TY - GEN
T1 - New analytic results for the incomplete Toronto function and incomplete Lipschitz-Hankel Integrals
AU - Sofotasios, Paschalis C.
AU - Freear, Steven
PY - 2011
Y1 - 2011
N2 - This paper provides novel analytic expressions for the incomplete Toronto function, T B(m, n, r), and the incomplete Lipschitz-Hankel Integrals of the modified Bessel function of the first kind, Ie μ,n(a, z). These expressions are expressed in closed-form and are valid for the case that m ≥ n and n being an odd multiple of 1/2, i.e. n ± 0.5 ∈ N Capitalizing on these, tight upper and lower bounds are subsequently proposed for both T B(m, n, r) function and Ie μ, n(a, z) integrals. Importantly, all new representations are expressed in closed-form whilst the proposed bounds are shown to be rather tight. To this effect, they can be effectively exploited in various analytical studies related to wireless communication theory. Indicative applications include, among others, the performance evaluation of digital communications over fading channels and the information-theoretic analysis of multiple-input multiple-output systems.
AB - This paper provides novel analytic expressions for the incomplete Toronto function, T B(m, n, r), and the incomplete Lipschitz-Hankel Integrals of the modified Bessel function of the first kind, Ie μ,n(a, z). These expressions are expressed in closed-form and are valid for the case that m ≥ n and n being an odd multiple of 1/2, i.e. n ± 0.5 ∈ N Capitalizing on these, tight upper and lower bounds are subsequently proposed for both T B(m, n, r) function and Ie μ, n(a, z) integrals. Importantly, all new representations are expressed in closed-form whilst the proposed bounds are shown to be rather tight. To this effect, they can be effectively exploited in various analytical studies related to wireless communication theory. Indicative applications include, among others, the performance evaluation of digital communications over fading channels and the information-theoretic analysis of multiple-input multiple-output systems.
KW - Closed-form representations
KW - fading
KW - Incomplete Lipschitz-Hankel Integrals
KW - Incomplete Toronto function
KW - Marcum Q-function
KW - special functions
KW - upper and lower bounds
UR - http://www.scopus.com/inward/record.url?scp=84860469303&partnerID=8YFLogxK
U2 - 10.1109/IMOC.2011.6169356
DO - 10.1109/IMOC.2011.6169356
M3 - Conference contribution
AN - SCOPUS:84860469303
SN - 9781457716621
T3 - SBMO/IEEE MTT-S International Microwave and Optoelectronics Conference Proceedings
SP - 44
EP - 47
BT - 2011 SBMO/IEEE MTT-S International Microwave and Optoelectronics Conference, IMOC 2011
T2 - 2011 SBMO/IEEE MTT-S International Microwave and Optoelectronics Conference, IMOC 2011
Y2 - 29 October 2011 through 1 November 2011
ER -