Matched Filter Bound Research Articles

Auxiliary Variable-Aided Hybrid Message Passing for Joint Channel, Phase Noise Estimation and Detection for Multi-User MIMO Systems

This paper considers a multi-user multiple-input multiple-output (MU-MIMO) system with independent phase noise (PN) at user terminals (UTs) due to non-synchronous noisy local oscillators. The conventional factor graph of MU-MIMO involves an observation factor with multiple high-dimensional variables in the form of multiplication and summation. In this work, the MU-MIMO factor graph is represented by introducing auxiliary variables, which enables the decomposition of the observation factor into several simpler sub-factors and then use different message passing techniques to obtain approximate marginals. Specifically, belief propagation and expectation propagation (BP-EP) are used for the linear factors for random walk process, modulation and coding, while mean field (MF) is used for non-linear factor in exponential form. To reduce the computational complexity, the non-Gaussian MF messages are approximated to be Gaussian by using the second order Taylor expansion at its belief obtained in the previous iteration. The proposed receiver has a quadratic computational complexity per symbol per iteration. Simulation results show that the performance of the proposed receiver is better than existing methods and is close to the matched filter bound (MFB) in terms of the bit error rate (BER).

Analytical Performance Evaluation of Massive MIMO Techniques for SC-FDE Modulations

In the Fifth Generation of telecommunications networks (5G), it is possible to use massive Multiple Input Multiple Output (MIMO) systems, which require efficient receivers capable of reaching good performance values. MIMO systems can also be extended to massive MIMO (mMIMO) systems, while maintaining their, sometimes exceptional, performance. However, we must be aware that this implies an increase in the receiver complexity. Therefore, the use of mMIMO in 5G and future generations of mobile receivers will only be feasible if they use very efficient algorithms, so as to maintain their excellent performance, while coping with increasing and critical user demands. Having this in mind, this paper presents and compares three types of receivers used in MIMO systems, for further use with mMIMO systems, which use Single-Carrier with Frequency-Domain Equalization (SC-FDE), Iterative Block Decision Feedback Equalization (IB-DFE) and Maximum Ratio Combining (MRC) techniques. This paper presents and compares the theoretical and simulated performance values for these receivers in terms of their Bit Error Rate (BER) and correlation factor. While one of the receivers studied in this paper achieves a BER performance nearly matching the Matched Filter Bound (MFB), the other receivers (IB-DFE and MRC) are more than 1 dB away from MFB. The results obtained in this paper can help the development of ongoing research involving hybrid analog/digital receivers for 5G and future generations of mobile communications.

Multi-user detection for the downlink of NOMA systems with multi-antenna schemes and power-efficient amplifiers

Non-orthogonal multiple access (NOMA) schemes have been recognized as a promising multiple access method for the fifth generation (5G) communication systems. In NOMA, multiple users can share the same physical channel, which allows for a substantial increase in capacity gains when comparing to conventional orthogonal multiple access (OMA) techniques. This paper considers the downlink transmission of NOMA schemes combined with single-carrier (SC) signals. We present a multi-antenna transmission technique that is compatible with highly efficient power amplifiers without requiring any pre-processing. Furthermore, a multi-user detection scheme based on iterative frequency-domain equalization (FDE) is presented. We show that besides the high power-efficiency of the transmission scheme, the system’s performance can be close to the matched filter bound (MFB).

Performance Analysis and Improvement for VAMP Soft Frequency-Domain Equalizers

The vector approximate message passing (VAMP) soft frequency-domain equalizer (SFDE) has been proposed for turbo equalization. It consists of an inner soft equalizer (ISE) and an inner soft slicer (ISS), which iteratively exchange block-wise extrinsic information to improve the equalization performance, analogous to the outer turbo iteration between a soft equalizer and a soft decoder. However, a comparison of the VAMP-SFDE with other types of self-iterative SFDEs, including the self-iterative block-wise soft interference cancellation (SI-BSIC) SFDE and the generalized approximate message passing (GAMP) SFDE, is lacking. Moreover, comprehensive performance analysis for the VAMP-SFDE is yet to be performed. In this paper, relations among the VAMP-SFDE, the SI-BSIC-SFDE, and the GAMP-SFDE are first revealed. After that, the performance analysis is provided for the VAMP-SFDE and it leads to an improved semi-adaptive damping (SAD) scheme for maintaining the independence between the ISS and ISE. The resulting SAD-VAMP-SFDE shows improved mean square error (MSE) evolution curves compared with the original VAMP-SFDE. The SAD-VAMP-SFDE-based turbo equalization outperforms those using the SI-BSIC-SFDE or GAMP-SFDE and approaches the matched filter bound (MFB) over low signal-to-noise ratio region. To further demonstrate its superiority, the SAD-VAMP-SFDE is employed to enable a near-capacity transceiver design, which adopts the serial concatenation of an irregular convolutional code and a unity-rate code on the transmitter side.

Symbol Error Rate Performance of Box-Relaxation Decoders in Massive MIMO

The maximum-likelihood (ML) decoder for symbol detection in large multiple-input multiple-output wireless communication systems is typically computationally prohibitive. In this paper, we study a popular and practical alternative, namely the Box-relaxation optimization (BRO) decoder, which is a natural convex relaxation of the ML. For iid real Gaussian channels with additive Gaussian noise, we obtain exact asymptotic expressions for the symbol error rate (SER) of the BRO. The formulas are particularly simple, they yield useful insights, and they allow accurate comparisons to the matched-filter bound (MFB) and to the zero-forcing decoder. For BPSK signals the SER performance of the BRO is within 3dB of the MFB for square systems, and it approaches the MFB as the number of receive antennas grows large compared to the number of transmit antennas. Our analysis further characterizes the empirical density function of the solution of the BRO, and shows that error events for any fixed number of symbols are asymptotically independent. The fundamental tool behind the analysis is the convex Gaussian min-max theorem.

Iterative Receiver Combining IB-DFE with MRC for Massive MIMO Schemes

Abstract: Once we are moving to the 5G system it is imperative to reduce the complexity of massive MIMO (Multiple-Input, Multiple Output) receivers. This paper considers the uplink transmission using massive MIMO combined with SC-FDE (Single-Carrier with Frequency-Domain Equalization). We propose an iterative frequency-domain receiver merging IB-DFE (Iterative Block Decision-Feedback Equalizer) with MRC (Maximal Ratio Combining). We propose a novel approach to reduce the complexity of the receiver by avoiding matrix inversions while maintaining a level of performance very close to the Matched Filter Bound (MFB), which makes it an excellent option for 5G systems.

Design and Analysis of Broadband Amplify-and-Forward Cooperative Systems: A Fractionally-Spaced Sampling Approach

In this paper, we propose novel fractionally-spaced frequency-domain equalizers for the amplify-and-forward cooperative systems. In the proposed equalization schemes, the sampling rate of the received signal remains at least as high as the Nyquist rate within the digital processing chain of the relay node(s), upon which a true fractionally-spaced equalization becomes feasible at the destination. Based on minimum-mean-square-error (MMSE) criterion, different equalization structures (linear and non-linear) are designed, and approximations for their bit error rate (BER) performance are presented. The BER performance of the proposed schemes are further lower bounded through a matched-filter bound (MFB) analysis which provides insight into system design such as optimum power allocation and relay selection strategy. Our results show that, under certain channel realizations and sampling phase errors (that may occur in the relay and destination terminals), the performance of the conventional symbol-spaced cooperative systems reduces to that of no relay scenario. However, the performance of cooperative systems with the proposed fractionally-spaced equalizers is independent of the samplers' phases, and as a result, full benefit of cooperation is retained.

Iterative Equalizer Based on Kalman Filtering and Smoothing for MIMO-ISI Channels

This paper proposes an iterative equalizer based on Kalman filtering and smoothing (IEKFS) for multiple-input multiple-output inter-symbol interference (MIMO-ISI) channels. A state-space model with a priori information and the corresponding Kalman filtering (KF) and Kalman smoothing (KS) operations are developed. The KF operations perform a linear minimum mean-square error (MMSE) equalization procedure with soft interference cancellation. In addition, the KF and KS operations produce and exchange the updated extrinsic information. During this IEKFS process, the soft estimate of a desired symbol does not participate in the equalization procedures for the desired symbol; only the feedback information of the other transmit symbols is used. Therefore, the proposed IEKFS performs iterative linear MMSE equalization based on the Kalman framework and turbo principle. The complexity of the IEKFS is linear with respect to the number of transmit signal vectors in a transmission block, and simulation results show that the IEKFS can achieve near-optimum bit error rate performances approaching the matched filter bound (MFB) of the channel in various environments.

An Iterative DFE Receiver for MIMO SC-FDMA Uplink

Ever since the adoption of the single carrier frequency division multiple access (SC-FDMA) scheme for the uplink in the Long Term Evolution (LTE) standard, there has been much interest in improved receiver algorithms for the same. Successive interference cancelation (SIC) based turbo receivers (Turbo SIC) have been proposed to tackle the multi-stream interference (MSI) for transmission modes such as spatial multiplexing (SM) and multiuser (MU) multiple input multiple output (MIMO). In addition, decision feedback equalizers (DFE) have been discussed as an alternative to the simple linear minimum mean square error (LMMSE) based receivers to suppress intersymbol interference (ISI) caused by the frequency selective multi-path channel. This paper proposes a DFE receiver variant based on parallel interference cancelation (PIC) with maximum likelihood detection (MLD) and ordered SIC (OSIC) principles to suppress ISI and MSI. Simulations show that the proposed receiver performs better than the existing SIC and DFE based receivers and achieves the matched filter bound (MFB) for both coded and uncoded systems.

Performance limits of conventional and widely linear DFT-precoded-OFDM receivers in wideband frequency-selective channels

This paper describes the limiting behavior of linear and decision feedback equalizers (DFEs) in single/multiple antenna systems employing real/complex-valued modulation alphabets. The wideband frequency-selective channel is modeled using a Rayleigh fading channel model with infinite number of time domain channel taps. Using this model, we show that the considered equalizers offer a fixed post detection signal-to-noise ratio (post-SNR) at the equalizer output that is close to the matched filter bound (MFB). General expressions for the post-SNR are obtained for zero-forcing (ZF)-based conventional receivers as well as for the case of receivers employing widely linear (WL) processing. Simulation is used to study the bit error rate (BER) performance of both minimum-mean-square-error (MMSE) and ZF-based receivers. Results show that the considered receivers advantageously exploit the rich frequency-selective channel to mitigate both fading and inter-symbol interference (ISI) while offering a performance comparable to the MFB.

Iterative Frequency-Domain Detection for IA-Precoded MC-CDMA Systems

Interference alignment (IA) is a promising technique that allows high capacity gains in interfering channels. On the other hand, iterative frequency-domain detection receivers based on the IB-DFE concept (Iterative Block Decision Feedback Equalization) can efficiently exploit the inherent space-frequency diversity of the MIMO MC-CDMA systems. In this paper we combine iterative IA precoding at the transmitter with IB-DFE based processing at the receiver for MC-CDMA systems. The receiver is designed in two steps: first a linear filter is used to mitigate the inter-user aligned interference, and then an iterative frequency-domain receiver is designed to efficiently separate the spatial streams in the presence of residual inter-user aligned interference at the output of the filter. The matrices for this non-linear space-frequency equalizer are obtained by minimizing the overall mean square error (MSE) of all data streams at each subcarrier. Our receiver structure is explicitly designed taking into account the residual inter-user interference, allowing both an efficient separation of the spatial streams and a reduction in the number of iterations of the IA procedure. We also propose a simple, yet accurate analytical approach for obtaining the performance of the proposed receiver structure. Our scheme achieves the maximum degrees of freedom provided by the IA precoding, while allowing an almost optimum space-diversity gain, with performance close to the matched filter bound (MFB).

A Factor Graph Approach to Joint OFDM Channel Estimation and Decoding in Impulsive Noise Environments

We propose a novel receiver for orthogonal frequency division multiplexing (OFDM) transmissions in impulsive noise environments. Impulsive noise arises in many modern wireless and wireline communication systems, such as Wi-Fi and powerline communications, due to uncoordinated interference that is much stronger than thermal noise. We first show that the bit-error-rate optimal receiver jointly estimates the propagation channel coefficients, the noise impulses, the finite-alphabet symbols, and the unknown bits. We then propose a near-optimal yet computationally tractable approach to this joint estimation problem using loopy belief propagation. In particular, we merge the recently proposed “generalized approximate message passing” (GAMP) algorithm with the forward-backward algorithm and soft-input soft-output decoding using a “turbo” approach. Numerical results indicate that the proposed receiver drastically outperforms existing receivers under impulsive noise and comes within 1 dB of the matched-filter bound. Meanwhile, with N tones, the proposed factor-graph-based receiver has only O(NlogN) complexity, and it can be parallelized.

고속 시변 채널 OFDM을 위한 저복잡도 양방향 탐색 순차적 간섭 제거

본 논문에서는 고속 시변 채널 OFDM을 위한 저복잡도 양방향 탐색 순차적 간섭 제거(Successive Interference Cancellation: SIC) 방식을 제안한다. SIC에서는 오류 전파에 의한 성능 저하 가능성으로 인하여 심볼 블록 내에서의 심볼 검출 순서가 전체적인 성능에 큰 영향을 미친다. 본 논문에서는 조건 심볼오류확률(Conditional Symbol Error Probability:CSEP)을 기준으로 최초로 검출되는 심볼을 결정하고, 그 다음 검출될 심볼은 기검출된 심볼군의 경계에서 양방향으로 탐색하여 CSEP를 갱신한 후 결정하는 방식을 이용한다. 컴퓨터 모의실험 결과 제안된 방식은 기존 방식과 비교하여 높은 SNR 영역에서 거의 동일한 계산량으로 보다 우수한 성능을 나타낸다. 제안된 방식은 비트에러율 = 10-5에서 성능 상한치인 정합필터 한계(Matched Filter Bound: MFB)에 2dB 이내로 접근하는 성능을 가진다.

SC-FDE for Offset Modulations: An Efficient Transmission Technique for Broadband Wireless Systems

It is widely accepted that SC-FDE (Single-Carrier with Frequency-Domain Equalization) is an excellent candidate for broadband wireless systems, especially when an efficient power amplification is intended. If grossly nonlinear power amplifiers are employed, conventional QPSK (Quaternary Phase Shift Keying) or QAM (Quadrature Amplitude Modulation) modulations should be replaced by offset modulations such as OQPSK (Offset QPSK) and OQAM (Offset QAM). In fact, offset signals have much lower dynamic range than non-offset signals, with OQPSK signals being able to have an almost constant envelope. This paper considers frequency-domain receiver design for OQPSK and OQAM schemes. It is shown that FDE (Frequency Domain Equalization) designed for non-offset modulations are not suitable for offset modulations due to the residual IQI (In-phase/Quadrature Interference), i.e. the interference between in-phase (I) and quadrature (Q) components at the sampling instants. Therefore, we propose several FDE designs where there is no IQI in the sampling instants as well as iterative FDE receivers with IQI cancellation. Our receivers have excellent performance, with the linear designs significantly outperforming linear FDE for non-offset modulations and the iterative designs with performance close to the MFB (Matched Filter Bound).

SC-FDE for Offset Modulations: An Efficient Transmission Technique for Broadband Wireless Systems

It is widely accepted that SC-FDE (Single-Carrier with Frequency-Domain Equalization) is an excellent candidate for broadband wireless systems, especially when an efficient power amplification is intended. If grossly nonlinear power amplifiers are employed, conventional QPSK (Quaternary Phase Shift Keying) or QAM (Quadrature Amplitude Modulation) modulations should be replaced by offset modulations such as OQPSK (Offset QPSK) and OQAM (Offset QAM). In fact, offset signals have much lower dynamic range than non-offset signals, with OQPSK signals being able to have an almost constant envelope. This paper considers frequency-domain receiver design for OQPSK and OQAM schemes. It is shown that FDE (Frequency Domain Equalization) designed for non-offset modulations are not suitable for offset modulations due to the residual IQI (In-phase/Quadrature Interference), i.e. the interference between in-phase (I) and quadrature (Q) components at the sampling instants. Therefore, we propose several FDE designs where there is no IQI in the sampling instants as well as iterative FDE receivers with IQI cancellation. Our receivers have excellent performance, with the linear designs significantly outperforming linear FDE for non-offset modulations and the iterative designs with performance close to the MFB (Matched Filter Bound).

Limiting Behavior of ZF/MMSE Linear Equalizers in Wideband Channels with Frequency Selective Fading

This letter establishes the near optimality of the linear equalizers (LEs) in multiple antenna systems with frequency selective fading. First, we show that a zero-forcing (ZF) LE employing N_r receiver antennas (where N_r>;1), achieves a fixed signal-to-noise-power-ratio (SNR) of Nr-1/N0 in an i.i.d. Rayleigh fading channel with infinite number of taps. The LE sacrifices one degree-of-freedom (DOF) for mitigating the multi-path fading channel and leaves remaining Nr-1 DOF for array gain. The maximum performance loss with respect to the matched filter bound (MFB) is shown to be 10 log (Nr-1/Nr) which becomes small in systems with large antenna arrays. Next, simulation is used to compare the performance of minimum-mean-square-error estimation (MMSE) and ZF receivers. It is shown that the MMSE based LE provides a significant advantage over ZF LE only for single antenna systems and the performance difference between the two methods becomes arbitrarily small with an increase in the number of receiver antennas.

Frequency domain decision feedback equalizer for time-reversal space-time block coding

In this paper, a frequency domain decision feedback equalizer is proposed for single carrier transmission with time-reversal space-time block coding (TR-STBC). It is shown that the diagonal decision feedback equalizer matrix can be calculated from the frequency domain channel response. Under the perfect feedback assumption, the proposed equalizer can approach matched filter bound (MFB). Compared with the existing time domain decision feedback equalizer, the proposed equalizer exhibits better performance with the same equalization complexity.

Performance bound for generalised multilevel-quadrature amplitude modulations constellations in multipath Rayleigh fading channels with imperfect channel estimation

The authors derive a lower bound on the performance of generalised multilevel quadrature amplitude modulations (M-QAM) in time-discrete multipath Rayleigh fading environments with imperfect channel estimation. The bound can be regarded as an extension of the well-known matched filter bound (MFB), taking into account the impact of imperfect channel knowledge. The analytical expressions derived allow the computation of the bit error rate for the different bit streams that can be mapped simultaneously onto M-QAM symbols using a hierarchical approach when unequal bit error protection is desired.

EST기반 변조에서 8 PSK와 16 QAM 에 대한 신호 검출

EST (Energy Spreading Transfonn) 기반의 변조는 광대역 무선통신에서 주파수 선택적 fading을 방지하는 효과적인 기술이다. 이 기법은 liner decoder의 복잡도를 가지면서 ISI (Inter-Symbol Interference)-free MFB (Matched Filter Bound) 에 근접한 성능을 나타낸다. EST 기반의 변조는 원래 QPSK에 대해 제안되었다. 하지만, 다중 fading 채널의 capacity를 최대한 이용하기 위해서 higher-order의 변조방식이 필요하다. 본 논문에서는 QPSK 에 대해 제안되었던 기존 EST 기반 변조를 재검토하고, 이를 8 PSK와 16 QAM으로 확장하는 것을 논의한다. 확장한 시스템의 성능은 Proakis B 채널과 8-tap fa이ng 채널에서의 가상실험을 통해 검증되었다. 8 PSK로 확장한 EST기반의 시스템은 MFB에 매우 근접한 성능을 보여주었지만 16 QAM으로 확장한 EST기반의 시스템은 MFB와의 성능 차이를 보여주었다. Energy spreading transform (EST) based modulation is an effective technique to combat frequency-selective fading in broadband wireless communication. It performs close to the inter-symbol interference (ISI)-free matched filter bound (MFB) only at the complexity of a linear detector. Originally, EST-based modulation has been proposed for QPSK. However, to fully utilize the capacity of multipath fading channels, higher-order modulations are also necessary. In this paper, we review the EST based modulation that has originally been proposed for QPSK and discuss its extension to 8 PSK and 16 QAM. The performance of the extended system is verified through simulation in Proakis B and 8-tap fading channel. The EST based modulation for 8 PSK shows the performance which is very close to MFB and the EST based modulation for 16 QAM shows the performance gap between its receiver and MFB.

A Novel Receiver Design for Single-Carrier Frequency Domain Equalization in Broadband Wireless Networks with Amplify-and-Forward Relaying

In this paper, we propose an efficient receiver design for single carrier frequency-domain equalization (SC-FDE) for relay-assisted transmission scenario over frequency selective channels. Building upon our earlier work, we propose a novel minimum mean square error (MMSE)-based receiver design tailored to broadband cooperative networks. We show that, by incorporating linear processing techniques, our MMSE-based receiver is able to collect full antenna and multipath diversity gains, while maintaining low complexity implementation. Specifically, under the assumption of perfect power control and high signal-to-noise ratio (SNR) for the underlying links and assuming either of source-to-relay (S → R) or relay-to-destination (R → D) links to be frequency selective Rician fading, our performance analysis demonstrates that the proposed receiver is able to achieve a maximum diversity order of min (LSR,LRD) + LSD + 2, where LSR, LRD, and LSD are the channel memory lengths for S → R, R → D, and source-to-destination (S → D) links, respectively. Simulation results demonstrate that our proposed receiver outperforms the conventional cooperative MMSE-SC-FDE receiver by performing close to the matched filter bound (MFB).