Patent Application
20230327718
A. Lawal, Q. Mayyala, K. Abed-Meraim, N. Iqbal and A. Zerguine, “Blind Signal Estimation Using Structured Subspace Technique,” in IEEE Transactions on Circuits and Systems II. Express Briefs, vol. 68, no. 8, pp. 3007-3011, 2021, doi: 10.1109/TCSII.2021.3065385 incorporated herein by reference in its entirety.
The inventors acknowledge the financial support provided by provided by the Deanship of Scientific Research of King Fand University of Petroleum and Minerals (KFUPM), Riyadh, Saudi Arabia under Research Grant SB181001.
The present disclosure is directed to blind signal estimation of single-input multiple-output (SIMO) finite impulse response (FIR) systems.
The “background” description provided herein is for the purpose of generally presenting the context of the disclosure. Work of the presently named inventors, to the extent it is described in this background section, as well as aspects of the description which may not otherwise qualify as prior art at the time of filing, are neither expressly or impliedly admitted as prior art against the present invention.
Blind system identification has application in a wide variety of fields, such as in satellite communication, image processing, seismic exploration, and biomedical image processing. Conventional methods for blind system identification transmit a known training sequence to a receiver that is then used for channel estimation. The obtained channel information is then used to estimate the transmitted signal. Such methods are widespread due to their simplicity, but have inefficiencies when it comes to bandwidth, power, and channel throughput. Moreover, there are some applications in which training sessions are not able to be used, such as in asynchronous wireless networks. Methods that do not require training sessions are preferable.
Blind system identification can be seen as an identification of channels and/or input signals, based only on the available output signals, with several algorithms taking different approaches. Several second-order statistics-based approaches have been employed, such as standard subspace (SS), cross-correlation (CR), two-step maximum likelihood, mutually reference equalizer (MR), and truncated transfer method (TTM). Of particular interest is the SS method, which is efficient in terms of estimation accuracy. Further developments of the SS method have led to a single-input multiple-output (SIMO) structure channel subspace (SCS) method for channel identification in a SIMO system. Of the listed methods, the SS, CR, TTM, and the SCS methods can be categorized as an “indirect method” that estimates the channel, then the output signal. The MRE methods has the desirable quality in that it is a “direct method” that can directly estimate the signal.
Each of the aforementioned methods for blind signal identification suffers from one or more drawbacks hindering their adoption. Accordingly, it is one object of the present disclosure to provide methods and systems for improved blind system identification, and in particular, direct estimation of the signal is desirable.
In an exemplary embodiment method for blind signal estimation for single-input multiple-output systems performed by a receiver is provided. The method comprises receiving, by two or more receiver antennas of the receiver, an observed signal comprising an input signal and an additive noise term. The method can then include forming a data matrix using the observed signals from the two or more receiver antennas computing a singular value decomposition of the data matrix. The method can then include generating a parameter matrix using matrices obtained from the singular value decomposition of the data matrix. The method can then include forming a Toeplitz signal matrix using the parameter matrix and estimating the input signal using the Toeplitz signal matrix
In another exemplary embodiment, a system for blind signal estimation is provided. The system comprises a transceiver comprising a transmitter antenna configured to transmit an input signal to a receiver. The system can also include the receiver comprising two or more transmitter antennas configured to receive the input signal and a processing module configured to perform a method including: receiving, by the two or more receiver antennas of the receiver, an observed signal comprising the input signal and an additive noise term; forming a data matrix using the observed signals from the two or more receiver antennas; computing a singular value decomposition of the data matrix; generating a parameter matrix using matrices obtained from the singular value decomposition of the data matrix; forming a Toeplitz signal matrix using the parameter matrix; and estimating the input signal using the Toeplitz signal matrix.
In yet another exemplary embodiment, a non-transitory computer readable medium having instructions stored therein that, when executed by one or more processors, cause the one or more processors to perform a method including: receiving, by two or more receiver antennas of the receiver, an observed signal comprising an input signal and an additive noise term; forming a data matrix using the observed signals from the two or more receiver antennas; computing a singular value decomposition of the data matrix; generating a parameter matrix using matrices obtained from the singular value decomposition of the data matrix; forming a Toeplitz signal matrix using the parameter matrix; and estimating the input signal using the Toeplitz signal matrix.
The foregoing general description of the illustrative embodiments and the following detailed description thereof are merely exemplary aspects of the teachings of this disclosure, and are not restrictive.
A more complete appreciation of this disclosure and many of the attendant advantages thereof will be readily obtained as the same becomes better understood by reference to the following detailed description when considered in connection with the accompanying drawings, wherein:
In the drawings, like reference numerals designate identical or corresponding parts throughout the several views. Further, as used herein, the words “a,” “an” and the like generally carry a meaning of “one or more,” unless stated otherwise.
Furthermore, the terms “approximately,” “approximate,” “about,” and similar terms generally refer to ranges that include the identified value within a margin of 20%, 10%, or preferably 5%, and any values therebetween.
Aspects of this disclosure are directed to a system, device, and method for blind signal estimation of a single-input multiple-output (SIMO) finite impulse response (FIR) system. Embodiments can be used in communications, image processing, or anywhere a signal is received by a receiver. Embodiments directly estimate input signals with no need for channel estimation, or the estimation of second-order statistics. Embodiments exploit the Toeplitz structure that is inherent in the signal's linear model. Embodiments provide a number of advantages over conventional methods. Embodiments provide for lower latency and lessen the impact of error propagation, which is common in ill-conditioned channels or weak channel estimations. Further, embodiments show high performance under adverse scenarios such as in short-burst communications and poor channel diversity.
The receiver 100 can receive the input signal s(t) using the array of receiver antennas. The input signal s(t) can pass through an unknown linear channel h(t) and be received in the presence of additive white Gaussian noise w(t) to yield the observed signal y(t) shown below:
y(t)=Σk=0L-1h(k)s(t−k)+w(t),t=0, . . . ,N−1 (1)
where h(k) is the finite impulse response (FIR) channel, L−1 is the channel order, and N is the total length of the sample. For p number of antenna, the model can be modified as follows:
y(t)=Σk=0L-1h(k)s(t−k)+w(t),t=0, . . . ,N−1 (2)
where y(t)=[y1(t), . . . , yp(t)]T is the vector collection of the p overserved signals, h(t)=[h1(t), . . . , hp(t)]T is the vector collection of the p different channels, and w(t)=[w1(t), . . . , wp(t)]T is the noise associated with each of the p different channels.
Assuming a reception of a window of Nw samples, the data can be stacked into a vector/matrix representation as follows:
y
N
(t)=HN
where yN
Considering the whole set of N samples, equation (3) can be rewritten to form a data matrix Y as:
Y=[y
N
(Nw−1)yN
Y=H
N
(h)SK+WN
where the signal matrix SK is defined as:
Here, K=Nw+L−1 and the matrix SK has a dimension of (Nw+L−1)×(N−Nw+1). The matrix WN
One existing approach, the subspace (SS) described in E. Moulines, P. Duhamel, J.-F. Cardoso, and S. Mayrargue, “Subspace methods for the blind identification of multichannel FIR filters,” IEEE Trans. Signal Process, vol. 43, no. 2, pp. 516-525, February 1995), which is incorporated herein by reference. The SS method exploits the Toeplitz structure of the channel matrix. The SIMO structure channel subspace (SIMO-SCS), as described in Q. Mayyala, K. Abed-Meraim, and A. Zerguine, “Structure-based subspace method for multichannel blind system identification,” IEEE Signal Process. Lett., vol. 24, no. 8, pp. 1183-1187, August 2017, which is incorporated herein by reference, method exploits both the Toeplitz structure of the channel matrix and the orthogonality criterion. One method to find the orthogonal component of HN
R
y
=H
N
(h)RsHN
where Rs represents the input signal covariance matrix. The singular value decomposition (SVD) of Ry is given as:
R
y
=V
s diag(λ12, . . . ,λK2)VsH+σw2VwVwH (8)
where λi for i=1, . . . , K are the principal eigenvalues of the covariance matrix Ry. Also, the columns of Vs and Vw span the signal and noise subspaces (the orthogonal complement), respectively.
Following similar logic, embodiments can exploit the Toeplitz structure of the signal matrix of equation (6) to estimate the signal directly instead of the channel. As such embodiments can thus estimate the signal directly without any prior knowledge or estimation of the channel. Among other benefits, this choice reduces errors that may be introduced due to the inversion of the estimated channel and avoids delay ambiguity that is often encountered. Further, the implementation of embodiments retains simplicity, and provides robustness to ill conditions channels.
Embodiments can directly obtain the SVD of the data matrix Y as:
Y=UΣV
H (9)
where U is a unitary matrix containing left singular vectors and has a dimension of pNw×pNw, Σ is a diagonal matrix of dimension pNw×D (with D=N−Nw+1) that contains all of the corresponding singular values, and V is a square unitary matrix of dimension D×D that contains right singular vectors. In the noiseless case (or asymptotically), the subspace spanned by the rows of the signal matrix SK coincide with the subspace spanned by the rows of VsH, which is the matrix formed by the first K rows of VH. Embodiments can thus directly search for the signal in the form of ŜK=QVsH. Here, Q can be chosen such that the Toeplitz structure of the signal matrix, given by equation (6), is preserved. This is achieved by minimizing the following structure-based cost function with respect to the square matrix Q shown below.
J=Σ
j=1
K-1Σi=1D-1|ŝ(i,j)−ŝ(i+1,j+1)|2 (10)
In this case, ŝ(i,j) refers to the (i,j)-th entry of the estimated signal ŜK. The cost function is built based on the Toeplitz structure of the signal matrix that is given in equation (6). The cost function J can be written in a compact form as:
J=∥J
D
Ŝ
K
J
K
−{tilde over (J)}
K
Ŝ
K
{tilde over (J)}
K∥2 (11)
where J{circumflex over (D)}ŜKJK is the top left submatrix of ŜK and {tilde over (J)}KŜK{tilde over (J)}K is the bottom right submatrix of ŜK. The left selection matrices are defined as JD=[ID-10(D−1),1], where 0(D−1),1 is an all zero column vector that contains zeros of dimension (D−1)×1, ID-1 is a square identity matrix of size (D−1), and JK=[IK-101,(K−1)]T. The right selection matrices are defined as {tilde over (J)}D=[0(D−1),1ID-1] and {tilde over (J)}K=[01,(K−1)IK-1]T.
The Kronecker product property of vec(ABC)=((CT⊗A)vec(B))=((CT ⊗A)b) can be applied to equation (11) to lead to equation (12) below.
J=∥((VsHJK)T⊗JD−(VSH{tilde over (J)}D)vec(Q)∥2
J=∥Kq|
2 (12)
The smallest eigenvalue of KHK corresponds to an eigenvector that is the optimal solution of the parameter vector q, under the unit norm constraint. The parameter vector q is then reshaped into the parameter matrix Q with a dimension of K×K. Once the parameter matrix Q is obtained, the signal is estimated by averaging over the diagonals of the Toeplitz signal matrix ŜK=QVsH.
In step 200, the receiver 110 can receive an observed signal using two or more receiver antennas (e.g., the first receiver antenna 112A, the second receiver antenna 112B, the p-th antenna 112p). The observed signal can have the form of equation (1), which comprises a first term that includes the product between the input signal and a channel term (i.e., h(k)s(t−K)), and an additive noise term (i.e., w(t)). The additive noise term can be white Gaussian noise and may be zero mean or be asymptotically zero. Each of the two or more receiver antennas of the receiver 110 can measure N samples of the input signal. For example, in simulations provided, N=100 and N=30 are used.
In step 202, the receiver 110 can form a data matrix using the observed signals. For example, the receiver 110 can form a signal vector yN
In step 204, the receiver 110 can compute a singular value decomposition of the data matrix. The singular value decomposition of the data matrix can result in two unitary matrices and is described by equation (9). Of particular interest is the matrix VH and the subsequent matrix VsH that comprise the right singular vectors.
In step 206, the receiver 110 can generate a parameter matrix using the matrices obtained from the singular value decomposition of the data matrix. The receiver 110 can minimize the cost function described by equation (12) to generate a parameter vector q. The parameter vector can then be reshaped to form the parameter matrix Q.
In step 208, the receiver 110 can form a signal matrix using the parameter matrix and one of the generated unitary matrices. The signal matrix can be formed by multiplying the parameter matrix with the generated unitary matrix comprising the right singular vectors (i.e., ŜK=QVsH).
In step 210, the receiver 110 can then estimate the input signal. For example, the receiver 110 can estimate over the diagonals of the signal matrix.
The dominant source of computational complexity in SS, SCS, and TTM algorithms follows from the computation of the square sample correlation matrix shown in equation (7) with a cost pNw(N−NW+1), and finding the corresponding SVD decomposition shown in equation (8) with a cost of O(pNw)3. Embodiments do not incur this cost, as embodiments directly estimate the signal without need of first estimating the channel. Further computations are saved by embodiments, as the above algorithms use a further equalization step to recover the transmitted signal.
Embodiments can efficiently estimate the transmitted signal blindly and directly without knowledge of the channel matrix. Moreover, there is no estimation of the correlation matrix of the received signal. Embodiments are deterministic, which provides superior performance over other conventional algorithms and is especially true for short burst signals. Embodiments are simple to implement and does not posses delay ambiguity. Embodiments can also be used for estimation with other matrix structures, where the SS method is applicable.
h
1=[1−2 cos θ1]T
h
2=[1−2 cos(θ+α)1]T
The absolute phase value of the zeros of h1 are represented by θ and the angular distance between the zeros of the two-channel is represented by α. An ill-conditioned system occurs when α is small (i.e., the distance between the zeros of the two channels is small, typically of order 10−1 or less). Conversely, the system is well-conditioned when α is large (typically in the range of π/6 to π/2). The SER is averaged over 100 Monte Carlo runs. The 4-QAM input signal and the additive noise are randomly generated for each Monte Carlo run. The data size used in the simulations is N=100 and the window is chosen to be Nw=5 unless noted otherwise.
Next, a reduced sample size is considered to test the performance of embodiments in the presence of a short data burst.
Embodiments are then tested for a fading channel. The fading channel considered is a two Raleigh channel (i.e., p=2), with a channel length of L=3.
The robusticity to channel length of embodiments are tested. A channel is randomly generated for increments between L=3 and L=6 while the SNR is fixed at 10 dB.
Finally, embodiments are tested by increasing the number of receiver antennas. The number of receiver antenna are increased to p=3. The third channel is defined by the following:
Next, further details of the hardware description of the computing environment according to exemplary embodiments is described with reference to
Further, the claims are not limited by the form of the computer-readable media on which the instructions of the inventive process are stored. For example, the instructions may be stored on CDs, DVDs, in FLASH memory, RAM, ROM, PROM, EPROM, EEPROM, hard disk or any other information processing device with which the computing device communicates, such as a server or computer.
Further, the claims may be provided as a utility application, background daemon, or component of an operating system, or combination thereof, executing in conjunction with CPU 901, 903 and an operating system such as Microsoft Windows 7, Microsoft Windows 10, Microsoft Windows 11, UNIX, Solaris, LINUX, Apple MAC-OS and other systems known to those skilled in the art.
The hardware elements in order to achieve the computing device may be realized by various circuitry elements, known to those skilled in the art. For example, CPU 901 or CPU 903 may be a Xenon or Core processor from Intel of America or an Opteron processor from AMD of America, or may be other processor types that would be recognized by one of ordinary skill in the art. Alternatively, the CPU 901, 903 may be implemented on an FPGA, ASIC, PLD or using discrete logic circuits, as one of ordinary skill in the art would recognize. Further, CPU 901, 903 may be implemented as multiple processors cooperatively working in parallel to perform the instructions of the inventive processes described above.
The computing device in
The computing device further includes a display controller 908, such as a NVIDIA GeForce GTX or Quadro graphics adaptor from NVIDIA Corporation of America for interfacing with display 910, such as a Hewlett Packard HPL2445w LCD monitor. A general purpose I/O interface 912 interfaces with a keyboard and/or mouse 914 as well as a touch screen panel 916 on or separate from display 910. General purpose I/O interface also connects to a variety of peripherals 916 including printers and scanners, such as an OfficeJet or DeskJet from Hewlett Packard.
A sound controller 920 is also provided in the computing device such as Sound Blaster X-Fi Titanium from Creative, to interface with speakers/microphone 922 thereby providing sounds and/or music.
The general purpose storage controller 924 connects the storage medium disk 904 with communication bus 926, which may be an ISA, EISA, VESA, PCI, or similar, for interconnecting all of the components of the computing device. A description of the general features and functionality of the display 910, keyboard and/or mouse 914, as well as the display controller 908, storage controller 924, network controller 906, sound controller 920, and general purpose I/O interface 912 is omitted herein for brevity as these features are known.
The exemplary circuit elements described in the context of the present disclosure may be replaced with other elements and structured differently than the examples provided herein. Moreover, circuitry configured to perform features described herein may be implemented in multiple circuit units (e.g., chips), or the features may be combined in circuitry on a single chipset, as shown on
In
For example,
Referring again to
The PCI devices may include, for example, Ethernet adapters, add-in cards, and PC cards for notebook computers. The Hard disk drive 1060 and CD-ROM 1066 can use, for example, an integrated drive electronics (IDE) or serial advanced technology attachment (SATA) interface. In one implementation the I/O bus can include a super I/O (SIO) device.
Further, the hard disk drive (HDD) 1060 and optical drive 1066 can also be coupled to the SB/ICH 1020 through a system bus. In one implementation, a keyboard 1070, a mouse 1072, a parallel port 1078, and a serial port 1076 can be connected to the system bus through the I/O bus. Other peripherals and devices that can be connected to the SB/ICH 1020 using a mass storage controller such as SATA or PATA, an Ethernet port, an ISA bus, a LPC bridge, SMBus, a DMA controller, and an Audio Codec.
Moreover, the present disclosure is not limited to the specific circuit elements described herein, nor is the present disclosure limited to the specific sizing and classification of these elements. For example, the skilled artisan will appreciate that the circuitry described herein may be adapted based on changes on battery sizing and chemistry or based on the requirements of the intended back-up load to be powered.
The functions and features described herein may also be executed by various distributed components of a system. For example, one or more processors may execute these system functions, wherein the processors are distributed across multiple components communicating in a network. The distributed components may include one or more client and server machines, which may share processing, as shown by
The above-described hardware description is a non-limiting example of corresponding structure for performing the functionality described herein.
Numerous modifications and variations of the present disclosure are possible in light of the above teachings. It is therefore to be understood that within the scope of the appended claims, the invention may be practiced otherwise than as specifically described herein.
The present application claims the benefit of priority to U.S. Prov. App. No. 63/329,993, entitled “Blind Adaptative Channel Estimation Using Structure Subspace Tracking”, filed on Apr. 12, 2022, and incorporated herein by reference in its entirety.
| Number | Date | Country | |
|---|---|---|---|
| 63329993 | Apr 2022 | US |
