Impulse Response Shortening for Discrete Multitone Transceivers using Convex Optimization Approach
In this paper we propose a new criterion for solving
the problem of channel shortening in multi-carrier systems. In a
discrete multitone receiver, a time-domain equalizer (TEQ) reduces
intersymbol interference (ISI) by shortening the effective duration of
the channel impulse response. Minimum mean square error (MMSE)
method for TEQ does not give satisfactory results. In [1] a new
criterion for partially equalizing severe ISI channels to reduce the
cyclic prefix overhead of the discrete multitone transceiver (DMT),
assuming a fixed transmission bandwidth, is introduced. Due to
specific constrained (unit morm constraint on the target impulse
response (TIR)) in their method, the freedom to choose optimum
vector (TIR) is reduced. Better results can be obtained by avoiding
the unit norm constraint on the target impulse response (TIR). In
this paper we change the cost function proposed in [1] to the cost
function of determining the maximum of a determinant subject to
linear matrix inequality (LMI) and quadratic constraint and solve the
resulting optimization problem. Usefulness of the proposed method
is shown with the help of simulations.
[1] N. Al-Dahir,and J.M. Cioffi, "Optimum finite-length equalization for
multicarrier transceivers", IEEE trans. on communications, vol.44, no.1,
Jan, 1996.
[2] G. Arsalan, B. L. Evans and S. Kiaei, "Equalization for discrete multitone
transceivers to maximize bit rate", IEEE Trans. on signal processing ,
vol.49,no.12,Dec. 2001.
[3] N. Al-Dahir,and J.M. Cioffi, "A bandwidth-optimized reduced complexity
equalized multicarrier transreceiver", IEEE Trans. on communications,
vol. 45, no. 8, Aug. 1997.
[4] F. Alizadeh, "Interior point methods in semidefinite programming with
applications to combinatorial optimization", SIAM journal of optimization,
5, pp.13-51, 1995.
[5] L. Vandenberghe, S. Boyd, and S. Wu, " Determinant maximization with
linear matrix inequality constraints", SIAM journal on matrix analysis
and applications, 19(2), pp. 499-533, 1998.
[6] P. S. Bullen, D. S. Mitrinovic, and P. M. Vasic, (eds), "Means and their
inequalities", D. Reidel pub. co., 1988.
[7] R. A. Horn and C. R. Johnson, "Matrix analysis", Cambridge Univ. Press,
1999.
[8] J. M. Cioffi, "A multicarrier primer", Amati. Commun. Corp., Stanford
Univ. Stanford, CA, T1E1.4/91-157, 1991.
[9] D. Daly, C. Heneghan, and A. D. Fagan, "Minimum mean squared error
impulse response shortening for discrete multitone transceivers", IEEE
Trans. on signal proc. vol.52, no.1, Jan. 2004.
[1] N. Al-Dahir,and J.M. Cioffi, "Optimum finite-length equalization for
multicarrier transceivers", IEEE trans. on communications, vol.44, no.1,
Jan, 1996.
[2] G. Arsalan, B. L. Evans and S. Kiaei, "Equalization for discrete multitone
transceivers to maximize bit rate", IEEE Trans. on signal processing ,
vol.49,no.12,Dec. 2001.
[3] N. Al-Dahir,and J.M. Cioffi, "A bandwidth-optimized reduced complexity
equalized multicarrier transreceiver", IEEE Trans. on communications,
vol. 45, no. 8, Aug. 1997.
[4] F. Alizadeh, "Interior point methods in semidefinite programming with
applications to combinatorial optimization", SIAM journal of optimization,
5, pp.13-51, 1995.
[5] L. Vandenberghe, S. Boyd, and S. Wu, " Determinant maximization with
linear matrix inequality constraints", SIAM journal on matrix analysis
and applications, 19(2), pp. 499-533, 1998.
[6] P. S. Bullen, D. S. Mitrinovic, and P. M. Vasic, (eds), "Means and their
inequalities", D. Reidel pub. co., 1988.
[7] R. A. Horn and C. R. Johnson, "Matrix analysis", Cambridge Univ. Press,
1999.
[8] J. M. Cioffi, "A multicarrier primer", Amati. Commun. Corp., Stanford
Univ. Stanford, CA, T1E1.4/91-157, 1991.
[9] D. Daly, C. Heneghan, and A. D. Fagan, "Minimum mean squared error
impulse response shortening for discrete multitone transceivers", IEEE
Trans. on signal proc. vol.52, no.1, Jan. 2004.
@article{"International Journal of Electrical, Electronic and Communication Sciences:51203", author = "Ejaz Khan and Conor Heneghan", title = "Impulse Response Shortening for Discrete Multitone Transceivers using Convex Optimization Approach", abstract = "In this paper we propose a new criterion for solving
the problem of channel shortening in multi-carrier systems. In a
discrete multitone receiver, a time-domain equalizer (TEQ) reduces
intersymbol interference (ISI) by shortening the effective duration of
the channel impulse response. Minimum mean square error (MMSE)
method for TEQ does not give satisfactory results. In [1] a new
criterion for partially equalizing severe ISI channels to reduce the
cyclic prefix overhead of the discrete multitone transceiver (DMT),
assuming a fixed transmission bandwidth, is introduced. Due to
specific constrained (unit morm constraint on the target impulse
response (TIR)) in their method, the freedom to choose optimum
vector (TIR) is reduced. Better results can be obtained by avoiding
the unit norm constraint on the target impulse response (TIR). In
this paper we change the cost function proposed in [1] to the cost
function of determining the maximum of a determinant subject to
linear matrix inequality (LMI) and quadratic constraint and solve the
resulting optimization problem. Usefulness of the proposed method
is shown with the help of simulations.", keywords = "Equalizer, target impulse response, convex optimization,matrix inequality.", volume = "2", number = "8", pages = "1582-5", }