Download design and low-complexity implementation of matrix–vector

www.pgembeddedsystems.com
DESIGN AND LOW-COMPLEXITY IMPLEMENTATION OF MATRIX–
VECTOR MULTIPLIER FOR ITERATIVE METHODS IN
COMMUNICATION SYSTEMS
ABSTRACT:
Iterative methods are basic building blocks of communication systems
and often represent a dominating part of the system, and therefore, they necessitate
careful design and implementation for optimal performance. In this brief, we
propose a novel field programmable gate arrays design of matrix–vector multiplier
that can be used to efficiently implement widely adopted iterative methods. The
proposed design exploits the sparse structure of the matrix as well as the fact that
spreading code matrices have equal magnitude entries. Implementation details and
timing analysis results are promising and are shown to satisfy most modern
communication system requirements.
EXISTING SYSTEM:
 Various flavors of hybrid methods that combine direct and iterative methods
have been devised.
 In the communication context and more precisely in CDMA systems, which
we will be considering in this brief, iterative methods have been used
extensively in estimation and detection problems.
 Other interference cancellation detectors that are based on faster iterative
methods have been devised recently.
www.pgembeddedsystems.com
PROPOSED SYSTEM:
In this brief, we propose a novel FPGA design and implementation of
matrix–vector multiplier that can be used to efficiently implement widely adopted
iterative methods such as residual norm steepest descent (RNSD), conjugate
gradient least square (CGLS), and residual norm Barzilai and Borwein (RNBB). In
this brief, we specifically focus on the design of a matrix–vector multiplication that
efficiently trades off between parallelism and delay. The proposed design balances
between parallelism and delay to achieve efficient hardware consumption by
exploiting sparsity of the multiplying matrix in the vector–matrix multiplication. In
addition, the hardware consumption is reduced further by exploiting the special
characteristic of orthogonal codes where entries of the spreading sequences are
equal in magnitude, and thus, can be scaled to 1 and −1.
www.pgembeddedsystems.com
LITERATURE SURVEY:
TITLE NAME: “Combining direct and iterative methods for the solution
of large systems in different application areas,”
AUTHOR NAME: I. S. Duff,
We first consider the size of problems that can currently be solved by sparse direct
methods. We then discuss the limitations of such methods, where current research
is going in moving these limitations, and how far we might expect to go with direct
solvers in the near future.his leads us to the conclusion that very large systems, by
which we mean three dimensional problems in more than a million degrees of
freedom, require the assistance of iterative methods in their solution. However,
even the strongest advocates and developers of iterative methods recognize their
limitations when solving difficult problems, that are problems that are poorly
conditioned and/or very unstructured. It is now universally accepted that
sophisticated pre conditioners must be used in such instances. A very standard and
sometimes successful class of preconditioners are based on incomplete
factorizations or sparse approximate inverses, but we very much want to exploit
the powerful software that we have developed for sparse direct methods over a
period of more than thirty years. We thus discuss various ways in which a
symbiotic relationship can be developed between direct and iterative methods in
order to solve problems that would be intractable for one class of methods alone. In
these approaches, we will use a direct factorization on a nearby" problem or on a
sub problem.
www.pgembeddedsystems.com
TITLE NAME: “Flexible inner-outer Krylov subspace methods,”
AUTHOR NAME: V. Simoncini and D. B. Szyld,
Flexible Krylov methodsrefersto a classof methodswhic h accept preconditioning
that can change from one step to the next. Given a Krylov subspace method, such
as CG, GMRES, QMR, etc. for the solution of a linear system Ax = b, instead of
having a fixed preconditioner M and the (right) preconditioned equation AM−1y =
b (Mx = y), one may have a different matrix, say Mk, at each step. In this paper,
the case where the preconditioner itself is a Krylov subspace method is studied.
There are several papers in the literature where such a situation is presented and
numerical examples given. A general theory is provided encompassing many of
these cases, including truncated methods. The overall space where the solution is
approximated is no longer a Krylov subspace but a subspace of a larger Krylov
space. We show how this subspace keeps growing as the outer iteration progresses,
thus providing a convergence theory for these inner-outer methods. Numerical tests
illustrate some important implementation aspects that make the discussed innerouter methods very appealing in practical circumstances.
www.pgembeddedsystems.com
TITLE NAME: “Linear interference cancellation in CDMA based on iterative
techniques for linear equation systems,”
AUTHOR NAME: P. H. Tan and L. K. Rasmussen,
It has previously been shown that well known iterations for solving a
set of linear equations correspond to linear interference cancellation structures.
Here, we suggest applying a block-wise iteration that consists of an outer and an
inner iteration. The outer iteration used is the Gauss-Seidel (GS) method, while for
the inner iteration, we study direct matrix inversion, the Jacobi over-relaxation
iteration, and the conjugate gradient iteration. When a true inner iteration is used,
this approach allows for a timely derivation of the acceleration parameters required
by advanced iterations. The block iteration is based on a symbol-level
implementation which leads to the same detection delay profile for both parallel
and serial structures at the expense of differences in the amount of serial
processing required. This is discussed in some detail and quantified for
comparison. The performance of the detectors is studied via computer simulations
where it is found that the block approach can provide significantly faster
convergence, leading to improved detection delay over the simpler GS iteration.
The improvements are obtained at the expense of an increase in the required serial
processing speed.
www.pgembeddedsystems.com
TITLE NAME: “Iterative least squares channel estimation in frequency
selective CDMA systems,”
AUTHOR NAME: A. Rizaner, H. Amca, A. H. Ulusoy, K. Hacioglu, and A. H.
Ulusoy,
Multiple access interference (MAI) is the main factor affecting the
performance of channel estimation techniques for code division multiple access
(CDMA) systems. Although, several multi-user channel estimation algorithms
have been proposed to mitigate MAI, these algorithms require high computational
complexities. In this paper, we address the problem of least squares (LS) mobile
channel estimation at high channel efficiency that requires a short training
sequence along with the spreading sequences. Then, we employ an efficient
iterative method based on conjugate gradient (CG) algorithm to reduce the
computational complexity of the estimation method.
TITLE NAME: “Optimization of linear iterative inter ference cancellation
receivers for CDMA communications,”
AUTHOR NAME:N. Albeanu and T. J. Lim,
Iterative methods to solve a linear equation system can be used to derive multistage
interference cancellers (ICs) that converge to the decorrelating or the minimum
mean-square error linear detectors. The link between linear multistage IC and
iterative solution methods is well known; however, the parameters needed for
fastest convergence are functions of the eigen values of the channel matrix.
www.pgembeddedsystems.com
SOFTWARE REQUIREMENTS:
 Xilinx ISE Design Suite 13.1
 Cadence-RTL Complier
 Cadence- encounter
REFERENCES:
[1] Y. Saad, Iterative Methods for Sparse Linear Systems, 2nd ed. Philadelphia,
PA, USA: SIAM, 2003.
[2] I. S. Duff, “Combining direct and iterative methods for the solution of large
systems in different application areas,” Centre Européen de Recherche et de
Formation Avancée en Calcul Scientifique, Toulouse, France, Tech. Rep.
TR/PA/04/128, 2004.
[3] N. Jamil, “A comparison of direct and indirect solvers for linear systems of
equations,” Int. J. Emerg. Sci., vol. 2, no. 2, pp. 310–321, Jun. 2012.
[4] V. Simoncini and D. B. Szyld, “Flexible inner-outer Krylov subspace
methods,” SIAM J. Numer. Anal., vol. 40, no. 6, pp. 2219–2239, 2003.
[5] P. H. Tan and L. K. Rasmussen, “Linear interference cancellation in CDMA
based on iterative techniques for linear equation systems,” IEEE Trans. Commun.,
vol. 48, no. 12, pp. 2099–2108, Dec. 2000.
www.pgembeddedsystems.com
[6] P. H. Tan and L. K. Rasmussen, “Linear interference cancellation in CDMA
based on iterative techniques for linear equation systems,” IEEE Trans. Commun.,
vol. 48, no. 12, pp. 2099–2108, Dec. 2000.
[7] A. Rizaner, H. Amca, A. H. Ulusoy, K. Hacioglu, and A. H. Ulusoy, “Iterative
least squares channel estimation in frequency selective CDMA systems,” in Proc.
AICT-ICIW, Feb. 2006, p. 86.
[8]
N.
Albeanu
and
T.
J.
Lim,
“Optimization
of
linear
iterative
interferencecancellation receivers for CDMA communications,” IEEE Trans.
Commun., vol. 52, no. 3, pp. 376–379, Mar. 2004.
[9] M. L. Honig, Advances in Multiuser Detection. Hoboken, NJ, USA: Wiley,
2009.
[10] A. Bentrcia and S. Alshebeili, “New linear PIC detectors based on nonmonotone line-search techniques,” Signal Process., vol. 92, no. 12, pp. 3085–3090,
2012.
[11] A. Bentrcia and S. Alshebeili, “Linear IC detectors for low to medium SNR
ill-conditioned communication systems with unknown noise variance,” EURASIP
J. Adv. Signal Process., vol. 2013, p. 180, Dec. 2013.
[12] A. Bentrcia and S. Alshebeili, “Competitive linear parallel interference
cancellation detection based on monotone line-search techniques,” IET Signal
Process., vol. 8, no. 5, pp. 521–529, Jul. 2013.