Consecutive Symbols Research Articles

Joint Time and Frequency Estimation for Multicarrier Transmission with Frequency Diversity

This letter proposes non-pilot-aided symbol timing and carrier frequency estimation methods in a multicarrier transmission system. To do this, multicarrier system uses a frequency diversity scheme over two consecutive data symbols with the combination of a cyclic time shift. Using the multicarrier signal equipped with frequency diversity, however, time and frequency are accurately estimated without any training symbol.

An algebraic approach to generate super‐set of perfect complementary codes for interference‐free CDMA

AbstractThis paper introduces an algebraic approach to generate the super‐set of perfect complementary (PC) codes suitable for new generation CDMA applications, characterized by isotropic multiple access interference (MAI) free and multipath interference (MI) free properties. The code design methodology proposed in this paper takes into account major impairing factors existing in real applications, such as MAI, MI, asynchronous transmissions, and random signs in consecutive symbols, such that a CDMA system using the generated codes can insure a truly interference‐free operation. Two important facts will be revealed by the analysis given in this paper. First, implementation of an interference‐free CDMA will never be possible unless using complementary code sets, such as the PC code sets generated in this paper. In other words, all traditional spreading codes working on an one‐code‐per‐user basis are not useful for implementation of an MAI‐free and MI‐free CDMA system. Second, to enable the interference‐free CDMA operation, the flock size of the PC codes should be made equal to the set size of the codes, implying that a PC code set can support as many users as the flock size of the code set. A systematic search has been carried out to generate the super‐set of various PC codes with the help of carefully selected seed codes belonging to distinct sub‐sets. This paper will also propose an implementation scheme based on multi‐carrier CDMA architecture and its performance is compared by simulations with the ones using traditional spreading codes. Copyright © 2006 John Wiley & Sons, Ltd.

Bounds on expansion in LZ'77-like coding

We investigate the maximum increase in number of phrases that results from changing k consecutive symbols in a string x having length n parsed using an LZ'77-like algorithm. We consider a class of compression algorithms that partition a sequence into a collection y of nonoverlapping, variable-length phrases and encode them. Each phrase either is a singleton or matches a substring that starts to its left. We show that changing a single symbol of x in position i can yield an expansion that is of order O(n-i)/sup 2/3/ as (n-i)/spl rarr//spl infin/. Our lower bound requires an alphabet size of O(n-i)/sup 1/3/. We also show that changing k consecutive symbols starting from position i can yield an expansion having a similar but somewhat more involved form. The paper contains both analytically derived upper and lower bounds, and algorithms for numerically computing tighter bounds. While deriving the bounds, we provide a detailed analysis of how expansion can arise when changing consecutive symbols. This problem is motivated by management policies for computer systems, such as the IBM Memory eXpansion Technology (MXT) or the IBM iSeries compressed disks, that use LZ'77-like coding on small compression units, such as 1-4 kbyte, and store the compressed data in memory or on disk tracks. Here, when a change of a portion of the compression unit occurs, for example, an L2 cache line, or a 512-byte disk sector, the data is recompressed and potentially stored in a different location. Knowing the maximum expansion, rather than the average expansion, is an important factor for designing policies for allocation and management of memory or disk space.

Noise reduction for channel estimation based on pilot-block averaging in DVB-T receivers

This paper proposes a noise-reduction method to improve the channel-estimation performance in digital video broadcasting-terrestrial (DVB-T) receivers. In DVB-T, the channel estimation is carried out through two processes of pilot signal estimation and channel coefficient interpolation and thus the performance of the channel estimation is seriously affected by the accuracy of the interpolation. Since the accuracy of the interpolation depends on signal-to-noise ratio, it is important to reduce noise existing at the reference coefficients for the interpolation. To achieve the reduction of noise, we use pilot-insertion type approximation in four consecutive OFDM symbols, which construct one block with the same channel coefficients at the same pilot positions. Considering the fade rate of channels, we average the estimated reference, channel coefficients corresponding to the same subcarriers in two or more blocks. Computer simulation shows that the proposed method improves the estimation performance by more than 1 dB in terms of the symbol error rate obtained after equalization.

The REAL Approach to Generate Orthogonal Complementary Codes for Next Generation CDMA Systems

This paper introduces a new approach to generate the orthogonal complementary (OC) codes suitable for new generation CDMA applications, characterized by isotropic multiple access interference (MAI) free and multipath interference (MI) free properties. The code design methodology proposed in this paper is named as “Real Environment Adaptation Linearization” (REAL) approach and it takes into account major impairing factors existing in real applications, such as MAI, MI, asynchronous transmissions and random signs in consecutive symbols. A CDMA system using the generated codes can ensure a truly interference-free operation. Two important facts will be revealed by the analysis given in this paper. First, implementation of an interference-free CDMA will never be possible unless using complementary code sets, such as the OC code sets. In other words, all traditional spreading codes working on an one-code-per-user basis are not useful for implementation of an MAI-free and MI-free CDMA system. Second, to enable the interference-free CDMA operation, the flock size of the OC codes should be made equal to the set size of the codes, implying that a OC code set can support as many users as the flock size of the code set. A systematic search has been carried out to generate the super-set of various OC codes with the help of carefully selected seed codes belonging to distinct sub-sets. This paper will also propose an implementation scheme based on multi-carrier CDMA architecture and its performance is compared by simulations with the ones using traditional spreading codes.

Common intervals in permutations

An interval of a permutation is a consecutive substring consisting of consecutive symbols. For example, 4536 is an interval in the permutation 71453682. These arise in genetic applications. For the applications, it makes sense to generalize so as to allow gaps of bounded size δ -1, both in the locations and the symbols. For example, 4527 has gaps bounded by 1 (since 3 and 6 are missing) and is therefore a δ -interval of 389415627 for δ =2. After analyzing the distribution of the number of intervals of a uniform random permutation, we study the number of 2-intervals. This is exponentially large, but tightly clustered around its mean. Perhaps surprisingly, the quenched and annealed means are the same. Our analysis is via a multivariate generating function enumerating pairs of potential 2-intervals by size and intersection size.\par

Hidden word statistics

We consider the sequence comparison problem, also known as “ hidden ” pattern problem, where one searches for a given subsequence in a text (rather than a string understood as a sequence of consecutive symbols). A characteristic parameter is the number of occurrences of a given pattern w of length m as a subsequence in a random text of length n generated by a memoryless source. Spacings between letters of the pattern may either be constrained or not in order to define valid occurrences. We determine the mean and the variance of the number of occurrences, and establish a Gaussian limit law and large deviations. These results are obtained via combinatorics on words, formal language techniques, and methods of analytic combinatorics based on generating functions. The motivations to study this problem come from an attempt at finding a reliable threshold for intrusion detections, from textual data processing applications, and from molecular biology.

A novel integer frequency offset estimator for OFDM

One of the principal disadvantages of Orthogonal Frequency Division Multiplexing (OFDM) is very sensitive to carrier frequency offset. The integer frequency offset has no effect on the orthogonality among the subcarriers, but it causes a circular shift and phase rotation of the received data symbols sequence, resulting in a Bit Error Rate(BER) of 0.5. In this paper, a novel integer frequency offset estimator for OFDM is derived based on maximum likelihood estimation technique and exploration of the differential relation between two consecutive OFDM data symbol sequences in frequency domain. Its performance is compared with the conventional method by computer simulations for the additive white Gaussian noise channel and a multipath fading channel. Simulation results show that the performance of the proposed estimator is better than the conventional estimator.

Low-complexity bit-interleaved coded DAPSK for Rayleigh-fading channels

We analyze the achievable performance of bit-interleaved coded differential amplitude and phase-shift keying (DAPSK) systems over frequency nonselective Rayleigh-fading channels with suboptimal differential detection assuming an ideal bit interleaving. The suboptimal differential detection in this work refers to the bit metric calculation based only on the difference between two consecutive symbols, in contrast to more complex maximum-likelihood (ML)-based differential detection, which makes use of all the observed consecutive symbols for its metric calculation in channel decoding. As benchmarks of coded system performance, we analyze the average mutual information (AMI) and cutoff rate of this system. Exact probability density functions of the suboptimal differential detector outputs are derived for this purpose. Comparative studies suggest that the performance loss of the suboptimal approach is in fact noticeable. Therefore, we also develop a low-complexity receiver structure in the framework of suboptimal differential detection that can approach the performance of ML-based system by suitably incorporating the amplitude statistics of received symbols. The theoretical framework developed in this paper is also confirmed by simulations using convolutional and turbo codes.

Differential MMSE: A Framework for Robust Adaptive Interference Suppression for DS-CDMA Over Fading Channels

The linear minimum mean-squared error (MMSE) criterion is known to provide adaptive algorithms for interference suppression in direct-sequence (DS) code-division multiple-access (CDMA) systems. However, standard MMSE adaptation is not robust to fast fading, being unable to compensate for rapid channel variations. In this paper, we provide a framework for deriving robust adaptive algorithms in this setting based on a new differential MMSE (DMMSE) criterion, which is a constrained optimization problem in which the quantity to be tracked is the ratio of the data appearing in two successive observation intervals. When applied to a DS-CDMA system with short spreading waveforms (i.e., with period equal to the symbol interval) operating over a flat-fading channel, the DMMSE criterion avoids tracking the fades, exploiting the negligible variation of the fading gain over two consecutive symbols. For frequency-selective fading, the DMMSE criterion is extended to provide a new eigenrake receiver which provides interference suppression and diversity combining without requiring explicit information regarding the desired user's propagation channel.

Binary Adaptive Coded Pilot Symbol Assisted Modulation Over Rayleigh Fading Channels Without Feedback

Pilot symbol assisted modulation (PSAM) is a standard approach for transceiver design for time-varying channels, with channel estimates obtained from pilot symbols being employed for coherent demodulation of the data symbols. In this paper, we show that PSAM schemes can be improved by adapting the coded modulation strategy at the sender to the quality of the channel measurement at the receiver, without requiring any channel feedback from the receiver. We consider performance in terms of achievable rate for binary signaling schemes. The transmitter employs interleaved codes, with data symbols coded according to their distance from the nearest pilot symbols. Symbols far away from pilot symbols encounter poorer channel measurements at the receiver and are therefore coded with lower rate codes, while symbols close to pilot symbols benefit from recent channel measurements and are coded with higher rate codes. The performance benefits from this approach are quantified in the context of binary signaling over time-varying Rayleigh fading channels described by a Gauss-Markov model. The spacing of the pilot symbols is optimized to maximize the mutual information between input and output in this setting. Causal and noncausal channel estimators of varying complexity and delay are considered. It is shown that, by appropriate optimization for the spacing between consecutive pilot symbols, the adaptive coding techniques proposed can improve achievable rate, without any feedback from the receiver to the sender. Moreover, channel estimation based on the two closest pilot symbols is generally close to optimal.

Joint Channel-State Estimation and Decoding of Low-Density Parity-Check Codes on the Two-State Noiseless/Useless BSC Block Interference Channel

We apply the density-evolution technique to determine the thresholds of low-density parity-check (LDPC) codes when the sum-product algorithm is employed to perform joint channel-state estimation and decoding. The channel considered is the two-state noiseless/useless binary symmetric channel (BSC) block interference channel, where a block of h consecutive symbols shares the same channel state, which is either a noiseless BSC (crossover probability 0) or a useless BSC (crossover probability 1/2). The channel state is selected independently and at random from block to block, according to a known prior distribution. The threshold of the joint channel-state estimation/decoding scheme when used over such a channel is shown to be greatly superior to that of a decoder that makes no attempt to estimate the channel state. These results are also confirmed by simulation. The maximum-likelihood (ML) performance of LDPC codes when used over this channel is investigated. Lower bounds on the error exponents of regular LDPC codes, when ML decoded, are shown to be close to the random coding channel error exponent when the LDPC variable node degree is high.

The exact rank-frequency function and size-frequency function of N-grams and N-word phrases with applications

N-grams are generalized words consisting of N consecutive symbols (letters), as they are used in a text. N-word phrases are general concepts consisting of N consecutive words, also as used in a text. Given the rank-frequency function of single letters (i.e., one-grams) or of single words (i.e., one-word phrases) being Zipfian, we determine in this paper, the exact rank-frequency function (i.e., the occurrence of N-grams or N-word phrases on each rank) and size-frequency distribution (i.e., the density of N-grams or N-word phrases on each occurrence density) of these N-grams and N-word phrases. This paper distinguishes itself from other ones on this topic by allowing no approximations in the calculations. This leads to an intricate rank-frequency function for N-grams and N-word phrases (as we knew before from unpublished calculations) but leads surprisingly, to a very simple size-frequency function f N for N-grams or N-word phrases of the form f N ( j ) = F j 1 + 1 / β ln N − 1 ( G j ) , where the Zipfian distribution of single letters or words is proportional to 1/ r β . The paper closes with the calculation of type/token averages μ N and type/token-taken averages μ* N for N-grams and N-word phrases, where we also verify the theoretically proved result μ* N ≥ μ N but where we also give estimates for the differences μ* N − μ N .

Receiver Design for Wavelet-Based Multicarrier CDMA Communications

Wavelet packets have good properties such as orthogonality and multirate flexibility, and have resulted in a number of works for its applications to code-division multiple-access (CDMA) communications. In this paper we investigate the use of a special set of the wavelet packets, i.e., the waveforms formed from a full binary wavelet packet tree, in multicarrier CDMA systems. In the conventional multicarrier CDMA systems, a simple frequency-domain combining receiver is commonly used to achieve frequency diversity. To combat multipath channel effects, guard intervals are inserted between consecutive symbols. On the other hand, wavelet packets have the property of localization in both time and frequency domains. A novel receiver design utilizing this property to achieve both frequency and time diversity is proposed and evaluated in this paper. This receiver eliminates the need for guard intervals. Simulations are given to support the system and receiver design. This analysis can be extended to the more general wavelet packet basis waveform sets.

Receiver designs for Alamouti coded OFDM systems in fast fading channels

In this paper, receiver designs for orthogonal frequency-division multiplexing (OFDM) systems that exploit the Alamouti transmit diversity technique are addressed. In Alamouti space-time coded OFDM systems, the simple Alamouti decoding at the receiver relies on the assumption that the channels do not change over an Alamouti codeword period (two consecutive OFDM symbol periods). Unfortunately, when the channel is fast fading, the assumption is not met, resulting in severe performance degradation. In this paper, a sequential decision feedback sequence estimation (SDFSE) scheme with an adaptive threshold (AT), a traditionally single-carrier equalization technique, is used to mitigate the performance degradation. A new method to set the threshold value is proposed. For small signal constellations like BPSK and QPSK, the SDFSE with an AT requires much lower complexity than a previous minimum mean square error approach at the cost of a small performance degradation. Furthermore, we show that the performance difference becomes smaller when channel estimation error is included. An adaptive effort sequence estimation (AESE) scheme is also proposed to furthur reduce the average complexity of the SDFSE scheme with an AT. The AESE scheme is based on the observation that a high Doppler frequency does not necessarily mean significant instantaneous channel variation. Simulations show the efficacy of the proposed SDFSE with an AT and the AESE.

Incremental paradigms of motif discovery.

We examine the problem of extracting maximal irredundant motifs from a string. A combinatorial argument poses a linear bound on the total number of such motifs, thereby opening the way to the quest for the fastest and most efficient methods of extraction. The basic paradigm explored here is that of iterated updates of the set of irredundant motifs in a string under consecutive unit symbol extensions of the string itself. This approach exposes novel characterizations for the base set of motifs in a string, hinged on notions of partial order. Such properties support the design of ad hoc data structures and constructs, and lead to develop an O(n(3)) time incremental discovery algorithm.

Analysis of rake reception with multiple symbol weight estimation for antipodal signaling

Consider a Rake receiver for coherent binary antipodal signaling with: 1) a delayed received signal configuration; 2) weight estimation by matched filtering using the reference signal along with the decisions of the previous M symbol intervals; and 3) predetection maximal-ratio combining (MRC). The weight estimation errors here are not independent of the additive noise, and do not fit into the Gaussian weighting error model for MRC. Here we analyze the error performance of the receiver by obtaining the conditional symbol error probability, conditioned on past decisions, from the characteristic function of the decision variable, and getting the unconditional error probability (UEP) for a block of M consecutive symbols using a Markov model of the decision process. The channel is Rayleigh fading with independent and identically distributed branch gains. Results show that the error performance of the Gaussian distributed weighting error model is a bound for that of multiple symbol weight estimation by matched filtering, and the steady state UEP decreases with increase of M, but the amount of decrease reduces as M increases.

Low complexity channel estimation for space~time coded wideband ofdm systems

In this article, channel estimation for space-time coded orthogonal-frequency division multiplexing (OFDM) systems is considered. By assuming that the channel frequency response is quasi-static over two consecutive OFDM symbols, we develop channel parameter estimators based on the use of space-time block coded (STBC) training blocks. Using an STBC training pattern, a low-rank Wiener filter-based channel estimator with a significant complexity reduction is proposed. A simplified approach for the optimal low-rank estimator is also proposed to further reduce the estimator complexity while retaining an accurate frequency domain channel estimation. Numerical results are provided to demonstrate the performance of the proposed low complexity channel estimators for space-time trellis coded OFDM systems.

Optimum multiuser noncoherent DPSK detection in generalized diversity rayleigh-fading channels

The jointly optimum multiuser noncoherent detector for differential phase-shift keying (DPSK) modulation over the generalized diversity Rayleigh-fading (GDRF) channel is derived and analyzed. The GDRF channel includes time/frequency/receiver antenna diversity and allows fading correlations between the various diversity branches of each user. Noncoherent detection here refers to the case where the receiver has neither knowledge of the instantaneous phases nor of the envelopes of the users' channels. Upper and lower bounds on the bit-error probability of the optimum detector are derived for a given user. For fast fading, when the fading coefficients vary from one symbol interval to the next (but are still essentially constant over one symbol interval), the detector asymptotically (for high signal-to-noise ratios (SNRs)) reaches an error floor, which is bounded from below and above for different fast fading scenarios. For slow fading, when the channel is constant for at least two consecutive symbol intervals, the upper bound is shown to converge asymptotically to the lower bound. Thus, the asymptotic efficiency of optimum multiuser DPSK detection can be determined and is found to be positive. In contrast to coherent detection, however, it is smaller than unity in general. Since the asymptotic efficiency is independent of the interfering users' signal strengths, the optimum detector is near-far resistant. While optimum multiuser detection is exponentially complex in the number of users, its performance provides the benchmark for suboptimal detectors. In particular, it is seen that the previously suggested post-decorrelative detectors can be far from satisfactory.

Precoded and vector OFDM robust to channel spectral nulls and with reduced cyclic prefix length in single transmit antenna systems

The performance of orthogonal frequency-division multiplexing (OFDM) systems may be degraded when intersymbol interference (ISI) channels have spectral nulls. Also, when ISI channels have many taps, the data rate overhead due to the insertion of the cyclic prefix is high. We first propose a precoded OFDM system that may improve the performance of the OFDM systems for spectral null channels. We also propose size K/spl times/x1 vector OFDM (VOFDM) systems that reduce the cyclic prefix length by K times compared to the conventional OFDM systems. The precoding scheme is simply to insert one or more zeros between each two sets of K consecutive information symbols, although it can be generalized to a general form. This precoding scheme may be able to remove the spectral nulls of an ISI channel without knowing the ISI channel. When no zero is inserted between each two sets of K consecutive information symbols and only each K consecutive symbols are blocked together, we obtain VOFDM systems. Both theoretical performance analysis and simulation results are presented. Finally, we compare the combination of the VOFDM systems and the unitary matrix modulation with the conventional OFDM systems and the phase-shift keying modulation, where both differential (noncoherent) and coherent modulations and demodulations are considered.