Steven A. Benno

Scaling functions robust to translations

The discrete wavelet transform (DWT) is popular in a wide variety of applications. Its sparse sampling eliminates redundancy in the representation of signals and leads to efficient processing. However, the DWT lacks translation invariance. This makes it ill suited for many problems where the received signal is the superposition of arbitrarily shifted replicas of a transmitted signal as when multipath occurs, for example. The paper develops algorithms for the design of orthogonal and biorthogonal compact support scaling functions that are robust to translations. Our approach is to maintain the critical sampling of the DWT while designing multiresolution representations for which the coefficient energy redistributes itself mostly within each subband and not across the entire time-scale plane. We obtain expedite algorithms by decoupling the optimization from the constraints on the scaling function. Examples illustrate that the designed scaling function significantly improves the robustness of the representation.

On Translation Invariant Subspaces and Critically SampledWavelet Transforms

The discrete wavelet transform (DWT) is attractive for many reasons. Its sparse sampling grid eliminates redundancy and is very efficient. Its localized basis functions are well suited for processing non–stationary signals such as transients. On the other hand, its lack of translation invariance is a major pitfall for applications such as radar and sonar, particularly in a multipath environment where numerous signal components arrive with arbitrary delays. The paper proposes the use of robust representations as a solution to the translation invariance problem. We measure robustness in terms of a mean square error for which we derive an expression that describes this translation error in the Zak domain. We develop an iterative algorithm in the Zak domain for designing increasingly robust representations. The result is an approach for generating multiresolution subspaces that retain most of their coefficient energy as the input signal is shifted. A typical robust subspace retains 98% of its energy, a significant improvement over more traditional wavelet representations.

Seamless SIP-based VoIP in disparate wireless systems and networks

In the emerging data networks, session initiation protocol (SIP)-based voice over IP (VoIP) is gaining wide-scale acceptance as a means of transporting voice over the packet data networks. With the emergence of interoperability between various third-generation (3G) cellular technologies such as 1xEV, 1xEV-DO, 1xEV-DV, and the Universal Mobile Telecommunications System (UMTS) on one hand and wireless LAN (WLAN) technologies such as 802.11a/b/g, HiperLAN/2, and Bluetooth∗ on the other, multimedia applications would have to interoperate seamlessly among several air interfaces. Mobile IP, a layer 3 protocol, maintains the data session across heterogeneous air interfaces but does not guarantee minimal or no packet loss when handing over a mobile node from one air interface to another. This paper first discusses a network architecture that supports seamless interoperability between 3G and WLAN and proposes autonomous layer 2 enhancements at the client side to support SIP-based multimedia applications in general and voice applications in particular. Finally, it discusses some other network issues that pose a challenge to providing VoIP in commercial networks in general, such as using SIP with network address translation (NAT) over mobile IP, and it specifically addresses the problem of performing VoIP in CDMA2000∗ 1XRTT.

Shiftable representations and multipath processing

In multipath communications environments, the received signal is a superposition of delayed, possibly frequency shifted, and scaled replicas of a base signal s(t). For a known signal s(t), the optimal receiver is matched to the multipath signal s/sub M/(t). In general, this requires the determination of the unknown parameters, a multidimensional optimization problem usually out of reach for most applications. By adapting the notion of shiftability to the multipath problem, the matched filter is found by inner products which are easier to implement than a multidimensional optimization. The paper introduces the concept of nearly shiftable and describes an explicit construction for designing increasingly nearly shiftable signals and demonstrating the improvement obtained in the context of the multipath problem.<<ETX>>