCRIPTION OF THE EMBODIMENTS

[0058] Before discussing the embodiments in any more detail, first an overview will be provided.

[0059] Embodiments seek to reduce the signals to be processed and in some cases the number of transceivers i.e. hardware chains required and consequently the overall hardware complexity and power consumption in an antenna array such as a MIMO system, particularly a massive MIMO system without compromising the performance of such a massive MIMO system.

[0060] In order to do this the use of sparsity techniques to characterize massive MIMO wireless channels and enable sub-Nyquist spatial sampling and perform channel estimation with reduced transceivers that would typically require significantly more antennas and transceivers is considered.

[0061] The focus is both on hardware design to reduce overall complexity as well as signal processing algorithms that decode and reconstruct a high resolution estimate of a signal.

[0062] In this regard the inventors recognised that there will be considerable correlation between signals received at multiple antenna elements in arrays such as MIMO and that such data when transformed to another domain such as from the time to the frequency domain would provide a sparse data set. Sparse data sets can be solved using compressive sensing techniques even where there are more unknowns than there are equations. Thus, techniques that combine and transform signals from different antenna elements are used, and these generate a reduced number of signals which are sparse and can therefore be analysed using compressive sensing techniques. In this way a reduced amount of signal data is provided to a signal processor which owing to the sparse nature of the data may still, using compressive sensing processing techniques that exploit the sparse nature of the data, be used to derive the original signals.

[0063] In this regard in order to be able to derive the original signals channel state information for the channels that the signals travel along needs to be derived. This is done using known pilot signals as input signals and analysing these in conjunction with the combined and transformed signals from the antenna. Compressive sensing techniques using a reconstruction algorithm are used to derive channel state information which in preferred cases reflects not only the signal path from the user equipment to the antenna but also coupling between antenna elements and imperfections in the radio frequency signal path within the antenna. This channel state information can then be used to derive original signals from the reduced sparse signals output by the antenna. In some embodiments the channel state information and in some cases the combining and transforming logic is periodically updated to reflect changes in environment and in the antenna itself.

[0064] FIG. 1 schematically shows a multiple input antenna array 10 according to an embodiment. The radio frequency signals received at the multiple antenna elements 20 are combined and transformed in combining and transforming logic 30 and a reduced number of sparse signals are output. The combining and transforming logic combines the different received signals in different ways, but preferably, a signal received at each antenna element will contribute to at least one of the reduced number of signals that are transmitted to transceivers 40. This logic may simply comprise circuitry with different path lengths and different combining elements or it may be formed to mirror a transforming matrix as is shown in FIG. 3B. Combining the received analogue signals at this point reduces the number of transceivers required saving on both power and hardware costs.

[0065] In this regard in a conventional system a transceiver would be required for each antenna element whereas due to the combining and transforming logic combining the received input signals such that the number of output signals is lower than the number of input signals received from each antenna element, fewer transceivers are required. Furthermore, this results in fewer signals being sent to the processing unit 50, resulting in fewer signal paths and a reduced processing capacity requirement.

[0066] FIG. 2 shows an alternative embodiment of the multiple input antenna where the transforming and combining logic 30 is arranged after the transceivers 40. Thus, in this case there is a transceiver for each antenna element and these convert the received RF analogue signals to digital signals that are then processed by the transforming and combining logic 30. This logic may be circuitry or it may be a software algorithm for transforming and combining the signals prior to sending a reduced number of signals to the CPU. In this regard the algorithm may take the form of a transforming matrix T which both transforms and combines the signals as is detailed below. The transforming matrix may be a single matrix T or it may be two matrices one performing the transformation to anther domain and a further one performing the combining step. FIG. 3A schematically shows a single transforming matrix operating on digital signals output from a plurality of transceivers. The matrix transforms and combines the signals thereby reducing the number of digital signals from N to P.

[0067] FIG. 3B schematically shows this matrix as the transforming and combining logic in an arrangement similar to that of FIG. 1 where the matrix operates on the RF signals and a reduced number of transceivers are required.

[0068] FIG. 4 schematically shows a modelling antenna array in joint angle-delay space that exploits sparsity and schematically shows the channels H for each user k as is explained in more detail below.

[0069] In one embodiment there is proposed a P×N RF transformation matrix T operating on N MIMO antenna elements and converting them to P RF signal paths, which are subsequently downconverted to digital base-band, sampled and post-processed to obtain a P×1 vector of received signals y as shown in FIG. 3. Typically N>>P, N≈4P.

[0070] The transformation matrix T can be seen as a random RF matrix or feeder network transforming N signals to P signals. The physical RF impairments such as coupling between antennas as well as amplitude, frequency and phase offsets between different RF components are also accounted and compensated with the reduced P signals.

[0071] Subsequently, we propose to use the P dimensional signals with compressive sensing tools exploiting the sparse nature of the wireless channel in joint angle-delay domain to obtain a high resolution estimate of the received signal.

[0072] This high resolution estimate of the wireless signal can be used to either obtain a high resolution channel state information (CSI) or to improve reception of weak signals at massive MIMO array with reduced transceivers. This setup will also help to reduce the overall energy consumption of RF and digital chains.

Model:

[0073] Consider a massive MIMO setup, made of say √{square root over (N)}×√{square root over (N)} antennas radiating and receiving signals from arbitrary user equipment or small cells through a frequency selective and multipath environment. For simplicity, the UEs transmit using one antenna element. Let K be the number of UEs and L be the order of their wireless channels due to the delay spreads of various multipaths. For simplicity and consistency of notation, we stack rows or columns of the massive MIMO antenna setup and denote them as an N×1 vector. The array geometry can be arbitrary (viz. linear, planar, non-uniform, etc) and contained in the overall antenna array response.

[0074] For notational simplicity, we assume the transmit antennas are omnidirectional omitted in subsequent discussions. The wireless channel order L=┌Wτmax┐+1, where W is the bandwidth and τ.sub.max corresponds to maximum time delay spread. The overall degree of freedom due to the introduction of the massive MIMO setup is D=NL.

[0075] In order to characterize this degree of redundancy, the discrete-time spatio temporal wireless channel is represented in a joint angle-delay space using an N×1 vector of order L:

[00001]$h^{\left(k\right)}\left[l\right]=\underset{r=1}{\overset{R}{.Math.}}.Math.a\left({\theta }_r\right).Math.H_v\left(l,r\right)=A_R.Math.h_v^{\left(k\right)}\left[l\right].Math..Math.\forall l\in 0,\mathrm{.Math.}.Math.,L-1.$

where A.sub.R is the antenna array response at the receiver for an angle of arrival θ.sub.r. The joint angle-delay space is characterised by resolution R spatially sampling the delay spread versions of wireless channel. Extending the antenna array model to K users, the overall wireless channel represented using an N×KL matrix:

H=A.sub.R└H.sub.v.sup.(1) . . . H.sub.v.sup.(K)┘ where H.sub.v.sup.(k)=└h.sub.v.sup.(k)[0], . . . ,h.sub.v.sup.(k)[L−1]┘.

[0076] The transmitted signals at time instant t=mT tε[o,T) for arbitrary m from all users are received at the MIMO array and stacked as an N×1 vector x[m]:

[00002]$x\left[m\right]=H\left[\begin{array}{c}{s}^{\left(1\right)}\left[m\right]\\ \mathrm{.Math.}\\ \mathrm{.Math.}\\ s^{\left(K\right)}\left[m\right]\end{array}\right]+\tilde{z}\left[m\right].Math..Math.\mathrm{where}.Math..Math.s^{\left(k\right)}\left[m\right]={\left[s^{\left(k\right)}\left[m\right],\mathrm{.Math.}.Math..Math.s^{\left(k\right)}\left[m-L+1\right]\right]}^T$

and s.sup.(k)[m] corresponds to user signal at time instant t=mT and {tilde over (z)}[m] is an N×1 vector containing additive noise.

Setup:

[0077] In order to reduce the hardware complexity of the overall setup as well as to reduce the number of transceivers, we propose to introduce an P×N RF transformation matrix T operating on N MIMO antenna elements and converting them to P RF signal paths, which are subsequently downconverted to digital base-band, sampled and post-processed to obtain a P×1 vector of received signals y:

y[m]={THs+z[m]}≈THs[m]+z[m].

[0078] The above transformation matrix T can be seen as a feeder network transforming signals from increased dimension to reduced dimension. However, it is not designed to produce a set of orthogonal beams or specific beams as in a Butler matrix. It is a random matrix designed to reduce the number of transceivers while exploiting the sparsity of the scattering environment to obtain a linear combination of signals at the antenna array.

[0079] In practice, a large MIMO array will introduce significant coupling between antenna elements when they are stacked close to each other. Coupling covers sparsity in angle but not in time, and for simplicity can be modelled as an N×N block tri-diagonal matrix M operating on the overall channel matrix H. In standard systems, the antenna elements are insulated and cased in order to minimize the propagation of surface waves and suppress coupling. Thus in standard systems, they can be approximated as an identity matrix: M.sub.standard=I. All these changes increase typically the design and manufacture cost of the MIMO array. By explicitly consider this coupling term within the overall expression and estimating the overall wireless channel+coupling coefficient, we alleviate this problem. The signal model can be written including the coupling matrix M as

y[m]=T[H.sub.M]s[m]+z[m]H.sub.M=MH.

[0080] The RF chains denoted by the RF{.} are subject to imperfections, non-linearities and loss. Typically, these terms must be estimated and calibrated in existing systems and their complexity increases for increasing N. The impairments can be modeled as an P×P diagonal matrix R operating on the output of the transformation matrix T.

[00003]$y\left[m\right]=\mathrm{RT}\left[H_M\right].Math.\underset{\_}{s}\left[m\right]+z\left[m\right].Math..Math.R=\left[\begin{array}{ccc}{r}_1& 0& 0\\ 0& \ddots & 0\\ 0& 0& r_P\end{array}\right].$

[0081] To reduce the hardware complexity, we refrain from estimating these components independently.

Methods—Compressive Sensing CS Based High Resolution Channel Estimation:

[0082] It would be desirable to essentially estimate the combined effect of the wireless channel H, coupling matrix M and the imperfections matrix R when used in combination with the reduced dimension transformation T. Note that we do not have to individually estimate each and every term, and a combined estimation of these terms is sufficient to subsequently apply detection algorithms and estimate signals from desired user. To this end, we assume that the massive MIMO array has knowledge of pilot signals from a given user and applies them to estimate the wireless channel.

[0083] Consider a pilot signal

[00004]$s\left(k\right)\left[t=\frac{m}{M}.Math.T\right]$

transmitted from user k and observed within the observation interval tεo,T). The discrete samples s(k)[1], . . . , s(k)[M] correspond to the pilot sequence. The massive MIMO array observe such sequences from all K users as

y[m]=RT[H.sub.M]s[n]+z[m].

[0084] Stacking these signals for the entire observation interval leads to

[00005]$\begin{array}{cc}\left[y\left[1\right],\mathrm{.Math.}.Math.,y\left[M\right]\right]={\mathrm{RTH}}_M\left[\underset{\_}{s}\left[1\right],\mathrm{.Math.}.Math.,\underset{\_}{s}\left[M\right]\right]+\left[z\left[1\right],\mathrm{.Math.}.Math.,z\left[M\right]\right].Math..Math..Math.Y=\underset{\underset{\mathrm{unknown}.Math..Math.R,H_M}{}}{{\mathrm{RTH}}_M}.Math..Math.\underset{\underset{\mathrm{data}:.Math.\mathrm{full}.Math..Math.\mathrm{row}.Math..Math.\mathrm{rank}}{}}{\underset{\_}{s}}+z& \left(2\right)\end{array}$

[0085] The pilot signals are assumed to be drawn from a random ensemble of i.i.d vectors and are uncorrelated with each other. For the observation interval M≧LK, S is a fat matrix with full row rank. Thus, there is a valid pseudo-inverse of S, and postmultiplying the above expression using S.sup.† and neglecting the noise terms for the moment:

YS.sup.†≈RT{tilde over (H)}Y≈RT{tilde over (H)}.

[0086] Applying the Kronecker product identity vec(ABC)=(C.sup.TA)vec(B) to the above expression leads to

vec[YS.sup.†]=HR)vec(T)y=Ht.

[0087] Typically in a CS based setup, the sparse signals are projected over a random basis, and the signals are reconstructed from this random projection. In the above expression, Φ can be seen as the random projection matrix usually seen in either basis pursuit or lasso reconstruction or Dantzig selector based CS techniques:

[00006]$\begin{array}{cc}{\underset{\_}{H}}^{\mathrm{CS}}=\arg .Math..Math.\underset{\underset{\_}{H}}{\min }.Math.{.Math.\underset{\_}{H}.Math.}_1.Math..Math.\mathrm{such}.Math..Math.\mathrm{that}.Math..Math.{.Math.\underset{\underset{\mathrm{Observation}+\mathrm{pilot}}{}}{Y.Math.{\underset{\_}{S}}^{†}}-\underset{\underset{\mathrm{known}.Math..Math.\mathrm{projections}}{}}{T}.Math..Math.\underset{\underset{\mathrm{unknown}.Math..Math.\mathrm{channel}}{}}{\underset{\_}{H}}.Math.}_{\infty }\le \mathrm{threshold}& \left(3\right)\end{array}$

[0088] Alternatively, they can be used in combination with greedy algorithms such as orthogonal matching pursuit or similar algorithms mentioned in [8]. For simplicity, the above optimization is represented as g.sub.CS=CS(Φ,y, threshold=ε).

[0089] Our massive MIMO array and the transformation matrix setup: TA.sub.R can be seen as this random transformation i.e. Φ=T, operating on sparse wireless channel H. Plugging the rest of the terms in the above expression leads to pilot

[00007]${\mathrm{CS}}^{}=\arg .Math..Math..Math.{.Math..Math.}_1.Math..Math.\mathrm{such}.Math..Math.\mathrm{that}.Math..Math.{.Math.y-\Psi .Math..Math.}_{\infty }\le \mathrm{threshold}.$

[0090] FIG. 5 shows a flow diagram schematically illustrating steps of a method for generating channel state information for a multiple input/multiple output antenna. In this embodiment, predetermined pilot signals are received at the antenna elements and these signals are multiplied by a P×N transformation matrix to generate P output signals where P is less than N and in this way, the number of signals are reduced. This transformation matrix also transforms the domain of the signals such that the signals produced are sparse. An analysis of the output and input signals is made to generate an estimate of the combined effect of the path of the signals, that is the wireless channel, the coupling between antenna elements and imperfections in the radio frequency components. From this channel state information is generated and stored for each signal channel.

[0091] FIG. 6 shows steps of a method performed at processing circuitry of a multiple input/multiple output antenna which uses the state information determined by the method of FIG. 5 to reconstruct input signals from the reduced sparse output signals received at the processing circuitry.

[0092] Signals from N antenna elements are received and these signals are multiplied by the P×N transformation matrix to generate P output sparse signals. The stored channel state information is then used to generate input signals from the P sparse output signals.

[0093] FIG. 7 shows steps of a method for periodically updating the channel state information in order to compensate for changes in the environment surrounding the antenna. Thus, periodically, predetermined pilot signals are received at the N antenna elements and these signals are multiplied by the transformation matrix to generate the reduced number of sparse output signals. The combined effect of the wireless channel, coupling of the antenna elements and imperfections in the radio channel elements are then considered by comparing the P output signals with the known input signals and channel state information for each signal channel is generated. It is then determined if this channel state information is very different to previously stored information.

[0094] In this regard, in some cases the question will not be is it different but is the channel state worse, such that changes for the better do not trigger an amendment of the transformation matrix. If the change is considered significant (or significantly worse), then the transformation matrix is amended and the procedure is repeated until channel state information that is similar to that previously received or better than that previously received is found. At this point the updated channel state information is stored as is the amended transformation matrix.

[0095] This procedure is performed periodically such that the system is able to respond to changes in the environment and in the antenna itself. In this regard, if one of the transceivers for example were to malfunction or its performance to deteriorate, then amendments in the transformation matrix may allow this to be compensated for and the performance of the antenna may remain at a similar level to that which it was previously.

[0096] A person of skill in the art would readily recognize that steps of various above-described methods can be performed by programmed computers. Herein, some embodiments are also intended to cover program storage devices, e.g., digital data storage media, which are machine or computer readable and encode machine-executable or computer-executable programs of instructions, wherein said instructions perform some or all of the steps of said above-described methods. The program storage devices may be, e.g., digital memories, magnetic storage media such as a magnetic disks and magnetic tapes, hard drives, or optically readable digital data storage media. The embodiments are also intended to cover computers programmed to perform said steps of the above-described methods.

[0097] The functions of the various elements shown in the Figures, including any functional blocks labelled as “processors” or “logic”, may be provided through the use of dedicated hardware as well as hardware capable of executing software in association with appropriate software. When provided by a processor, the functions may be provided by a single dedicated processor, by a single shared processor, or by a plurality of individual processors, some of which may be shared. Moreover, explicit use of the term “processor” or “controller” or “logic” should not be construed to refer exclusively to hardware capable of executing software, and may implicitly include, without limitation, digital signal processor (DSP) hardware, network processor, application specific integrated circuit (ASIC), field programmable gate array (FPGA), read only memory (ROM) for storing software, random access memory (RAM), and non-volatile storage. Other hardware, conventional and/or custom, may also be included. Similarly, any switches shown in the Figures are conceptual only. Their function may be carried out through the operation of program logic, through dedicated logic, through the interaction of program control and dedicated logic, or even manually, the particular technique being selectable by the implementer as more specifically understood from the context.

[0098] It should be appreciated by those skilled in the art that any block diagrams herein represent conceptual views of illustrative circuitry embodying the principles of the invention. Similarly, it will be appreciated that any flow charts, flow diagrams, state transition diagrams, pseudo code, and the like represent various processes which may be substantially represented in computer readable medium and so executed by a computer or processor, whether or not such computer or processor is explicitly shown.

[0099] The description and drawings merely illustrate the principles of the invention. It will thus be appreciated that those skilled in the art will be able to devise various arrangements that, although not explicitly described or shown herein, embody the principles of the invention and are included within its spirit and scope. Furthermore, all examples recited herein are principally intended expressly to be only for pedagogical purposes to aid the reader in understanding the principles of the invention and the concepts contributed by the inventor(s) to furthering the art, and are to be construed as being without limitation to such specifically recited examples and conditions. Moreover, all statements herein reciting principles, aspects, and embodiments of the invention, as well as specific examples thereof, are intended to encompass equivalents thereof.