Basis Expansion Model Research Articles

Doubly-Selective Channel Estimation Using Data-Dependent Superimposed Training and Exponential Basis Models

Channel estimation for single-user frequency- selective time-varying channels is considered using superimposed training. The time-varying channel is assumed to be well- approximated by a complex exponential basis expansion model (CE-BEM). A periodic (non-random) training sequence is arithmetically added (superimposed) at low power to the information sequence at the transmitter before modulation and transmission. In existing first-order statistics-based channel estimators, the information sequence acts as interference resulting in a poor signal-to-noise ratio (SNR). In this paper a data-dependent superimposed training sequence is used to cancel out the effects of the unknown information sequence at the receiver on channel estimation. A performance analysis is presented. We also consider the issue of superimposed training power allocation. Several illustrative computer simulation examples are presented.

Joint channel and phase noise estimation in OFDM using KL expansion

In mobile orthogonal frequency division multiplexing (OFDM) systems, time-varying channels result in severe intercarrier interference (ICI). At the same time, random phase noise introduced by the oscillator also causes two effects: the common phase error (CPE), and the ICI. The upper two factors together greatly degrade the OFDM system performance. However, the existing ICI reduction method is only aimed at a single interference source, i.e., either time-varying channels or phase noise. So, it cannot solve the actual case. In this paper, we analyze the ICI generated by the two factors together and propose a pilot-aided joint time-varying channel and phase noise estimation algorithm based on Karhunen-Lòeve basis expansion model (KL-BEM). The model is optimal in the minimum mean square error (MMSE) sense. So, it can make ICI reduction more effective. Simulation results confirm our theoretical results and illustrate that the proposed algorithm is capable of jointly estimating time-varying channels and phase noise.

A Joint OFDM Channel Estimation and ICI Cancellation for Double Selective Channels

Orthogonal frequency division multiplexing (OFDM) systems suffer significantly from inter-carrier interference (ICI) caused by double selective channels. In this paper, we develop a two-stage hybrid channel estimation and ICI cancellation structure for OFDM. The double selective channels are approximated by an improved Basis Expansion Model (BEM), which is more accurate than the conventional BEM when the normalized Doppler frequency is smaller than one. Based on this improved model, a new ICI cancellation scheme is proposed to reduce ICI impact. Simulation results show that the framework performs well.

Time-Multiplexed Training for Time-Selective Channels

Pilot-assisted channel estimation is considered in this letter, where the channel is assumed to be time-selective and can be accurately fit by a basis expansion model. The position and power of the pilots are crucial to the mean square error of the channel estimator. In this paper, we present nonlinear integer programming algorithms to optimize the position and power of the pilots. In comparison with the traditional equi-distant/powered pilot structure, the solution obtained from the proposed algorithms yields a better performance.

Space-frequency-Doppler coded OFDM over the time-varying Doppler fading channels

In this paper, space-frequency-Doppler coded OFDM (SFDO-OFDM) scheme over the time-varying Doppler fading channels via the time-frequency duality is proposed. Based on the basis expansion model (BEM) and the time-frequency duality, through the circulant matrix diagonalized processing, the nonlinear time-varying Doppler fading channel is dually converted to the virtual frequency-selective linear channels. With OFDM module, subgrouping the subcarriers in OFDM through the block matrix method and fatherly general complex orthogonal coding (GCOD) on each corresponding block subcarriers, SFDO-OFDM codes for the general multiple input multiple output (MIMO) is thus constructed. And concatenating it with the signal constellation precoding, full maximum diversity gains including the inherent Doppler fading are achieved. Theoretical analysis and corroborating simulation results demonstrate that, comparing with existing Doppler coding alternatives, the proposed scheme can effectively and robustly combat the Doppler fading with high bandwidth efficiency and even lower bit error ratio (BER).

Pilot-Assisted Time-Varying Channel Estimation for OFDM Systems

In this paper, we deal with channel estimation for orthogonal frequency-division multiplexing (OFDM) systems. The channels are assumed to be time-varying (TV) and approximated by a basis expansion model (BEM). Due to the time-variation, the resulting channel matrix in the frequency domain is no longer diagonal, but approximately banded. Based on this observation, we propose novel channel estimators to combat both the noise and the out-of-band interference. In addition, the effect of a receiver window on channel estimation is also studied. Our claims are supported by simulation results, which are obtained considering Jakes' channels with fairly high Doppler spreads

IQ-Imbalance Compensation for OFDM in the Presence of IBI and Carrier-Frequency Offset

In this paper, we propose a frequency-domain equalization technique for orthogonal frequency division multiplexing (OFDM) transmission over frequency-selective channels. We consider the case where the receiver analog front-end suffers from IQ-imbalance and the local oscillator suffers from carrier-frequency offset (CFO). While the IQ-imbalance results in a mirroring effect, the CFO induces inter-carrier interference (ICI). In addition to ICI, we consider the channel delay spread is larger than the cyclic prefix (CP). This means that inter-block interference (IBI) is present. The frequency-domain equalizer is obtained by transferring a time-domain equalizer (TEQ) to the frequency-domain resulting in a per-tone equalizer (PTEQ). Due to the presence of IQ-imbalance the conventional TEQ (where only one TEQ is applied to the received sequence) is not sufficient to cope with the mirroring effect. A sufficient TEQ consists of two time-domain filters; one applied to the received sequence and another applied to a conjugated version of the received sequence. For the case of IQ-imbalance and CFO, the TEQs are designed according the basis expansion model (BEM) which showed to be able to cope with the ICI problem. Finally, in addition to the frequency-domain PTEQ design procedure, a training-based RLS type initialization scheme for direct per-tone equalization is also proposed

Estimation and Direct Equalization of Doubly Selective Channels

We propose channel estimation and direct equalization techniques for transmission over doubly selective channels. The doubly selective channel is approximated using the basis expansion model (BEM). Linear and decision feedback equalizers implemented by time-varying finite impulse response (FIR) filtersmay then be used to equalize the doubly selective channel, where the time-varying FIR filters are designed according to the BEM. In this sense, the equalizer BEM coefficients are obtained either based on channel estimation or directly. The proposed channel estimation and direct equalization techniques range from pilot-symbol-assisted-modulation- (PSAM-) based techniques to blind and semiblind techniques. In PSAM techniques, pilot symbols are utilized to estimate the channel or directly obtain the equalizer coefficients. The training overhead can be completely eliminated by using blind techniques or reduced by combining training-based techniques with blind techniques resulting in semiblind techniques. Numerical results are conducted to verify the different proposed channel estimation and direct equalization techniques.

Low-complexity equalization of time-varying channels with precoding

This correspondence deals with time-varying (TV) single-input multiple-output (SIMO) channels, which are both frequency selective (due to high data rate) and time selective (due to mobility). A complex exponential basis expansion model (CE-BEM) is used to model the channel. We consider a block transmission system, where on the transmit side a precoder is employed to enable the maximum available diversity for a CE-BEM channel. After direct decoding on the receive side, the resulting channel resembles a finite-impulse-response (FIR) filter on both block and symbol level. We therefore propose an equalizer that bears a structure analogous to the effective channel. In comparison with a standard block minimum mean-square error decision-feedback equalizer (BMMSE-DFE) that involves the inversion of a large-size matrix, the proposed parametric equalizer renders a similar performance but at a lower computational cost if there are multiple outputs present. Another contribution of this correspondence is a semiblind algorithm to estimate this equalizer when the channel state information is not available: the equalizer taps and the information symbol estimates are refined recursively by means of normalized least-mean-squares (NLMS) adaptation.

Low-Complexity Banded Equalizers for OFDM Systems in Doppler Spread Channels

Recently, several approaches have been proposed for the equalization of orthogonal frequency-division multiplexing (OFDM) signals in challenging high-mobility scenarios. Among them, a minimum mean-squared error (MMSE) block linear equalizer (BLE), based on a band LDL factorization, is particularly attractive for its good tradeoff between performance and complexity. This paper extends this approach towards two directions. First, we boost the BER performance of the BLE by designing a receiver window specially tailored to the band LDL factorization. Second, we design an MMSE block decision-feedback equalizer (BDFE) that can be modified to support receiver windowing. All the proposed banded equalizers share a similar computational complexity, which is linear in the number of subcarriers. Simulation results show that the proposed receiver architectures are effective in reducing the BER performance degradation caused by the intercarrier interference (ICI) generated by time-varying channels. We also consider a basis expansion model (BEM) channel estimation approach, to establish its impact on the BER performance of the proposed banded equalizers.

Doubly Selective Channel Estimation Using Superimposed Training and Exponential Bases Models

Channel estimation for single-input multiple-output (SIMO) frequency-selective time-varying channels is considered using superimposed training. The time-varying channel is assumed to be described by a complex exponential basis expansion model (CE-BEM). A periodic (nonrandom) training sequence is arithmetically added (superimposed) at a low power to the information sequence at the transmitter before modulation and transmission. A two-step approach is adopted where in the first step we estimate the channel using CE-BEM and only the first-order statistics of the data. Using the estimated channel from the first step, a Viterbi detector is used to estimate the information sequence. In the second step, a deterministic maximum-likelihood (DML) approach is used to iteratively estimate the SIMO channel and the information sequences sequentially, based on CE-BEM. Three illustrative computer simulation examples are presented including two where a frequency-selective channel is randomly generated with different Doppler spreads via Jakes' model.

Frequency-Shift Zero-Forcing Time-Varying Equalization for Doubly Selective SIMO Channels

This paper deals with the problem of designing linear time-varying (LTV) finite-impulse response zero-forcing (ZF) equalizers for time- and frequency-selective (so-called doubly selective) single-input multiple-output (SIMO) channels. Specifically, relying on a basis expansion model (BEM) of the rapidly time-varying channel impulse response, we derive the canonical frequency-domain representation of the minimal norm LTV-ZF equalizer, which allows one to implement it as a parallel bank of linear time-invariant filters having, as input signals, different frequency-shift (FRESH) versions of the received data. Moreover, on the basis of this FRESH representation, we propose a simple and effective low-complexity version of the minimal norm LTV-ZF equalizer and we discuss the relationships between the devised FRESH equalizers and a LTV-ZF equalizer recently proposed in the literature. The performance analysis, carried out by means of computer simulations, shows that the proposed FRESH-LTV-ZF equalizers significantly outperform their competitive alternative.

Estimation and equalization of doubly selective channels using known symbol padding

This paper considers the situation where users that experience high-mobility transmit data over frequency-selective channels, resulting in a doubly selective channel model (i.e., time- and frequency-selective channels) and this within the framework of Known Symbol Padding (KSP) transmission. KSP is a recently proposed block transmission technique where short sequences of known symbols acting as guard bands are inserted between successive blocks of data symbols. This paper proposes three novel channel estimation methods that allow for an accurate estimation of the time-varying transmission channel solely relying on the knowledge of the redundant symbols introduced by the KSP transmission scheme. The first method is a direct adaptive one while the others rely on a recently proposed model, the Basis Expansion Model (BEM), where the doubly selective channel is approximated with high accuracy using a limited number of complex exponentials. An important characteristic of the proposed methods is that they exploit all the received symbols that contain contributions from the training sequences and blindly filter out the contribution of the unknown surrounding data symbols. Besides these channel identification methods, the classical KSP equalizers are adapted to the context of doubly selective channels, which allows evaluation of the bit-error-rate (BER) performance of a KSP transmission system relying on the proposed channel estimation methods in the context of doubly selective channels. Simulation results show that KSP transmission is indeed a suitable transmission technique toward the delivery of high data rates to users experiencing a high mobility, when adapted KSP equalizers are used in combination with the proposed channel estimation methods.

Blind Space-Time Multiuser Channel Estimation in Time-Varying DS-CDMA Systems

A multistep linear prediction (MSLP) approach is presented for blind channel estimation for short-code direct sequence code division multiple access signals in time-varying multipath channels using a receiver antenna array. The time-varying channel is assumed to be described by a complex exponential basis expansion model. First, a recently proposed MSLP approach to blind channel estimation for time-varying single-input multiple-output (SIMO) systems is extended to time-varying multiple-input multiple-output (MIMO) systems to define a subspace. Second, the knowledge of the spreading code of a desired user is exploited in conjunction with the signal subspace to estimate the time-varying channel of the desired user up to an unknown time-invariant scale factor. Equalization/detection for the desired user can be then carried out if the information sequence is differentially encoded/decoded. Sufficient conditions for channel identifiability are investigated. Three illustrative simulation examples are provided.

Block-Differential Modulation Over Doubly Selective Wireless Fading Channels

Differential encoding is known to simplify receiver implementation because it by-passes channel estimation. However, over rapidly fading wireless channels, extra transceiver modules are necessary to enable differential transmission. Relying on a basis expansion model for time and frequency selective (doubly selective) channels, we derive such a generalized block-differential (BD) codec and prove that it achieves maximum Doppler and multipath diversity gains, while affording low-complexity maximum-likelihood decoding. We further show that existing BD systems over frequency-selective or time-selective channels follow as special cases of our novel system. Simulations using the widely accepted Jakes' model corroborate our theoretical analysis.

Space-time-Doppler block coding for correlated time-selective fading channels

Coping with time-selective fading channels is challenging but also rewarding, especially with multiantenna systems, where joint space-Doppler diversity and coding gains can be collected to enhance performance of wireless mobile links. These gains have not been quantified, and space-time coded systems maximizing joint space-Doppler benefits have not been designed. Based on a parsimonious basis expansion model for the underlying time-selective (and possibly correlated) channels, we quantify these gains in closed form. Furthermore, we develop space-time-Doppler coded systems that guarantee the maximum possible space-Doppler diversity, along with the largest coding gains within all linearly coded systems. Our three novel designs exploit knowledge of the maximum Doppler spread, and each offers a uniquely desirable tradeoff, including high spectral efficiency, low decoding complexity, and high performance. Our analytical results are confirmed by simulations and reveal the relative of merits of our three designs in comparison with an existing approach.

Time-varying FIR equalization for doubly selective channels

We propose a time-varying (TV) finite impulse response (FIR) equalizer for doubly selective (time- and frequency-selective) channels. We use a basis expansion model (BEM) to approximate the doubly selective channel and to design the TV FIR equalizer. This allows us to turn a complicated equalization problem into an equivalent simpler equalization problem, containing only the BEM coefficients of both the doubly selective channel and the TV FIR equalizer. The minimum mean-square error (MMSE) as well as the zero-forcing (ZF) solutions are considered. Comparisons with the block linear equalizer (BLE) are made. The TV FIR equalization we propose here unifies and extends many previously proposed serial equalization approaches. In contrast to the BLE, the proposed TV FIR equalizer allows a flexible tradeoff between complexity and performance. Moreover, through computer simulations, we show that the performance of the proposed MMSE TV FIR equalizer comes close to the performance of the ZF and MMSE BLE, at a point where the design as well as the implementation complexity are much lower.

Blind Identification of Time-Varying Channels Using Multistep Linear Predictors

Blind estimation of a class of single-input multiple-output (SIMO) time-varying channels is considered using only the second-order statistics of the data. The time-varying channel is assumed to be described by a complex exponential basis expansion model (CE-BEM). The multistep linear predictors-based method for blind identification of time-invariant channels is extended to time-varying channels represented by a CE-BEM. Sufficient conditions for channel identifiability are investigated. The proposed method requires the knowledge of the active basis functions in the CE-BEM. It is not as sensitive to overestimation of the channel length as some of the existing methods. Computer simulation examples are presented to illustrate the approach and to compare it with three existing approaches.

Block Differential Encoding for Rapidly Fading Channels

Rapidly fading channels provide Doppler-induced diversity, but are also challenging to estimate. To bypass channel estimation, we derive two novel block differential (BD) codecs. Relying on a basis expansion model for time-varying channels, our differential designs are easy to implement, and can achieve the maximum possible Doppler diversity. The first design (BD-I) relies on a time-frequency duality, based on which we convert a time-varying channel into multiple frequency-selective channels, and subsequently into multiple flat-fading channels using orthogonal frequency-division multiplexing. Combined with a group partitioning scheme, BD-I offers flexibility to trade off decoding complexity with performance. Our second block differential design (BD-II) improves the bandwidth efficiency of BD-I at the price of increased complexity at the receiver, which relies on decision-feedback decoding. Simulation results corroborate our theoretical analysis, and compare with competing alternatives.

Orthogonal multiple access over time- and frequency-selective channels

Suppression of multiuser interference (MUI) and mitigation of time- and frequency-selective (doubly selective) channel effects constitute major challenges in the design of third-generation wireless mobile systems. Relying on a basis expansion model (BEM) for doubly selective channels, we develop a channel-independent block spreading scheme that preserves mutual orthogonality among single-cell users at the receiver. This alleviates the need for complex multiuser detection, and enables separation of the desired user by a simple code-matched channel-independent block despreading scheme that is maximum-likelihood (ML) optimal under the BEM plus white Gaussian noise assumption on the channel. In addition, each user achieves the maximum delay-Doppler diversity for Gaussian distributed BEM coefficients. Issues like links with existing multiuser transceivers, existence, user efficiency, special cases, backward compatibility with direct-sequence code-division multiple access (DS-CDMA), and error control coding, are briefly discussed.