Approximation of L\"owdin Orthogonalization to a Spectrally Efficient Orthogonal Overlapping PPM Design for UWB Impulse Radio

In this paper we consider the design of spectrally efficient time-limited pulses for ultrawideband (UWB) systems using an overlapping pulse position modulation scheme. For this we investigate an orthogonalization method, which was developed in 1950 by Per-Olov L\"owdin. Our objective is to obtain a set of N orthogonal (L\"owdin) pulses, which remain time-limited and spectrally efficient for UWB systems, from a set of N equidistant translates of a time-limited optimal spectral designed UWB pulse. We derive an approximate L\"owdin orthogonalization (ALO) by using circulant approximations for the Gram matrix to obtain a practical filter implementation. We show that the centered ALO and L\"owdin pulses converge pointwise to the same Nyquist pulse as N tends to infinity. The set of translates of the Nyquist pulse forms an orthonormal basis or the shift-invariant space generated by the initial spectral optimal pulse. The ALO transform provides a closed-form approximation of the L\"owdin transform, which can be implemented in an analog fashion without the need of analog to digital conversions. Furthermore, we investigate the interplay between the optimization and the orthogonalization procedure by using methods from the theory of shift-invariant spaces. Finally we develop a connection between our results and wavelet and frame theory.Comment: 33 pages, 11 figures. Accepted for publication 9 Sep 201

Hard-input-hard-output capacity analysis of UWB BPSK systems with timing errors

The hard-input-hard-output capacity of a binary phase-shift keying (BPSK) ultrawideband system is analyzed for both additive white Gaussian noise and multipath fading channels with timing errors. Unlike previous works that calculate the capacity with perfect synchronization and/or multiple-access interference only, our analysis considers timing errors with different distributions, as well as the interpath (IPI), interchip (ICI), and intersymbol (ISI) interferences, as in practical systems. The sensitivity of the channel capacity to the timing error is examined. The effects of pulse shape, the multiple-access technique, the number of users, and the number of chips are studied. It is found that time hopping is less sensitive to the pulse shape and that the timing error has higher capacity than direct sequence due to its low duty of cycle. Using these results, one can choose appropriate system parameters for different applications

Performance of Bit Error Rate and Power Spectral Density of Ultra Wideband with Time Hopping Sequences.

This thesis focuses on several modulation methods for an ultra wideband (UWB) signal. These methods are pulse position modulation (PPM), binary phase shift keying (BPSK), on/off key shifting (OOK), and pulse amplitude modulation (PAM). In addition, time hopping is considered for these modulation schemes, where the capacity per time frame of time hopping PPM is studied using different spreading ratios. This thesis proves that with the addition of time hopping to all types of modulated UWB signals, the performance of power spectral density improves in all aspects, despite the increase of data per time frame. Note that despite the increase of data per frame, the bit error rate remains the same as standard non-time hopping UWB modulated signals

Time-Hopping Multicarrier Code-Division Multiple-Access

A time-hopping multicarrier code-division multiple-access (TH/MC-CDMA) scheme is proposed and investigated. In the proposed TH/MC-CDMA each information symbol is transmitted by a number of time-domain pulses with each time-domain pulse modulating a subcarrier. The transmitted information at the receiver is extracted from one of the, say $M$, possible time-slot positions, i.e., assuming that $M$-ary pulse position modulation is employed. Specifically, in this contribution we concentrate on the scenarios such as system design, power spectral density (PSD) and single-user based signal detection. The error performance of the TH/MC-CDMA system is investigated, when each subcarrier signal experiences flat Nakagami-$m$ fading in addition to additive white Gaussian noise (AWGN). According to our analysis and results, it can be shown that the TH/MC-CDMA signal is capable of providing a near ideal PSD, which is flat over the system bandwidth available, while decreases rapidly beyond that bandwidth. Explicitly, signals having this type of PSD is beneficial to both broadband and ultra-wide bandwidth (UWB) communications. Furthermore, our results show that, when optimum user address codes are employed, the single-user detector considered is near-far resistant, provided that the number of users supported by the system is lower than the number of subcarriers used for conveying an information symbol

An enhanced pulse position modulation (PPM) in ultra-wideband (UWB) systems

Simplicity, transmission rate, and bit error rate (BER) performance are three major concerns for ultra-wideband (UWB) systems. The main advantage of existing pulse-position modulation (PPM) schemes is simplicity, but their BER performance is poorer than that of an on-off-keying (OOK) modulation scheme, and their transmission rate is lower than that of an OOK scheme. In this research project, I will explore a novel PPM scheme, which can maintain the simplicity of the PPM schemes as well as achieve a BER performance and a transmission rate similar to the OOK scheme. During the research, I will thoroughly investigate the relationship between pulse position allocation and the BER performance and the transmission rate of UWB systems through computer simulations and theoretical analysis, and develop a whole set of design rules for the novel PPM scheme

Ultra-wideband technology for short-range wireless communication

The ultra-wideband (UWB) radio core idea is to open large amounts of spectrum to a variety of users with little mutual interference between them. While ultra-wideband is being championed by several commercial companies, this technology has not followed the conventional path where commercial interest is preceded by years of academic research. This work attempts to fill in some of the gap by studying fundamental properties of communications with impulse-based radio UWB signals. We study jam resistance and capacity of UWB. Jam resistance is analyzed for binary pulse position modulation (PPM) with the interference being modeled as correlated Gaussian. Closed-form expressions are provided for the jam resistance of a PPM UWB system utilizing rectangular pulses. Simple approximations are obtained for special cases (narrowband interference). Such analysis is extended to other practical UWB waveforms such as Gaussian and Rayleigh monocycles. It is shown that under some conditions, the UWB jam resistance is superior to that of direct sequence spread spectrum (DS-SS). In the second part of this work, we study the capacity of the single-user UWB communication systems utilizing M-ary PPM and bi-phase as well as on-off keying modulation scheme over additive white Gaussian noise (AWGN) and multipath channels. Starting from the known capacity of M-ary modulated signals, the computation of UWB capacity over the AWGN channel takes into account UWB specific constraints. The constraints are the power spectrum density limitation under Federal Communications Commission (FCC) Part 15 rules and the spreading ratio required to achieve a specified jam resistance level. UWB capacity over AWGN channel is expressed as a function of spreading ratio and communication range. Trade-offs between capacity and range of communications and between capacity and spreading ratio are explored. We extend the study of capacity of UWB communications to the multipath channel using the modified S-V model proposed by the IEEE 802.15.3a task group. The complementary cumulative distribution function (CCDF) of the capacities, subject to the FCC power spectral density (PSD) limitation, are obtained for the all Rake (ARake) and selective Rake (SRake) receivers. In both of the cases, maximum ratio combining is employed. Finally, the capacity of multiple-access UWB communications is studied over the AWGN channel. Under certain assumptions, the multiple-access noise component at the receiver is modeled as Gaussian. An expression for the UWB capacity of the multiple-access channel is developed as a function of number of users

Frequency and time hopping PPM UWB multiple access communication scheme

In this paper we propose frequency and time hopping pulse position modulation (FTH-PPM) ultra wideband (UWB) for multiple access communications.We have derived and investigated the bit error probability for the multi-user synchronous transmitter case in multipath channels with Additive White Gaussian Noise (AWGN). Simulation results show that bit error probability performance of FTH-PPM UWB out performs the time hopping pulse position modulated (TH-PPM) UWB system. It also show that multiuser capacity of FTH-PPM UWB system is much better than TH-PPM UWB system