ScholarBank@NUShttps://scholarbank.nus.edu.sgThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Thu, 26 Nov 2020 00:53:13 GMT2020-11-26T00:53:13Z50121- New tight bounds on the pairwise error probability for unitary space-time modulationshttps://scholarbank.nus.edu.sg/handle/10635/56805Title: New tight bounds on the pairwise error probability for unitary space-time modulations
Authors: Li, R.; Yuen Kam, P.
Abstract: We present two upper bounds and one lower bound on the pairwise error probability (PEP) of unitary space-time modulation (USTM) over the Rayleigh fading channel. The two new upper bounds are the tightest so far, and the new lower bound is the tightest at low signal-to-noise ratio. Some implications for USTM constellation design are also pointed out. © 2005 IEEE.
Fri, 01 Apr 2005 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/568052005-04-01T00:00:00Z
- New representations and bounds for the generalized marcum Q-function via a geometric approach, and an applicationhttps://scholarbank.nus.edu.sg/handle/10635/82754Title: New representations and bounds for the generalized marcum Q-function via a geometric approach, and an application
Authors: Li, R.; Kam, P.Y.; Fu, H.
Abstract: The generalized Marcum Q-function of order m, Qm(a, b), is interpreted geometrically as the probability of a 2m-dimensional, real, Gaussian random vector z2m, whose mean vector has a Frobenius norm of a, lying outside of a hyperball B2m o,b of 2m dimensions, with radius b, and centered at the origin O. Based on this new geometric view, some new representations and closed-form bounds are derived for Qm(a, b). For the case that m is an odd multiple of 0.5, a new closed-form representation is derived, which involves only simple exponential and erfc functions. For the case that m is an integer, a pair of new, finite-integral representations for Q m(a, b) is derived. Some generic exponential bounds and erfc bounds are also derived by computing the probability of z2m lying outside of various bounding geometrical shapes whose surfaces tightly enclose, or are tightly enclosed by the surface of B2m o,b. These bounding shapes consist of an arbitrarily large number of parts. As their closeness of fit with B2m o,b improves, our generic bounds approach the exact value of Qm(a, b). The function Qm(a, b) is proved to be an increasing function of its order when 2m is a positive integer. Thus, Qm+0.5(a, b) and Qm-0.5(a, b) can be used as tight upper and lower bounds, respectively, on Qm(a, b). Their average is a good approximation to Qm(a, b). An application of our new representations and bounds is also given. © 2010 IEEE.
Fri, 01 Jan 2010 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/827542010-01-01T00:00:00Z
- Averages of the product of two Gaussian Q-functions over fading statistics and applicationshttps://scholarbank.nus.edu.sg/handle/10635/55178Title: Averages of the product of two Gaussian Q-functions over fading statistics and applications
Authors: Li, R.; Kam, P.Y.
Abstract: The averages of the product of two Gaussian Q-functions over the Nakagami-m and the Rician fading distributions are evaluated. The results obtained are applied to deriving closed-form bounds on the average bit error probability for a variety of single channel, partially coherent, differential and quadratic detections. © 2007 IEEE.
Mon, 01 Jan 2007 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/551782007-01-01T00:00:00Z
- Simple tight exponential bounds on the first-order Marcum Q-function via the geometric approachhttps://scholarbank.nus.edu.sg/handle/10635/84184Title: Simple tight exponential bounds on the first-order Marcum Q-function via the geometric approach
Authors: Kam, P.Y.; Li, R.
Abstract: The geometric interpretation of the first-order Marcum Q-function, Q(a, b), has been shown as the probability that a complex, Gaussian random variable Z̃ with real, nonzero mean a takes on values outside of a circular region CO,b of radius b centered at the origin O. Based on this interpretation, many new, simple, tight, upper/lower exponential bounds on Q(a, b) are easily obtained by computing the probability of Z lying outside of some simple geometrical shapes, such as circular regions, semicircular regions, sectors, and angular sectors of annuli, whose boundaries tightly enclose, or are tightly enclosed by the boundary of CO,b. The new bounds presented here only involve two exponential functions, and the best of them are in most cases much tighter than the best existing exponential bounds. In addition to these bounds, more new bounds can be obtained by using similar methods. Even some bounds in the literature can also be obtained via this geometric approach. ©2006 IEEE.
Sun, 01 Jan 2006 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/841842006-01-01T00:00:00Z
- Generalized quadratic receivers for unitary space-time modulation over Rayleigh fading channelshttps://scholarbank.nus.edu.sg/handle/10635/56122Title: Generalized quadratic receivers for unitary space-time modulation over Rayleigh fading channels
Authors: Li, R.; Kam, P.Y.
Abstract: We propose the generalized quadratic receivers (GQRs) for unitary space-time modulation over flat Rayleigh fading channels. The GQRs realize the performance improvement potential, known to be approximately 2-4 dB, between the quadratic receiver (QR) and the coherent receiver (CR), by performing channel estimation without the help of additional training signals that consume additional bandwidth. They are designed for various unitary space-time constellations (USTC) in which signal matrices may or may not contain explicit inherent training blocks, and may be orthogonal or nonorthogonal to one another. As the channel memory span exploited for channel estimation increases, the error probability of the GQRs reduces from that of the QR to that of the CR. The GQRs work well for both slow and fast fading channels, and the performance improvement increases as the channel fade rate decreases. For a class of USTC with the orthogonal design structure, the GQR is simplified to a form whose complexity can be less than the complexity of the QR or even that of the simplified form of the QR. © 2007 IEEE.
Mon, 01 Oct 2007 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/561222007-10-01T00:00:00Z
- Computing and bounding the generalized Marcum Q-function via a geometric approachhttps://scholarbank.nus.edu.sg/handle/10635/83573Title: Computing and bounding the generalized Marcum Q-function via a geometric approach
Authors: Li, R.; Kam, P.Y.
Abstract: The generalized Marcum Q-function, Qm(a,b), is here explained geometrically as the probability of a 2m-dimensional, real, Gaussian random vector, whose mean vector has a Frobenius norm of a, lying outside of a hypersphere of 2m dimensions, with radius b, and centered at the origin. Based on this new geometric interpretation, a new closed-form representation for Qm (a, b) is derived for the case where m is an odd multiple of 0.5. This representation involves only the exponential and the erfc functions, and thus is easy to handle, both numerically and analytically. For the case where m is an even multiple of 0.5, Qm+0.5(a,b) and Qm-0.5(a,b), which can be evaluated using our new representation mentioned above, are shown to be tight upper and lower bounds on Qm(a,b), respectively. They are shown in most cases to be much tighter than the existing bounds in the literature, and are valid for the entire ranges of a and b concerned. Their average is also a good approximation to Qm(a,b). ©2006 IEEE.
Sun, 01 Jan 2006 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/835732006-01-01T00:00:00Z
- Computing and bounding the first-order Marcum Q-function: A geometric approachhttps://scholarbank.nus.edu.sg/handle/10635/55388Title: Computing and bounding the first-order Marcum Q-function: A geometric approach
Authors: Kam, P.Y.; Li, R.
Abstract: A geometric interpretation of the first-order Marcum Q-function, Q(a, b), is introduced as the probability that complex, Gaussian random variable with real mean a, takes on values outside of a disk CO,b of radius b centered at the origin O. This interpretation engenders a fruitful approach for deriving new representations and tight, upper and lower bounds on Q(a, b). The new representations obtained involve finite-range integrals with pure exponential integrands. They are shown to be simpler and more robust than their counterparts in the literature. The new bounds obtained include the generic exponential bounds which involve an arbitrarily large number of exponential functions, and the simple erfc bounds which involve just a few erfc functions, together with exponential functions in some cases. The new generic exponential bounds approach the exact value of Q(a, b) as the number of exponential terms involved increases. These generic exponential bounds evaluated with only two terms and the new simple erfc bounds are much tighter than the existing exponential bounds in most cases, especially when the arguments a and b are large. Thus, in many applications requiring further analytical manipulations of Q(a, b), these new bounds can lead to some closed-form results which are better than the results available so far. © 2008 IEEE.
Tue, 01 Jul 2008 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/553882008-07-01T00:00:00Z
- Generalized quadratic receivers for unitary space-time constellations with orthogonal design over Rayleigh fading channelshttps://scholarbank.nus.edu.sg/handle/10635/70414Title: Generalized quadratic receivers for unitary space-time constellations with orthogonal design over Rayleigh fading channels
Authors: Li, R.; Kam, P.Y.
Abstract: Unitary space-time modulation is a transmit diversity technique for the nonselective Rayleigh fading channel. It was proposed for noncoherent detection without any channel state information (CSI) at the receiver. However, with perfect CSI at the receiver, the performance improvement is known to be approximately 2-4 dB. In order to exploit this improvement potential and keep the merit of not wasting bandwidth resources for additional training signals, we propose a generalized quadratic receiver (GQR) for a class of unitary space-time constellations with orthogonal design over the Rayleigh fading channel. As the channel memory span exploited by this GQR for channel estimation increases, the error probability of the GQR reduces from that of the conventional quadratic receiver to that of the coherent receiver. This performance improvement increases as the channel fade rate decreases. In addition, the complexity of the simplified GQR can be less than that of the noncoherent receiver. © 2005 IEEE.
Sat, 01 Jan 2005 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/704142005-01-01T00:00:00Z
- Generalized quadratic receivers for orthogonal and nonorthogonal unitary space-time constellations over rayleigh fading channelshttps://scholarbank.nus.edu.sg/handle/10635/70413Title: Generalized quadratic receivers for orthogonal and nonorthogonal unitary space-time constellations over rayleigh fading channels
Authors: Li, R.; Kam, P.Y.
Abstract: We propose the generalized quadratic receivers (GQRs) for orthogonal and general nonorthogonal unitary spacetime constellations, respectively, over the flat Rayleigh fading channel. The GQRs exploit the performance improvement potential, known to be approximately 2-4 dB, between the noncoherent quadratic receiver (QR) and the coherent receiver (CR), without wasting bandwidth resources for additional training signals. For both the cases of orthogonal and nonorthogonal unitary space-time constellations, as the channel memory span exploited for channel estimation increases, the error probabilities of the GQRs reduce from that of the QR and approach that of the CR. The GQRs are shown to be effective for both slow and fast fading channels, and the performance improvements increase as the channel fade rate decreases. © 2006 IEEE.
Sun, 01 Jan 2006 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/704132006-01-01T00:00:00Z
- Generic exponential bounds on the generalized Marcum Q-function via the geometric approachhttps://scholarbank.nus.edu.sg/handle/10635/83759Title: Generic exponential bounds on the generalized Marcum Q-function via the geometric approach
Authors: Li, R.; Kam, P.Y.
Abstract: The generalized Marcum Q-function, Qm(a, b), can be interpreted geometrically as the probability of a 2m-dimensional, real, Gaussian random vector Z2m, whose mean vector has a Frobenius norm of a, lying outside of a hyperball double-struck B signO,b 2m], of 2m dimensions, with radius b, and centered at the origin O. Based on this geometric view, we propose some new generic exponential bounds on Qm(a, b) for the case where m is an integer. These generic exponential bounds are obtained by computing the probability of Z2m lying outside of some bounding geometrical shapes whose surfaces tightly enclose, or are tightly enclosed by the surface of double-struck B sign O,b 2m]. The bounding geometrical shapes used in the derivation consist of an arbitrarily large number of parts. As their closeness of fit with double-struck B sign O,b 2m improves, the generic exponential bounds obtained approach the exact value of Qm(a, b). These generic exponential bounds only involve the exponential function, and thus, are easy to handle in analytical computations. Our numerical results show that when evaluated with a few terms, these generic exponential bounds are much tighter than the existing exponential bounds in the literature for a wide range of arguments. For the case of a > b, our generic upper exponential bound is the first upper exponential bound on Qm(a, b). © 2007 IEEE.
Mon, 01 Jan 2007 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/837592007-01-01T00:00:00Z
- Generic exponential bounds and erfc-bounds on the marcum Q-function via the geometric approachhttps://scholarbank.nus.edu.sg/handle/10635/83758Title: Generic exponential bounds and erfc-bounds on the marcum Q-function via the geometric approach
Authors: Kam, P.Y.; Li, R.
Abstract: The first-order Marcum Q-function, Q(a, b), can be interpreted geometrically as the probability that a complex, Gaussian random variable Z̃ with real mean a, takes on values outside of a circular region C O,b of radius b centered at the origin O. Bounds can thus be easily obtained by computing the probability of Z̃ lying outside of some geometrical shapes whose boundaries tightly enclose, or are tightly enclosed by the boundary of CO,b. In this paper, the bounding shapes are chosen to be a set of sectors or angular sectors of annuli to generate generic exponential bounds, and to be a set of rectangles to generate generic erfcbounds. These generic exponential bounds and erfc-bounds involve an arbitrarily large number of exponential functions and erfc functions, respectively, and are shown to approach the exact value of Q(a, b) as the number of terms involved increases. © 2006 IEEE.
Sun, 01 Jan 2006 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/837582006-01-01T00:00:00Z
- A new geometric view of the first-order marcum Q-function and some simple tight erfc-boundshttps://scholarbank.nus.edu.sg/handle/10635/83382Title: A new geometric view of the first-order marcum Q-function and some simple tight erfc-bounds
Authors: Kam, P.Y.; Li, R.
Abstract: A geometric interpretation of the first-order Marcum Q-function, Q(a,b), is introduced as the probability that a complex, Gaussian random variable with real, nonzero mean a, takes on values outside of a circular region Cb of radius b centered at the origin. This interpretation engenders a fruitful approach for deriving new representations and tight, upper/lower erfc-bounds on Q(a,b). The new representations involve finite-range integrals that facilitate analytical and numerical computations, and are simpler than similar ones in the literature. The new, simple erfc-bounds are easily obtained by using simple geometrical shapes that tightly enclose, or are tightly enclosed by the circle Cb. They involve only a few terms of erfc and exponential functions, and are close to, or even tighter than the existing bounds that involve the modified Bessel function. © 2006 IEEE.
Sun, 01 Jan 2006 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/833822006-01-01T00:00:00Z