Low-complexity LSMR equalisation of FrFT-based multicarrier systems in doubly dispersive channels

The discrete fractional Fourier transform (FrFT) has been suggested to enhance performance over DFT-based multicarrier systems when transmitting over doubly-dispersive channels. In this paper, we propose a novel low-complexity equaliser for inter-symbol and inter-carrier interference arising in such multicarrier transmission system. Due to a lower spreading in the FrFT-domain compared to the DFTchannel matrix as compared to the DFT domain, the equaliser cam approximate the fractional-domain channel matrix by a band matrix. Further, we utilise the least squares minres (LSMR) algorithm in the calculation of the equalisation, which exhibits attractive numerical properties and low complexity. Simulation results demonstrate the superior performance of the proposed LSMR equaliser over benchmark schemes

Pulse Shaping, Localization and the Approximate Eigenstructure of LTV Channels

In this article we show the relation between the theory of pulse shaping for WSSUS channels and the notion of approximate eigenstructure for time-varying channels. We consider pulse shaping for a general signaling scheme, called Weyl-Heisenberg signaling, which includes OFDM with cyclic prefix and OFDM/OQAM. The pulse design problem in the view of optimal WSSUS--averaged SINR is an interplay between localization and "orthogonality". The localization problem itself can be expressed in terms of eigenvalues of localization operators and is intimately connected to the concept of approximate eigenstructure of LTV channel operators. In fact, on the L_2-level both are equivalent as we will show. The concept of "orthogonality" in turn can be related to notion of tight frames. The right balance between these two sides is still an open problem. However, several statements on achievable values of certain localization measures and fundamental limits on SINR can already be made as will be shown in the paper.Comment: 6 pages, 2 figures, invited pape

A Message Passing Detection based Affine Frequency Division Multiplexing Communication System

The next generation of wireless communication technology is anticipated to address the communication reliability challenges encountered in high-speed mobile communication scenarios. An Orthogonal Time Frequency Space (OTFS) system has been introduced as a solution that effectively mitigates these issues. However, OTFS is associated with relatively high pilot overhead and multiuser multiplexing overhead. In response to these concerns within the OTFS framework, a novel modulation technology known as Affine Frequency Division Multiplexing (AFDM) which is based on the discrete affine Fourier transform has emerged. AFDM effectively resolves the challenges by achieving full diversity through parameter adjustments aligned with the channel's delay-Doppler profile. Consequently, AFDM is capable of achieving performance levels comparable to OTFS. As the research on AFDM detection is currently limited, we present a low-complexity yet efficient message passing (MP) algorithm. This algorithm handles joint interference cancellation and detection while capitalizing on the inherent sparsity of the channel. Based on simulation results, the MP detection algorithm outperforms Minimum Mean Square Error (MMSE) and Maximal Ratio Combining (MRC) detection techniques.Comment: 8 pages, 7 figure

AFDM vs OTFS: A Comparative Study of Promising Waveforms for ISAC in Doubly-Dispersive Channels

This white paper aims to briefly describe a proposed article that will provide a thorough comparative study of waveforms designed to exploit the features of doubly-dispersive channels arising in heterogeneous high-mobility scenarios as expected in the beyond fifth generation (B5G) and sixth generation (6G), in relation to their suitability to integrated sensing and communications (ISAC) systems. In particular, the full article will compare the well-established delay-Doppler domain-based orthognal time frequency space (OTFS) and the recently proposed chirp domain-based affine frequency division multiplexing (AFDM) waveforms. Both these waveforms are designed based on a full delay- Doppler representation of the time variant (TV) multipath channel, yielding not only robustness and orthogonality of information symbols in high-mobility scenarios, but also a beneficial implication for environment target detection through the inherent capability of estimating the path delay and Doppler shifts, which are standard radar parameters. These modulation schemes are distinct candidates for ISAC in B5G/6G systems, such that a thorough study of their advantages, shortcomings, implications to signal processing, and performance of communication and sensing functions are well in order. In light of the above, a sample of the intended contribution (Special Issue paper) is provided below

A Group-Theoretic Approach to the WSSUS Pulse Design Problem

We consider the pulse design problem in multicarrier transmission where the pulse shapes are adapted to the second order statistics of the WSSUS channel. Even though the problem has been addressed by many authors analytical insights are rather limited. First we show that the problem is equivalent to the pure state channel fidelity in quantum information theory. Next we present a new approach where the original optimization functional is related to an eigenvalue problem for a pseudo differential operator by utilizing unitary representations of the Weyl--Heisenberg group.A local approximation of the operator for underspread channels is derived which implicitly covers the concepts of pulse scaling and optimal phase space displacement. The problem is reformulated as a differential equation and the optimal pulses occur as eigenstates of the harmonic oscillator Hamiltonian. Furthermore this operator--algebraic approach is extended to provide exact solutions for different classes of scattering environments.Comment: 5 pages, final version for 2005 IEEE International Symposium on Information Theory; added references for section 2; corrected some typos; added more detailed discussion on the relations to quantum information theory; added some more references; added additional calculations as an appendix; corrected typo in III.

NOVEL OFDM SYSTEM BASED ON DUAL-TREE COMPLEX WAVELET TRANSFORM

The demand for higher and higher capacity in wireless networks, such as cellular, mobile and local area network etc, is driving the development of new signaling techniques with improved spectral and power efficiencies. At all stages of a transceiver, from the bandwidth efficiency of the modulation schemes through highly nonlinear power amplifier of the transmitters to the channel sharing between different users, the problems relating to power usage and spectrum are aplenty. In the coming future, orthogonal frequency division multiplexing (OFDM) technology promises to be a ready solution to achieving the high data capacity and better spectral efficiency in wireless communication systems by virtue of its well-known and desirable characteristics. Towards these ends, this dissertation investigates a novel OFDM system based on dual-tree complex wavelet transform (D

Affine Frequency Division Multiplexing With Index Modulation

Affine frequency division multiplexing (AFDM) is a new multicarrier technique based on chirp signals tailored for high-mobility communications, which can achieve full diversity. In this paper, we propose an index modulation (IM) scheme based on the framework of AFDM systems, named AFDM-IM. In the proposed AFDM-IM scheme, the information bits are carried by the activation state of the subsymbols in discrete affine Fourier (DAF) domain in addition to the conventional constellation symbols. To efficiently perform IM, we divide the subsymbols in DAF domain into several groups and consider both the localized and distributed strategies. An asymptotically tight upper bound on the average bit error rate (BER) of the maximum-likelihood detection in the existence of channel estimation errors is derived in closed-form. Computer simulations are carried out to evaluate the performance of the proposed AFDM-IM scheme, whose results corroborate its superiority over the benchmark schemes in the linear time-varying channels. We also evaluate the BER performance of the index and modulated bits for the AFDM-IM scheme with and without satisfying the full diversity condition of AFDM. The results show that the index bits have a stronger diversity protection than the modulated bits even when the full diversity condition of AFDM is not satisfied

Optimal channel equalization for filterbank transceivers in presence of white noise

Filterbank transceivers are widely employed in data communication networks to cope with inter-symbol-interference (ISI) through the use of redundancies. This dissertation studies the design of the optimal channel equalizer for both time-invariant and time-varying channels, and wide-sense stationary (WSS) and possible non-stationary white noise processes. Channel equalization is investigated via the filterbank transceivers approach. All perfect reconstruction (PR) or zero-forcing (ZF) receiver filterbanks are parameterized in an affine form, which eliminate completely the ISI. The optimal channel equalizer is designed through minimization of the mean-squared-error (MSE) between the detected signals and the transmitted signals. Our main results show that the optimal channel equalizer has the form of state estimators, and is a modified Kalman filter. The results in this dissertation are applicable to discrete wavelet multitone (DWMT) systems, multirate transmultiplexers, orthogonal frequency division multiplexing (OFDM), and direct-sequence/spread-spectrum (DS/SS) based code division multiple access (CDMA) networks. Design algorithms for the optimal channel equalizers are developed for different channel models, and white noise processes, and simulation examples are worked out to illustrate the proposed design algorithms