Showing papers in "IEEE Transactions on Communications in 2001"

Convergence behavior of iteratively decoded parallel concatenated codes

Abstract: Mutual information transfer characteristics of soft in/soft out decoders are proposed as a tool to better understand the convergence behavior of iterative decoding schemes. The exchange of extrinsic information is visualized as a decoding trajectory in the extrinsic information transfer chart (EXIT chart). This allows the prediction of turbo cliff position and bit error rate after an arbitrary number of iterations. The influence of code memory, code polynomials as well as different constituent codes on the convergence behavior is studied for parallel concatenated codes. A code search based on the EXIT chart technique has been performed yielding new recursive systematic convolutional constituent codes exhibiting turbo cliffs at lower signal-to-noise ratios than attainable by previously known constituent codes.

A quasi-orthogonal space-time block code

Abstract: It has been shown that a complex orthogonal design that provides full diversity and full transmission rate for a space-time block code is not possible for more than two antennas. Previous attempts have been concentrated in generalizing orthogonal designs which provide space-time block codes with full diversity and a high transmission rate. We design rate one codes which are quasi-orthogonal and provide partial diversity. The decoder of the proposed codes works with pairs of transmitted symbols instead of single symbols.

Degrees of freedom in adaptive modulation: a unified view

Abstract: We examine adaptive modulation schemes for flat-fading channels where the data rate, transmit power, and instantaneous BER are varied to maximize spectral efficiency, subject to an average power and BER constraint. Both continuous-rate and discrete-rate adaptation are considered, as well as average and instantaneous BER constraints. We find the general form of power, BER and data rate adaptation that maximizes spectral efficiency for a large class of modulation techniques and fading distributions. The optimal adaptation of these parameters is to increase the power and data rate and decrease the BER as the channel quality improves. Surprisingly, little spectral efficiency is lost when the power or rate is constrained to be constant. Hence, the spectral efficiency of adaptive modulation is relatively insensitive to which degrees of freedom are adapted.

Generalized linear precoder and decoder design for MIMO channels using the weighted MMSE criterion

Abstract: We address the problem of designing jointly optimum linear precoder and decoder for a MIMO channel possibly with delay-spread, using a weighted minimum mean-squared error (MMSE) criterion subject to a transmit power constraint. We show that the optimum linear precoder and decoder diagonalize the MIMO channel into eigen subchannels, for any set of error weights. Furthermore, we derive the optimum linear precoder and decoder as functions of the error weights and consider specialized designs based on specific choices of error weights. We show how to obtain: (1) the maximum information rate design; (2) QoS-based design (we show how to achieve any set of relative SNRs across the subchannels); and (3) the (unweighted) MMSE and equal-error design for fixed rate systems.

Intercarrier interference self-cancellation scheme for OFDM mobile communication systems

Abstract: For orthogonal frequency-division multiplexing (OFDM) communication systems, the frequency offsets in mobile radio channels distort the orthogonality between subcarriers resulting in intercarrier interference (ICI). This paper studies an efficient ICI cancellation method termed ICI self-cancellation scheme. The scheme works in two very simple steps. At the transmitter side, one data symbol is modulated onto a group of adjacent subcarriers with a group of weighting coefficients. The weighting coefficients are designed so that the ICI caused by the channel frequency errors can be minimized. At the receiver side, by linearly combining the received signals on these subcarriers with proposed coefficients, the residual ICI contained in the received signals can then be further reduced. The carrier-to-interference power ratio (CIR) can be increased by 15 and 30 dB when the group size is two or three, respectively, for a channel with a constant frequency offset. Although the redundant modulation causes a reduction in bandwidth efficiency, it can be compensated, for example, by using larger signal alphabet sizes. Simulations show that OFDM systems using the proposed ICI self-cancellation scheme perform much better than standard systems while having the same bandwidth efficiency in multipath mobile radio channels with large Doppler frequencies.

On the distribution of the peak-to-average power ratio in OFDM signals

Abstract: The distribution of the peak-to-average power ratio (PAPR) in strictly band-limited orthogonal frequency-division multiplexing (OFDM) signals is studied. Assuming that the base-band OFDM signal is characterized as a band-limited complex Gaussian process, we first attempt to derive the exact distribution of the PAPR in the band-limited OFDM signals. Since this distribution cannot be expressed in a closed form, we further develop a simple closed-form approximation, based on the level-crossing rate analysis. Comparisons of the proposed distributions with those obtained by computer simulations show good agreement and convergence with an increase in the number of subcarriers.

On channel estimation and detection for multicarrier signals in fast and selective Rayleigh fading channels

Abstract: Time-domain channel estimation and detection techniques are presented for multicarrier signals in a fast and frequency-selective Rayleigh fading channel. As a consequence of the time-varying channel, the orthogonality between subcarriers is destroyed in conventional frequency-domain approaches, resulting in interchannel interference, which increases an irreducible error floor in proportion to the normalized Doppler frequency. An important feature of the proposed technique is the ability to exploit the time-selective channel as a provider of time diversity. This enables us to achieve performance superior to any other structure without increasing bandwidth or incorporating redundancy, in order to reduce the complexity of the estimator, we apply the theory of optimal low rank approximation to a minimum mean squared error channel estimator and present a theoretical calculation of mean squared error and simulations to confirm that the estimator is robust to changes in channel characteristics.

Bounds on the interchannel interference of OFDM in time-varying impairments

Abstract: In this article, tight and universal bounds have been derived for the interchannel interference (ICI) of an orthogonal frequency-division multiplexing (OFDM) signal resulting from Doppler spread. The universal bound depends only on the product of the maximum Doppler frequency and the OFDM symbol duration. The tight bound also depends on the variance of the Doppler spectrum. Compared with the exact ICI expressions derived by other researchers, these bounds are easier to evaluate and can provide useful insight.

Channel estimation for OFDM transmission in multipath fading channels based on parametric channel modeling

Abstract: We present an improved channel estimation algorithm for orthogonal frequency-division multiplexing mobile communication systems using pilot subcarriers. This algorithm is based on a parametric channel model where the channel frequency response is estimated using an L-path channel model. In the algorithm, we employ the ESPRIT (estimation of signal parameters by rotational invariance techniques) method to do the initial multipath time delays acquisition and propose an interpath interference cancellation delay locked loop to track the channel multipath time delays. With the multipath time delays information, a minimum mean square error estimator is derived to estimate the channel frequency response. It is demonstrated that the use of the parametric channel model can effectively reduce the signal subspace dimension of the channel correlation matrix for the sparse multipath fading channels and, consequently, improve the channel estimation performance.

Optimum receiver design for OFDM-based broadband transmission .II. A case study

Abstract: This paper details on the design of OFDM receivers. Special attention is paid to the OFDM-specific receiver functions necessary to demodulate the received signal and deliver soft information to the outer receiver for decoding. In part I of the paper, the effects of nonideal transmission conditions have been thoroughly analyzed. To show the impact of the synchronization algorithms-which are most critical in OFDM-on system performance and complexity we consider the design of a complete receiver consisting of symbol synchronization, carrier/sampling clock synchronization and channel estimation. The performance of the algorithms is analyzed and a qualitative estimate of the resulting complexity is given. This allows one to draw conclusions concerning the achievable system performance under realistic complexity assumptions.

Blind estimation of symbol timing and carrier frequency offset in wireless OFDM systems

Abstract: Orthogonal frequency-division multiplexing (OFDM) systems are highly sensitive to synchronization errors. We introduce an algorithm for the blind estimation of symbol timing and carrier frequency offset in wireless OFDM systems. The proposed estimator is an extension of the Gini-Giannakis (see IEEE Trans. Commun., vol.46, p.400-411, 1998) estimator for single-carrier systems. It exploits the cyclostationarity of OFDM signals and relies on second-order statistics only. Our method can be applied to pulse shaping OFDM systems with arbitrary time-frequency guard regions, OFDM based on offset quadrature amplitude modulation, and biorthogonal frequency-division multiplexing systems. We furthermore propose the use of different subcarrier transmit powers (subcarrier weighting) and periodic transmitter precoding to achieve a carrier frequency acquisition range of the entire bandwidth of the OFDM signal, and a symbol timing acquisition range of arbitrary length. Finally, we provide simulation results demonstrating the performance of the new estimator.

Limitations of sum-of-sinusoids fading channel simulators

Abstract: Rayleigh signal fading due to multipath propagation in wireless channels is widely modeled using sum-of-sinusoids simulators. In particular, Jakes' (1994) simulator and derivatives of Jakes' simulator have gained widespread acceptance. Despite this, few in-depth studies of the simulators' statistical behavior have been reported in the literature. Here, the extent to which Jakes' simulator adequately models the multipath Rayleigh fading propagation environment is examined. The results show that Jakes' simulator does not reproduce some important properties of the physical fading channel. Some possible improvements to Jakes' simulator are examined. The significances of the number and the symmetries of the Doppler frequency shifts on the validity of the simulator's reproduction of the physical fading channel are elucidated.

Probability of error calculation of OFDM systems with frequency offset

Abstract: Orthogonal frequency-division multiplexing (OFDM) is sensitive to the carrier frequency offset (CFO), which destroys orthogonality and causes intercarrier interference (ICI), Previously, two methods were available for the analysis of the resultant degradation in performance. Firstly, the statistical average of the ICI could be used as a performance measure. Secondly, the bit error rate (BER) caused by CFO could be approximated by assuming the ICI to be Gaussian. However, a more precise analysis of the performance (i.e., BER or SER) degradation is desirable. In this letter, we propose a precise numerical technique for calculating the effect of the CFO on the BER or symbol error in an OFDM system. The subcarriers can be modulated with binary phase shift keying (BPSK), quaternary phase shift keying (QPSK), or 16-ary quadrature amplitude modulation (16-QAM), used in many OFDM applications. The BPSK case is solved using a series due to Beaulieu (1990). For the QPSK and 16-QAM cases, we use an infinite series expression for the error function in order to express the average probability of error in terms of the two-dimensional characteristic function of the ICI.

Virtual branch analysis of symbol error probability for hybrid selection/maximal-ratio combining in Rayleigh fading

Abstract: We derive analytical expressions for the symbol error probability (SEP) for a hybrid selection/maximal-ratio combining (H-S/MRC) diversity system in multipath-fading wireless environments. With H-S/MRC, L out of N diversity branches are selected and combined using maximal-ratio combining (MRC). We consider coherent detection of M-ary phase-shift keying (MPSK) and quadrature amplitude modulation (MQAM) using H-S/MRC for the case of independent Rayleigh fading with equal signal-to-noise ratio averaged over the fading. The proposed problem is made analytically tractable by transforming the ordered physical diversity branches, which are correlated, into independent and identically distributed (i.i.d.) "virtual branches," which results in a simple derivation of the SEP for arbitrary L and N. We further obtain a canonical structure for the SEP of H-S/MRC as a weighted sum of the elementary SEPs, which are the SEPs using MRC with i.i.d. diversity branches in Rayleigh fading, or equivalently the SEPs of the nondiversity (single-branch) system in Nakagami fading, whose closed-form expressions are well-known. We present numerical examples illustrating that H-S/MRC, even with L/spl Lt/N, can achieve a performance close to that of N-branch MRC.

Performance analysis of combined transmit-SC/receive-MRC

Abstract: The average bit-error rate of transmit antenna selection combined with receive maximum-ratio combining is computed as a function of the transmit antenna update rate when using binary phase-shift keying in flat Rayleigh fading channels. This scheme achieves an order of diversity equal to the product of the number of transmit and receive antennas. Therefore, it can gain significant diversity benefits over traditional receive diversity schemes by distributing the antennas over the transmit and receive side.

Per tone equalization for DMT-based systems

Abstract: An alternative receiver structure is presented for discrete multitone-based systems. The usual structure consisting of a (real) time-domain equalizer in combination with a (complex) 1-tap frequency-domain equalizer (FEQ) per tone, is modified into a structure with a (complex) multitap FEQ per tone. By solving a minimum mean-square-error problem, the signal-to-noise ratio is maximized for each individual tone. The result is a larger bit rate while complexity during data transmission is kept at the same level. Moreover, the per tone equalization is shown to have a reduced sensitivity to the synchronization delay.

Adaptive antennas at the mobile and base stations in an OFDM/TDMA system

Abstract: Several smart antenna systems have been proposed and demonstrated at the base station (BS) of wireless communications systems, and these have shown that significant system performance improvement is possible. We consider the use of adaptive antennas at the BS and mobile stations (MS), operating jointly, in combination with orthogonal frequency-division multiplexing. The advantages of the proposed system includes reductions in average error probability and increases in capacity compared to conventional systems. Multiuser access, in space, time, and through subcarriers, is also possible and expressions for the exact joint optimal antenna weights at the BS and MS under cochannel interference conditions for fading channels are derived. To demonstrate the potential of our proposed system, analytical along with Monte Carlo simulation results are provided.

Blind adaptive algorithms for minimum variance CDMA receivers

Abstract: Constrained optimization methods have received considerable attention as a means to derive blind multiuser receivers with low complexity. The receiver's output variance is minimized subject to appropriate constraints which depend on the multipath structure of the signal of interest. When multipath is present, the constraint equations can be written in parametric form, and the constraint parameters jointly optimized with the linear receiver's parameters. We develop adaptive solutions for this joint, constrained optimization problem. Both stochastic gradient and recursive least-square-type algorithms are developed. The performance of the proposed methods is compared with other blind and trained methods and turns out to be close to the trained minimum mean-square-error receiver.

Finite-alphabet based channel estimation for OFDM and related multicarrier systems

Abstract: Novel blind channel estimators based on the finite alphabet property of information symbols are derived in this paper for OFDM and related multicarrier code-division multiple access (MC-CDMA) systems. The resulting algorithms are applicable not only to standard OFDM transmitters with cyclic prefix, but also to the zero padded OFDM transmissions that improve symbol recovery at the expense of altering the transmitter and complicating the equalizer. Based on FFT-processed received data, channel identifiability is guaranteed regardless of channel zero locations and various channel estimation algorithms become available by trading on the complexity for performance. Unlike existing blind channel estimators, the proposed alternatives require short data records especially for PSK transmissions. The inherent scalar ambiguity is easily resolved because it has unit amplitude and phase values drawn from a finite set. Decoupling channel from symbol estimation enables a phase-directed operation that improves upon decision-directed schemes that are known to suffer from error propagation. Practical issues are also addressed including the presence of frequency guard intervals, constellation and power loading, various frame designs, coded transmissions as well as semi-blind and online implementations for systems with training sequences. The algorithms are tested with simulations and also compared with existing alternatives in a realistic HIPERLAN/2 setting.

FIR channel-shortening equalizers for MIMO ISI channels

Abstract: Finite-length delay-optimized multi-input multi-output (MIMO) equalizers that optimally shorten the impulse response memory of frequency-selective MIMO channels are derived. The MIMO equalizers are designed to minimize the average energy of the error sequence between the equalized MIMO channel impulse response and an MIMO target impulse response (TIR) with shorter memory. Two criteria for optimizing the MIMO TIR are analyzed and compared. The presented analytical framework encompasses a multitude of previously-studied finite-length equalization techniques.

Analysis of low-complexity windowed DFT-based MMSE channel estimator for OFDM systems

Abstract: Low-complexity windowed discrete Fourier transform (DFT)-based minimum mean square error (MMSE) channel estimators are proposed and analyzed for both the interpolation and noninterpolation cases for orthogonal frequency-division multiplexing (OFDM) mobile communications systems. In the proposed method, the frequency domain data windowing is used to reduce the aliasing errors for the interpolation case and get better noise filtering performance for the noninterpolation case. The time domain MMSE weighting is also used to suppress the channel noise for both cases. Moreover, the optimal generalized Hanning window shape is searched to minimize the channel estimation mean square error (MSE). Analysis and simulation results show that the proposed method performance is close to the optimal MMSE estimator and is much better than the direct DFT-based estimator for both cases. Compared with the optimal MMSE estimator, however, the computation load of the proposed method can be significantly reduced because the IDFT/DFT transforms can be implemented with the fast algorithms IFFT/FFT.

A multicarrier system based on the fractional Fourier transform for time-frequency-selective channels

Abstract: Traditional multicarrier techniques perform a frequency-domain decomposition of a channel characterized by frequency-selective distortion in a plurality of subchannels that are affected by frequency flat distortion. The distortion in each independent subchannel can then be easily compensated by simple gain and phase adjustments. Typically, digital Fourier transform schemes make the implementation of the multicarrier system feasible and attractive with respect to single-carrier systems. However, when the channel is time-frequency-selective, as it usually happens in the rapidly fading wireless channel, this traditional methodology fails. Since the channel frequency response is rapidly time-varying, the optimal transmission/reception methodology should be able to process nonstationary signals. In other words, the subchannel carrier frequencies should be time-varying and ideally decompose the frequency distortion of the channel perfectly at any instant in time. However, this ideally optimal approach presents significant challenges both in terms of conceptual and computational complexity. The idea disclosed in this work is that a nonstationary approach can be approximated using signal bases that are especially suited for the analysis/synthesis of nonstationary signals. We propose in fact the use of a multicarrier system that employs orthogonal signal bases of the chirp type that in practice correspond to the fractional Fourier transform signal basis. The significance of the methodology relies on the important practical consideration that analysis/synthesis methods of the fractional Fourier type can be implemented with a complexity that is equivalent to the traditional fast Fourier transform.

Error rates for Nakagami-m fading multichannel reception of binary and M-ary signals

Abstract: This paper derives new closed-form formulas for the error probabilities of single and multichannel communications in Rayleigh and Nakagami-m (1960) fading. Closed-form solutions to three generic trigonometric integrals are presented as part of the main result, providing a unified method for the derivation of exact closed-form average symbol-error probability expressions for binary and M-ary signals with L independent channel diversity reception. Both selection-diversity and maximal-ratio combining (MRC) techniques are considered. The results are generally applicable for arbitrary two-dimensional signal constellations that have polygonal decision regions operating in a slow Nakagami-m fading environments with positive integer fading severity index. MRC with generically correlated fading is also considered. The new expressions are applicable in many cases of practical interest. The closed-form expressions derived for a single channel reception case can be extended to provide an approximation for the error rates of binary and M-ary signals that employ an equal-gain combining diversity receiver.

Serially concatenated continuous phase modulation with iterative decoding

Abstract: Serially concatenated and interleaved continuous phase modulation (CPM) with iterative decoding is investigated. An a posteriori probability (APP) algorithm for CPM is developed based on the classic APP algorithm for channel codes. The system is analyzed through upper bounds on the average bit error probability. For coded and interleaved minimum shift keying, the weight spectrum is computed, resulting in a transfer function bound. This is cumbersome for a general CPM system; instead, only the most significant error events contributing to the weight spectrum are identified. Simulations show that, firstly, these events give a satisfactory view of system performance when equal outer codes are used, and secondly, that remarkably good performance can be obtained for some simple systems. Finally, power spectral densities and bandwidths are computed, allowing for a bandwidth/performanee comparison of different combinations.

Improved space-time coding for MIMO-OFDM wireless communications

Abstract: Improved space-time coding for multiple-input multiple-output orthogonal frequency division multiplexing is studied for wireless systems using QPSK modulation for four transmit and four receive antennas. A 256-state code is shown to perform within 3 dB of outage capacity (and within 2 dB with perfect channel estimation), which is better than any other published result without using iterative decoding.

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

Abstract: 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.

Cramer-Rao lower bounds for QAM phase and frequency estimation

Abstract: In this paper, we present the true Cramer-Rao lower bounds (CRLBs) for the estimation of phase offset for common quadrature amplitude modulation (QAM), PSK, and PAM signals in AWGN channels. It is shown that the same analysis also applies to the QAM, FSK, and PAM CRLBs for frequency offset estimation. The ratio of the modulated to the unmodulated CRLBs is derived for all QAM, PSK, and PAM signals and calculated for specific cases of interest. This is useful to determine the limiting performance of synchronization circuits for coherent receivers without the need to simulate particular algorithms. The hounds are compared to the existing true CRLBs for an unmodulated carrier wave (CW), BPSK, and QPSK. We investigated new and existing QAM phase estimation algorithms in order to verify the new phase CRLB. This showed that new minimum distance estimator performs close to the QAM bound and provides a large improvement over the power law estimator at moderate to high signal-to-noise ratios.

A squaring method to simplify the decoding of orthogonal space-time block codes

Abstract: We present a squaring method to simplify the decoding of orthogonal space-time block codes in a wireless communication system with an arbitrary number of transmit and receive antennas. Using this squaring method, a closed-form expression of signal-to-noise ratio after space-time decoding is also derived. It gives the same decoding performance as the maximum-likelihood ratio decoding while it shows much lower complexity.

Simple and accurate methods for outage analysis in cellular mobile radio systems-a unified approach

Abstract: Two unified expressions for computing the refined outage criterion (which considers the receiver noise) in cellular mobile radio systems are derived using the Laplace and Fourier inversion formulas. Since these expressions do not impose any restrictions on the signal statistics while being easy to program, they provide a powerful tool for outage analysis over generalized fading channels. We also assess compatibility and applicability of previously published approaches that treat noise as cochannel interference (noise-limited model) or consider a minimum detectable receiver signal threshold and receiver noise. The outage probability in an interference-limited case can be evaluated directly by setting the minimum power threshold to zero. The analysis of correlated interferers is presented. Results are also developed for a random number of interferers. Several new closed-form expressions for the outage probability are also derived. Some previous studies have suggested approximating Rician desired signal statistics by a Nakagami-m (1960) model (with positive integer fading severity index) to circumvent the difficulty in evaluating the outage in Rician fading. The suitability of this approximation is examined by comparing the outage performance under these two fading conditions. Surprisingly, some basic results for Nakagami-m channel have been overlooked, which has led to misleadingly optimistic results with the Nakagami-m approximation model. However, similar approximation for the interferer signals is valid.

Attainable throughput of an interference-limited multiple-input multiple-output (MIMO) cellular system

Abstract: We investigate the high spectral efficiency capabilities of a cellular data system that combines the following: 1) multiple transmit signals, each using a separately adaptive modulation; 2) adaptive array processing at the receiver; and 3) aggressive frequency reuse (reuse in every cell). We focus on the link capacity between one user and its serving base station, for both uncoded and ideally coded transmissions. System performance is measured in terms of average data throughput, where the average is over user location, shadow fading, and fast fading. We normalize this average by the total bandwidth, call it the mean spectral efficiency, and show why this metric is a useful representation of system capability. We then quantify it, using simulations, to characterize multiple-input multiple-output systems performance for a wide variety of channel conditions and system design options.