Ioannis Kanaras

Spectrally Efficient FDM Signals: Bandwidth Gain at the Expense of Receiver Complexity

This paper investigates the transmission of Frequency Division Multiplexed (FDM) signals, where carrier orthogonality is intentionally violated in order to increase bandwidth efficiency. In analogy to conventional OFDM, signal generation relies on an Inverse Fractional Fourier Transform (IFRFT) that can be implemented with O(N log2 N) algorithmic complexity. Optimal Maximum Likelihood (ML) detection is overly complex due to the presence of substantial Intercarrier Interference (ICI). Consequently, we investigate an alternative detection mechanism based on the Generalized Sphere Decoding (GSD) algorithm. We examine the bandwidth efficiency and the error performance in Additive White Gaussian Noise (AWGN), for various FDM signal parameters. In particular, we show that it is possible to detect optimally and efficiently FDM signals, with 25% bandwidth gain with respect to analogous OFDM signals. This indicates that the transmission of spectrally efficient non orthogonal FDM signals is tangible.

A Truncated SVD approach for fixed complexity spectrally efficient FDM receivers

Spectrally Efficient Frequency Division Multiplexing (SEFDM) systems aim to reduce the utilized spectrum by multiplexing non-orthogonal overlapped carriers. Since the per carrier transmission rate is maintained, SEFDM yields higher spectral efficiency relative to an equivalent Orthogonal Frequency Division Multiplexing (OFDM) system. Yet, due to the loss of the orthogonality, detection of the SEFDM system requires overly complex detectors. In this work, new SEFDM receivers that offer substantial complexity reduction with a competitive Bit Error Rate (BER) performance are presented. The Truncated Singular Value Decomposition (TSVD) is proposed as an efficient tool to overcome the ill conditioning of the system caused by the orthogonality collapse. The performance of the system with respect to the system size and spectrum saving is examined by extensive numerical simulations. It is shown that the TSVD detector outperforms linear detectors such as Zero Forcing (ZF) and Minimum Mean Squared Error (MMSE) detectors in terms of BER. Furthermore, a combination of TSVD with the Fixed Sphere Decoder (FSD) algorithm is proposed and tested for the first time. This novel FSD-TSVD receiver achieves near -optimum performance in terms of BER with a fixed and reduced complexity for systems with bandwidth savings of up to 40%.

Joint channel equalization and detection of Spectrally Efficient FDM signals

This paper investigates the transmission in time dispersive channels of Spectrally Efficient Frequency Division Multiplexed (SEFDM) signals, where carrier orthogonality is intentionally violated in order to increase bandwidth efficiency. Sufficient statistics of the transmitted SEFDM signal can be obtained by projecting the received signal onto an orthonormal base generated at the receiver using an Iterative Modified Gram Schmidt (IMGS) procedure. In order to reduce the computational complexity resulting from Inter-Carrier Interference (ICI), detection has been implemented based on a Regularized Sphere Decoding (RSD) algorithm. The proposed scheme was previously tested in Additive White Gaussian Noise (AWGN) for various SEFDM signal parameters. In the present work, these results are extended to account for the effect of time dispersive channels. Randomly generated SEFDM symbols are used as pilots to provide estimates of the channel impulse response in systems with or without cyclic prefixes. A joint equalization-detection is subsequently performed in a RSD stage. We show that it is possible to detect optimally SEFDM signals of small dimensionality (e.g. N = 32), with up to 20% bandwidth gain with respect to OFDM systems of the same symbol-rate. This indicates that the wireless transmission of non orthogonal SEFDM signals is tangible.

A Fast Constrained Sphere Decoder for Ill Conditioned Communication Systems

This letter proposes a fast constrained sphere decoder for ill conditioned communications systems that exhibits less complexity than but similar performance to the generalised sphere decoder. The operational principle is based on i) the reduction of the search space by setting the hypersphere initial radius to be equal to the distance to a semidefinite program (SDP) estimate; and ii) the introduction of a heuristic pruning rule to limit the GSD spanning tree. The new algorithm achieves significant reduction in the required computational effort at the expense of a small error penalty for large dimensional systems in low signal to noise ratio (SNR) regimes.

A practical system for improved efficiency in frequency division multiplexed wireless networks

Spectral efficiency is a key design issue for all wireless communication systems. Orthogonal frequency division multiplexing (OFDM) is a very well-known technique for efficient data transmission over many carriers overlapped in frequency. Recently, several studies have appeared that describe spectrally efficient variations of multi-carrier systems where the condition of orthogonality is dropped. Proposed techniques suffer from two weaknesses: firstly, the complexity of generating the signal is increased. Secondly, the signal detection is computationally demanding. Known methods suffer either unusably high complexity or high error rates because of the inter-carrier interference. This study addresses both problems by proposing new transmitter and receiver architectures whose design is based on using the simplification that a rational spectrally efficient frequency division multiplexing (SEFDM) system can be treated as a set of overlapped and interleaving OFDM systems. The efficacy of the proposed designs is shown through detailed simulation of systems with different signal types and carrier dimensions. The decoder is heuristic but in practice produces very good results that are close to the theoretical best performance in a variety of settings. The system is able to produce efficiency gains of up to 20% with negligible impact on the required signal-to-noise ratio.

Masked M-QAM OFDM: A simple approach for enhancing the security of OFDM systems

This paper investigates the secure transmission of Orthogonal Frequency Division Multiplexing (OFDM) signals, masked under non-orthogonal FDM signals of approximately the same overall bandwidth. Carrier orthogonality of traditional OFDM is intentionally violated in order to generate an encrypted signal at the physical layer, without any loss in bandwidth efficiency or extra overhead. A symmetric secret key is used for the modulation of part of the FDM signal while the original information symbol modulates the remaining carriers. The encrypted FDM signal generation takes place in an IFFT stage by simple truncation of part of its output. At the receiver, a straightforward suppression of the induced Inter-Carrier Interference (ICI) is performed before the OFDM demodulator, based on knowledge of the secret key. The key holder subsequently uses the traditional OFDM FFT demodulator to extract the information symbol. We demonstrate that an eavesdropper cannot demodulate the transmitted FDM signal by reduced complexity detection methods due to its severe ill-conditioning. Conversely, they have to rely on vectorial Maximum Likelihood detection of exponential complexity. Furthermore, in real noisy environments the eavesdropper detection capability is further affected by the abrupt shrinking of the FDM demodulator detection regions.

A new quasi-optimal detection algorithm for a non orthogonal Spectrally Efficient FDM

Non-orthogonal Spectrally Efficient Frequency Division Multiplexing (SEFDM) signals of a small dimensionality can be optimally detected using the Sphere Decoder (SD) algorithm. However, the employment of such detectors is restricted by two factors; the ill-conditioning of the SEFDM projections matrix in the system linear statistical model and the sensitivity of the SD complexity to noise. A solution to the latter could be given by a fixed complexity detection based on the Semidefinite Programming (SDP). Notwithstanding, SDP error performance appears to be suboptimal. In order to diminish the error performance gap between the SDP and the optimal detector we propose a modified SD that investigates only the points of the SEFDM lattice within a hypersphere whose size is determined by a first SDP estimate. In addition, the new SD tree is pruned to include only the branches that have a heuristically predefined Hamming distance from the SDP estimate. We show that the introduced scheme achieves a quasi optimal Bit Error Rate (BER) for an SEFDM scheme with 20% spectral gain compared to Orthogonal FDM (OFDM). Moreover, we demonstrate by simulation that the new scheme is superior in terms of computational effort compared to an equivalent SDP - brute force Maximum Likelihood (ML) scheme. Finally, it is shown that the new pruned SD reduces by more than 30% the number of the visits to the nodes of the SD tree made by the conventional SD using the Schnorr Euchner (SE) reordering strategy.

A combined MMSE-ML detection for a spectrally efficient non orthogonal FDM signal

In this paper, we investigate the possibility of reliable and computationally efficient detection for spectrally efficient non-orthogonal Multiplexing (FDM) system, exhibiting varying levels of intercarrier interference. Optimum detection is based on the Maximum Likelihood (ML) principle. However, ML is impractical due to its computational complexity. On the other hand, linear detection techniques such as Zero Forcing (ZF) and Minimum Mean Square Error (MMSE) exhibit poor performance. Consequently, we explore the combination of MMSE estimation with ML estimation around a neighborhood of the MMSE estimate. We evaluate the performance of the different schemes in Additive White Gaussian Noise (AWGN), with reference to the number of FDM carriers and their frequency separation. The combined MMSE-ML scheme achieves a near optimum error performance with polynomial complexity for a small number of BPSK FDM carriers. For QPSK modulation the performance of the proposed system improves for a large number of ML comparisons. In all cases, the detectability of the FDM signal is bounded by the signal dimension and the carriers frequency distance.

Investigation of a Semidefinite Programming detection for a spectrally efficient FDM system

Recent years have witnessed some interest in Spectrally Efficient Frequency Division Multiplexing (SEFDM) communications systems, where subcarrier orthogonality is intentionally violated to improve the spectral efficiency at the expense of system complexity. This paper investigates reliable polynomial-time hard detection techniques for SEFDM systems, by relaxing the optimal combinatorial Maximum Likelihood (ML) detection to a Semidefinite Program (SDP). SDP can be solved in almost cubic complexity over the number of the SEFDM subcarriers, N. However, the relaxation results into a degradation of the system error performance. In particular, we study the effect of the number of SEFDM subcarriers, N, and the subcarrier separation, Δf, on the SDP relaxation gap in the presence of Additive White Gaussian Noise (AWGN). We find that as N increases and/or Δf decreases, the SDP estimate gradually diverges from the optimal solution. To overcome this problem, we propose the use of a boxed ML procedure around the SDP estimate. We show by simulation that the SDP-ML combination approximates the optimum detection for N ≤ 32 subcarriers and up to 20% of bandwidth reduction with respect to an equivalent Orthogonal FDM (OFDM). Our SDP results show a small error penalty when compared to optimal Sphere Decoders (SD), whose computational effort is random and noise dependant, and thereby indicate that our proposed technique is useable in practical SEFDM systems with a moderate number of subcarriers.