Raised Cosine Spectrum Research Articles

Jitter floor elimination for blind feedforward/feedback symbol‐timing recovery exploiting the extended zero‐crossing property

SummaryCarrier‐blind and non‐data‐aided recovery of the symbol timing is of paramount importance in digital receivers, that is, detailed knowledge about carrier frequency and phase or any pilot sequence is not necessary for proper operation. In this context, feedforward algorithms are particularly helpful in packet‐oriented systems, where rapid and stable acquisition of the major transmission parameters is essential for subsequent processing stages. On the other hand, feedback algorithms are typically used to track small deviations from the stable equilibrium point. In the current paper, we propose a new approach for blind feedforward and feedback recovery of the symbol timing, which needs just one or two samples per symbol. The method is characterized by a second filter operated in parallel to the receiver‐matched filter. Under Nyquist conditions, exemplified by baseband pulses having a square‐root raised cosine spectrum, this filter exhibits an impulse response satisfying the extended zero‐crossing property, that is, it vanishes for all integer multiples of the symbol period including the origin. Using this idea for symbol‐timing recovery, it is shown that the annoying jitter floor – typical for most timing recovery schemes and caused by inter‐symbol interference – can be avoided irrespective of the selected modulation scheme. Copyright © 2015 John Wiley & Sons, Ltd.

On the Application of Raised-Cosine Wavelets for Multicarrier Systems Design

New orthogonal wavelet transforms can be designed by changing the wavelet basis functions or by constructing new low-pass filters (LPF). One family of wavelet may appeal, in use, to a particular application than another. In this study, the wavelet transform based on raised-cosine spectrum is used as an independent orthogonal wavelet to study multicarrier modulation behaviour over multipath channel environment. Then, the raised-cosine wavelet is compared with other well-known orthogonal wavelets that are used, also, to build multicarrier modulation systems. Traditional orthogonal wavelets do not have side-lobes, while the raised-cosine wavelets have lots of side-lobes; these characteristics influence the wavelet behaviour. It will be shown that the raised-cosine wavelet transform, as an orthogonal wavelet, does not support the design of multicarrier application well like the existing well-known orthogonal wavelets.

Generation of Spectrally Efficient Nyquist-WDM QPSK Signals Using Digital FIR or FDE Filters at Transmitters

Nyquist pulse shaping can be used to increase the spectral efficiency (SE) by narrowing the signal spectrum without introducing intersymbol interference in a wavelength-division-multiplexed (WDM) system. In this paper, we investigate the complexity and performance of pulse shaping at the transmitter side using digital finite-impulse-response (FIR) or frequency-domain-equalization (FDE) filters to increase the SE in a polarization-division-multiplexed quadrature-phase-shift-keyed WDM system. Simulation results show that FIR filters with 17 taps allow for a reduction in channel spacing to 1.1 times the symbol rate within a 1 dB penalty. The root-raised-cosine spectrum shape has better performances than the raised-cosine spectrum shape with that channel spacing. An FDE filter with a fast Fourier transform size of 64 and an overlap length of 8 points performs slightly better than a 17-tap FIR filter.

Linear phase matched filter design with causal real symmetric impulse response

Linear phase matched filter design for pulse transmission without Intersymbol Interference is presented. The delayed time-domain raised-cosine pulse is considered for the output of the shaping filter at the transmitter. To approximate the transmit filter, a linear phase denominator polynomial is used, and transmission zero pairs are placed on the j ω -axis in accordance with the attenuation response of the time-domain raised-cosine pulse. The combination of even symmetry of the time response, and j ω -axis transmission zero pairs leads to a linear phase pulse shaping filter which is its own match. The maximum number of finite transmission zero pairs for zero pulse amplitude at t = 0 is derived. The generated pulse is time-limited and has negligible energy outside the main lobe, and better performance in the presence of jitter than the standard raised-cosine spectrum pulse. The received pulse is time-limited and band-limited.

Generalized raised-cosine filters

Data transmission over bandlimited channels requires pulse shaping to eliminate or control intersymbol interference (ISI). Nyquist filters provide ISI-free transmission. Here we introduce a phase compensation technique to design Nyquist filters. Phase compensation can be applied to the square-root of any zero-phase bandlimited Nyquist filter with normalized excess bandwidth less than or equal to one. The resulting phase compensated square-root filter is also a Nyquist filter. In the case of a raised-cosine spectrum, the phase compensator has a simple piecewise-linear form. Such a technique is particularly useful to accommodate two different structures for the receiver, one with a filter matched to the transmitting filter and one without a matched filter. We also use the phase compensation technique to characterize a more general family of Nyquist filters which subsumes raised-cosine spectra. These generalized raised-cosine filters offer more flexibility in filter design. For instance, the rate of asymptotic decay of the filter impulse response may be increased, or the residual ISI, introduced by truncation of the impulse response, may be minimized. Design examples are provided to illustrate these choices.

Reduction of error floor of differential PSK in mobile radio channels by adaptive sampling

We investigate the error floor of both differential BPSK and differential /spl pi//4-QPSK with adaptive sampling in two-delay fading channels where the excess delay is smaller than a bit length. For basic DBPSK (i.e., using rectangular pulseshape), the error floor can be eliminated completely, but has finite values for pulses with raised-cosine spectrum. For a/4 DQPSK, the error floor is reduced by only a factor on the order of two as compared to fixed sampling.

Orthonormal wavelets with simple closed-form expressions

Two classes of orthonormal wavelets that have simple closed-form expressions are derived from pulses with the raised-cosine spectrum. These wavelets, which are bandlimited and polynomial-decaying in time, are found to be particular examples of the Lemarie-Meyer (1992, 1993) wavelets. The derivation reveals interesting connections between wavelet construction and intersymbol interference (ISI)-free signaling for digital communications.

Symbol synchronization using signal samples and interpolation

A method for symbol synchronization using two unsynchronized signal samples per symbol is presented. Signal values between the sample points are calculated by interpolation and then processed digitally to find a suitable strobe point. The interpolated value at the strobe point is used for data detection or input to an equalizer. Simulations show that low variance timing estimates can be made for pulses with raised-cosine spectra degraded by quadratic delay distortion.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Symbol synchronization using baud-rate sampling and data-sequence-dependent signal processing

An algorithm for symbol timing recovery using baud-rate sampling is presented. Using this algorithm, the decoded data sequence is scanned for particular data patterns that yield samples which need only to be added or subtracted to give an estimate of the required timing function. The statistics of occurrence of these data patterns are calculated for random binary data. The variance of the timing function estimates is calculated for pulses with raised-cosine spectra that have been degraded by quadratic delay distortion and is shown to be lower, in most cases, than for other synchronizers using baud-rate sampling.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Bandwidth Efficiency and Probability of Error Performance of MSK and Offset QPSK Systems

In this paper a model of Minimum Shift Keying (MSK) is introduced, an analysis of which shows that the theoretical maximum bandwidth efficiency of MSK is 2 bits/s/Hz, the same as for Quadrature Phase Shift Keying (QPSK) and Offset Quadrature Phase Shift Keying (Offset QPSK). The filtering necessary to achieve minimum spectrum width as well as a raised cosine spectrum while maintaining the condition of zero intersymbol interference for Offset QPSK is reviewed, and the equivalent filtering for MSK derived. In addition, partioning of this filtering between transmitter and receiver for optimum probability of error (P e ) versus receiver input signal to noise ( S/N ) ratio is given. Computer simulation results are presented for a MSK system and an Offset QPSK system, both filtered for 0%, 50% and 100% excess bandwidth raised cosine spectrum. The results show fully open eyes at the decision threshold input for all cases. They also show that when filtered to give the same spectrum the different system have identical P e versus S/N performance, S/N being defined at the input to the receiver decision threshold, i.e., after all the filtering for the desired raised cosine spectrum. This performance is best for 100% excess bandwidth filtering and worst for 0% excess bandwidth filtering.

The Effects of the Amplitude and Delay Slope Components of Frequency Selective Fading on QPSK, Offset QPSK and 8 PSK Systems

Amplitude and delay slope are significant components of inband distortion resulting from multipath fading. In this paper, we present and compare computer simulated results of signal to noise ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S/N</tex> ) degradation for probability of error (P <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</inf> ) of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> , due to these distortion components on Quadrature Phase Shift Keying (QPSK), Offset Quadrature Phase Shift Keying (Offset QPSK) and 8 Phase Shift Keying(8 PSK)systems. For all systems the transmitter and receiver filtering is modeled so as to provide a 50% excess bandwidth raised cosine spectrum at the receiver detector input. The QPSK and Offset QPSK systems are studied with bit rates of 44.7 Mbits/s, the so-called T3 rate, and the 8 PSK system is studied with bit rates of 44.7 Mbits/s and 67 Mbits/s, a 67 Mbit/s 8 PSK system having the same modulated frequency spectrum as 44.7 Mbit/s QPSK and Offset QPSK systems. When the frequency spectrum is the same for all systems, then for a given amplitude slope, results show that QPSK is the least degraded, followed by Offset QPSK, then 8 PSK, and for a given delay slope, Offset QPSK is the least degraded, followed by QPSK, than 8 PSK. When the bit rate is the same for all systems, then for a given amplitude slope, QPSK is the least degraded. 8 PSK is less degraded than Offset QPSK for values of amplitude slope less than 0.47 dB/MHz, but more degraded for higher values. For equal bit rates and a given delay slope, Offset QPSK is the least degraded, followed by 8 PSK, then QPSK. By relating degradation results to published information on the occurrence of amplitude and delay slope distortion components during multipath fading, estimates of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S/N</tex> degradation for a P <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</inf> of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> due to these distortion components as a function of frequency selective fade depth are made. Finally, measured <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S/N</tex> degradations for a P <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</inf> of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> due to amplitude and delay slope on a 44.7 Mbit/s Offset QPSK system with filtering similar to the computer model are presented and compared to the computer simulation results.

Use of sample-and-hold delay circuits for synthesis of raised-cosine filters

A new technique is described in which f.e.t. sample-and-hold delay circuits are used to shape a square-wave digital pulse into a pulse whose spectrum approximates to a raised-cosine spectrum with 100% roll off. The technique, which is entirely digital, is examined both theoretically and experimentally, and it is found that the raised-cosine spectrum can be synthetised simply, and to a high degree of accuracy. The technique is easier to implement than methods based on conventional network synthesis.