Multipath Diversity Research Articles

Performance Analysis of QRD-Based Cyclically Prefixed Single-Carrier Transmissions With Opportunistic Scheduling

The maximum average achievable rate and the outage probability of the opportunistic scheduling over the cyclically prefixed (CP) single-carrier (SC) downlink transmissions are analyzed. In the user terminal, the QR-decomposition (QRD)-based receiver is employed to maintain the multipath diversity gain. Based on the proposed receiver, closed-form expressions for the maximum average achievable rate and the outage probability can be derived using the property of the circulant matrix. In addition, the outage diversity gain is obtained at high average signal-to-noise ratio (SNR). Simulations verified the derived analysis.

Low Complexity Hybrid Smart Antenna with Directional Elements over Frequency Selective Fading Channel

In this paper, a low complexity hybrid smart antenna system with directional elements and reduced-size digital beamformer is proposed to combat the inter-symbol interference (ISI) problem over frequency-selective fading channels. The conventional smart antenna systems with omni-directional elements utilize the full-size digital beamformer to suppress interference and obtain the optimum performance. However, the proposed hybrid smart antenna system with directional elements can split the linear receive array into two subarrays. One subarray contains the elements with no ISI, which can be processed with a simple maximum ratio combiner (MRC). The second subarray includes the elements with the ISI interference, which require the use of a reduced-size optimum beamformer for interference suppression. Finally, the outputs of the two subarrays are combined for optimal detection of the transmitted signals. Simulation results confirm that the proposed low complexity hybrid smart antenna system can provide robust performance under the multipath fading channel with ISI, and outperform the conventional smart antenna systems due to the use of directional antennas and utilization of multipath diversity gain.

ICI mitigation and diversity gain for OFDM systems in time‐varying multipath fading channels

AbstractIn orthogonal frequency division multiplexing (OFDM) systems, channels' rapid variations cause intercarrier interference (ICI), resulting in performance degradation. Although ICI caused by channels' variations makes the reliable signal detection difficult, it also introduces Doppler diversity, which can be exploited to improve the system performance. In this paper, an ICI mitigation and Doppler‐multipath diversity technique based on fractionally sampling at the receiver is proposed for OFDM systems over time‐varying multipath fading channels. To reduce the computation burden of minimum mean‐square error (MMSE) equaliser with successive detection (SD), an efficient algorithm is presented by using the property of matrix decomposition. The algorithm avoids direct or recursive computation of matrix inversion, thereby reducing the computation complexity and ensuring numerical stability. Simulations show that the proposed techniques can collect both Doppler and multipath diversity gains with moderate complexities. Copyright © 2010 John Wiley & Sons, Ltd.

Differential Quasi-Orthogonal Space-Frequency Trellis Codes

Two rate-one differential quasi-orthogonal space-frequency trellis codes (DQOSFTCs) for multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) channels are proposed. The DQOSFTCs are systematically constructed within an OFDM symbol period, by combining unitary quasi-orthogonal trellis codes and differential modulation over the frequency domain (DF-QOSFTC) or time domain (DT-QOSFTCs). Besides multipath diversity, our DQOSFTCs achieve high-coding gain and simple decoding when the channel state information is not available at both the transmitter and the receiver. Simulation results show that our proposed codes significantly outperform the existing differential space-frequency trellis codes.

Multiuser detectors for band-limited direct-sequence code-division multiple-access systems with multitone jamming and generalised- K fading

In this study, the authors analyse the bit-error rate (BER) performance of band-limited direct-sequence code-division multiple-access (DS-CDMA) systems employing two types of multiuser detectors, namely, linear decorrelator with whitening (LDW) and linear minimum mean-squared error (MMSE) detector over frequency-selective multipath channels with multitone jamming (MTJ). The authors consider the generalised-K distribution in order to include both shadowing and small-scale fading effects. Generalised-K distribution is generic and versatile as it can incorporate various composite fading and shadowing effects observed in wireless communication channels with mathematical tractability. The authors derive analytical BER expressions that are functions of band-limited pulse shapes, MTJ parameters and shadowing and fading parameters of the wireless channel. The system incorporates either a Nyquist pulse or a cosine band-limited pulse shape. Numerical results show that the systems with cosine pulse demonstrate better BER performance than the ones with Nyquist pulse in the presence of MTJ. Furthermore, in the presence of MTJ, MMSE-based systems demonstrate improved BER performance as compared to LDW-based systems. The authors also observe that the systems employing two-dimensional scheme, that is, the combination of space and multipath diversity, outperform the ones with multipath diversity scheme.

Improved Design of Trellis Space-time Code for High Spatial-and Multipath Diversity in MIMO-OFDM Fading Channels

Improved Design of Trellis Space-time Code for High Spatial-and Multipath Diversity in MIMO-OFDM Fading Channels

Quasi-Orthogonal Space-Time-Frequency Trellis Codes for Two Transmit Antennas

In this letter, we propose two full-rate space-time-frequency trellis code (STFTC) designs for multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems. The first proposal based on rotating constellation is called extended super-orthogonal STFTC (Ex-SOSTFTC). The second proposal, called Quasi-Orthogonal STFTCs (QOSTFTCs), combines set partitioning and the structure of quasi-orthogonal space-frequency designs in a systematic way. In addition to spatial diversity, the proposed codes provide multipath diversity and achieve high-coding gain over a frequency selective fading channel. Simulation results show the proposed codes significantly outperform the existing STFTC designs.

Performance Analysis of OFDM Repeater Networks with Spatial Fading Correlation

This paper analyzes the performance of the OFDM diversity systems with the spatial fading correlation when the network includes an RF repeater. In case of OFDM transmission, since the combining scheme is usually employed in the frequency domain, the correlation between different subchannels should be considered. In a multipath channel, correlation varies over subchannels depending on the channel delay profile and the spatial correlation between each individual delayed paths. In this study, a multipath channel is constructed by the repeated signal instead of natural multipath due to cluttered environments and the system performance with spatial correlation per subcarrier is evaluated. Previously, it is reported that the effect of correlation can be reduced by the Time Shifted Sampling (TSS) technique which relies on the multipath diversity. Numerical results indicate that the TSS technique is also effective in reducing the effect of correlation for the multipath channels constructed by the repeaters.

On the Full Diversity Property of A Space-Frequency Code Family with Multiple Carrier Frequency Offsets in Cooperative Communication Systems

Space-frequency (SF) coded orthogonal frequency division multiplexing (OFDM) systems have been recently proposed for cooperative communications to achieve both full cooperative and full multipath diversities without the time synchronization requirement. In this paper, we show that the full diversity property still holds for a family of SF codes (rotation-based SF codes) when there are multiple carrier frequency offsets (CFOs) from relay nodes under the condition that the absolute values of the normalized CFOs are less than 0 . 5 . We then prove that this full diversity property can be preserved if we seek to reduce the receiver complexity by using a zero forcing (ZF) method to equalize the multiple CFOs, before applying maximum likelihood (ML) decoding. Furthermore, by exploiting the properties of SF codes, we show that a specific permuted version of this family of SF codes can still achieve full diversity even when the inter-carrier interference (ICI) matrix is singular. This is possible as long as the maximum absolute value of the normalized CFOs is not less than 0 . 5 . However, in this case the ZF method cannot be directly used to reduce the decoding complexity. To avoid the necessity of jointly considering all the subcarriers, two suboptimal detection methods are proposed in which full diversity is achieved even for singular ICI matrix. All these imply that the SF coded OFDM system is robust to both timing errors and frequency offsets.

Performance of asynchronous two-relay two-hop wireless cooperative networks

In wireless cooperative networks, the asynchronism between the relays can be a source of diversity which is similar in its essence to the multipath diversity of frequency selective channels. In this context, an asynchronous two-relay cooperative wireless network is studied for Decode-and-Forward (DF) and Amplify-and-Forward (AF) protocols. The outage probability in the high Signal to Noise Ratio (SNR) regime is derived and the impact of the relative delay between the two relays on this outage probability is evaluated. It is shown that for a sufficiently high relative delay, the outage probability performance becomes independent from the relative delay and approaches from the synchronous protocol performance. Besides, an optimization of the power distribution between the transmitting nodes of the network is carried out in the high SNR regime based on the outage probability minimization. Moreover, the Diversity Multiplexing Tradeoff (DMT) of the network is characterized for the two cooperative protocols DF and AF. The DMT curve does not depend on the relative delay as long as the latter is non-zero.

Efficient Multipath Diversity Receiver for STBC Block Transmission System

A space-time and multipath diversity combining algorithm is presented for STBC single carrier block transmission system with two transmit and one receive antennas. The initial solution is achieved by an STBC-based frequency domain equalizer, and the multipath components in the received signal are decoupled by this initial solution and channel state information. Finally, STBC combining is carried out on each decoupled multipath component separately, and then the single carrier output branches are combined further using the maximal ratio combining (MRC) algorithm.

Achieving full diversity and fast ML decoding via simple analog network coding for asynchronous two-way relay networks

In this paper, we propose a simple analog network coding (ANC) scheme for asynchronous two-way relay networks where two sources exchange information through the relay nodes. In our proposed scheme, we consider a wireless scenario with frequency selective fading channels. Orthogonal frequency-division multiplexing (OFDM) is implemented at the two sources and then the OFDM blocks are transmitted to the relay nodes in the first time slot. In the second time slot, at the relay nodes, the ANC that has a few simple operations are implemented on the received mixed signals and then the processed signals are broadcasted to the two sources to finish the information exchange. In this scheme, at each source, when recovering the designed information transmitted from another source, the received signals have the orthogonal space time block code (OSTBC) structure or the quasi-orthogonal space time block code (QOSTBC) structure on each subcarrier. By a proper power allocation, the two sources can achieve full spatial diversity and fast ML decoding without the requirement of symbol level synchronization. By the repetition across the subcarriers, multi-path diversity available in frequency selective fading channels can be also exploited. Moreover, the proposed ANC scheme is also valid for multi-way relay networks where multiple sources exchange information.

Distributed space-time-frequency coding for cooperative OFDM systems

A distributed space-time-frequency (STF) coding scheme is proposed for cooperative OFDM (C-OFDM) systems with three terminals over quasi-static frequency-selective Rayleigh fading channels. The outage probability is derived and its tight closed-form lower bound is presented. Asymptotic analysis indicates that the proposed scheme can achieve both spatial and multipath (frequency) diversity. The theoretical analysis of the proposed STF coded scheme is further implemented by the distributed group STF block coding (D-GSTFBC) scheme based on the subcarrier grouping technique. Simulation results confirm the previously introduced theoretical analysis.

Training Design for Repetitive-Slot-Based CFO Estimation in OFDM

Carrier frequency offset (CFO) estimation is a key challenge in wireless systems employing orthogonal frequency-division multiplexing (OFDM) modulation. Often, CFO estimation is carried out using a preamble made of a number, say <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">J</i> , of repetitive slots (RS). We here focus on the issue of optimal RS preamble design using the Cramer-Rao bound (CRB) averaged over the channel, which is assumed to be Rayleigh. We show that the optimal value of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">J</i> is a tradeoff between the multipath diversity gain and the number of unknowns to be estimated. In the case of correlated channel taps, we also show that uniform power loading of the active subcarriers is not optimal (in contrast with the uncorrelated case) and better power loading schemes are proposed. The proposed power loading schemes consist of allocating more power to activated carriers with higher signal-to-noise ratios. Simulation-based performance results of the maximum likelihood estimator support the CRB-based theoretical results.

Amplify-and-forward cooperative OFDM with multiple-relays: performance analysis and relay selection methods

In this paper, we investigate a cooperative system with multiple relays and amplify-and-forward relaying over frequency-selective channels. To extract the available multipath diversity, we employ orthogonal frequency division multiplexing (OFDM) with precoding. Through the derivation of pairwise error probability (PEP), we demonstrate that PEP is not a simple exponential function of the signal-to-noise ratio (SNR), but it includes a term that involves some power of logarithm of the SNR. If that term is ignored, the diversity order is given by the summation of the channel length in the direct link and the minimum of channel lengths in each relaying link confirmed by simulation results. Based on the PEP expression, we also propose two relay selection strategies; one is on a per-subcarrier basis and the other is on an all-subcarrier basis. Our simulation results indicate that both strategies result in performance improvements although the per-subcarrier method performs better.

Near-optimal and suboptimal receivers for multiuser UWB impulse radio systems in multipath

In this paper, near-optimal and suboptimal receivers are proposed for multiuser ultra-wideband (UWB) impulse radio (IR) systems in dense multipath channels, where <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">non-Gaussian</i> multiuser interference (MUI) seen at each finger of a RAKE receiver is taken into account. The receivers exploit two dimensional diversity that is offered by UWB signaling, namely multipath diversity and repetition diversity (i.e., repetition coding). Non-Gaussian modeling of the MUI results in employing a nonlinear process at each finger, jointly considering the desired users, path gain being estimated and the order associated with MUI statistics. For this, the MUI statistics are characterized in terms of their second and fourth order moments, especially considering the channel <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sparseness</i> and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">cluster overlapping</i> observed in realistic UWB channels, which leads to modeling the MUI by a <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">generalized</i> Gaussian distribution. It is shown that the MUI statistics exhibit non-Gaussian nature even for relatively large number of users, and the diversity gain against MUI can be significant when relatively small number of users coexist.

MRC in the Presence of Asynchronous Cochannel Interference Over Frequency-Selective Rayleigh Fading Channels

This paper studies the performance of Rake receivers with maximal ratio combining (MRC) in the presence of cochannel interference over slowly varying frequency-selective fading channels with combined spatial receive antenna diversity and temporal multipath diversity. Two models for the instantaneous powers of the residual multipath components and the resolved cochannel interfering signals, which represent the overall interfering signals, are employed. The first model considers the phase asynchronism between the desired signal replicas and interfering signals, whereas the second model assumes that the instantaneous powers of interfering signals incoherently add up. The desired signal replicas and interfering signals are assumed to experience statistically independent Rayleigh fading processes with arbitrary statistics. For the system model previously described, new closed-form expressions for the probability density function (pdf) of the combined signal-to-interference-plus-noise ratio (SINR) are derived. These expressions are then used to obtain formulas for various performance measures. The case study under consideration and the corresponding derived expressions for the statistical measures generalize many previous results and can usefully be employed to investigate the impact of various system and channel parameters on the performance of Rake receivers with MRC in the presence of cochannel interference.

Joint application of STBC and RAKE receivers in multipath Rayleigh fading channels

This letter investigates the issues on joint application of STBC systems and RAKE receivers in a CDMA system. We show the advantages of using STBC-RAKE receivers in multipath Rayleigh fading channels via error probability analysis and extensive computer simulations. Specifically, this study leads to a better understanding of the interplay between spatial diversity by STBC and multipath diversity via RAKE receivers.

Analysis of BPSK modulated asynchronous band-limited DS-CDMA systems with diversity receivers over Generalised- K fading channels

The authors studied bit-error rate (BER) performance of asynchronous band-limited direct-sequence code-division multiple-access (DS-CDMA) systems with various diversity-combining receivers over Generalised-K fading channels. The effects of band-limited pulse shapes, multitone jamming, multiple-access interference as well as both flat and frequency-selective fading are considered. The Generalised-K model is adopted in order to include the effects of shadowing and fading of a wireless channel. The authors consider binary phase-shift keying as the modulation technique. The analytical expressions are valid for any arbitrary value of Generalised-K distribution parameters. Two types of band-limited pulses, namely spectrum raised cosine and Beaulieu–Tan–Damen (BTD) pulses, are incorporated in the analysis. Numerical results show that the system with BTD pulse outperforms the one with SRC pulse for various diversity-combining receivers under various channel conditions. Furthermore, by incorporating a minimum mean-square error stage in the multipath diversity receiver, the BER performance can be further improved.

Signal Detection in a Space–Frequency Coded Cooperative Communication System With Multiple Carrier Frequency Offsets by Exploiting Specific Properties of the Code Structure

In cooperative communications, carrier frequency offsets (CFOs) between pairs of nodes may be different, making CFO compensation difficult, if not impossible. These multiple CFOs may drastically degrade the performance of a space-frequency (SF)-coded cooperative system. In this paper, we consider the signal-detection problem in an SF-coded cooperative communication system with multiple CFOs, where the SF codes are rotational based and can achieve both full spatial and full multipath diversity orders in a multiantenna system. By exploiting the structure of the SF codes, we propose three signal detection methods to deal with the multiple CFOs problem in the SF-coded orthogonal frequency-division multiplexing (OFDM) system - the minimum mean-squared error (MMSE) filtering method, the two-stage simple frequency-shift Q taps method, and the multiple fast Fourier transform (M-FFT) method - all of which offer different tradeoffs between performance and computational complexity. Simulation results indicate that our proposed detection methods work well, as long as the carrier frequency offsets between nodes are not unreasonably large.