Belief Propagation over SISO/MIMO Frequency Selective Fading Channels

Kaynak, M.N.; Duman, Tolga M.; Kurtas, E.

doi:10.1109/twc.2007.05779

Cited by 18 publications

(18 citation statements)

References 11 publications

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“…This algorithm requires the computational complexity that increases exponentially with the number of ISI channel taps, the modulation size, and the number of transmit antennas. To reduce the complexity, soft-output detection methods based on the belief propagation (BP) algorithm were also proposed in [27]- [29]. They compute the the LLR values using an iterative message-passing algorithm based on the factor graph constructed by a ISI channel.…”

Section: A Related Workmentioning

confidence: 99%

“…Second, Q-BCJR combines multiple observations obtained from receive antennas, so the conditional PMF is characterized in a product form that computes the joint probability of receiving the multiple observations. The relation in (29) also shows that different pairs of (s ′ , s) ∈ k∈K V n,k may have the same conditional PMF, so it may not be computed for every pair of (s ′ , s) ∈ k∈K V n,k . This fact contributes to a complexity reduction achieved by Q-BCJR, which will be discussed in the sequel.…”

Section: A Quantized Bcjr (Q-bcjr)mentioning

confidence: 99%

“…These additional steps do not affect the resulting LLR in (30), because any product operation on the marginal probability does not change the LLR values. Compute γ n (s ′ , s) for (s ′ , s) ∈ k∈K V n,k from (28) and (29). 5: end for 6: Initialize α 0 (s) = I{s = 0 (LD−1)Ntx } and β N d +LD−1 (s) = I{s = 0 (LD−1)Ntx }.…”

Section: A Quantized Bcjr (Q-bcjr)mentioning

confidence: 99%

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Soft-Output Detection Methods for Sparse Millimeter-Wave MIMO Systems With Low-Precision ADCs

Jeon

Hong

et al. 2019

IEEE Trans. Commun.

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The use of low-precision analog-to-digital converters (ADCs) is a low-cost and power-efficient solution for a millimeter wave (mmWave) multiple-input multiple-output (MIMO) system operating at sampling rates higher than a few Gsample/sec. This solution, however, can make significant frame-errorrates (FERs) degradation due to inter-subcarrier interference when applying conventional frequencydomain equalization techniques. In this paper, we propose computationally-efficient yet near-optimal soft-output detection methods for the coded mmWave MIMO systems with low-precision ADCs. The underlying idea of the proposed methods is to construct an extremely sparse inter-symbol-interference (ISI) channel model by jointly exploiting the delay-domain sparsity in mmWave channels and a high quantization noise caused by low-precision ADCs. Then we harness this sparse channel model to create a trellis diagram with a reduced number of states or a factor graph with very sparse edge connections.Using the reduced trellis diagram, we present a soft-output detection method that computes the loglikelihood ratios (LLRs) of coded bits by optimally combining the quantized received signals obtained from multiple receive antennas using a forward-and-backward algorithm. To reduce the computational complexity further, we also present a low-complexity detection method using the sparse factor graph to compute the LLRs in an iterative fashion based on a belief propagation algorithm. Simulations results demonstrate that the proposed soft-output detection methods provide significant FER gains compared to the existing frequency-domain equalization techniques in a coded mmWave MIMO system using oneor two-bit ADCs. Index TermsMillimeter wave communications, multiple-input-multiple-output (MIMO), low-precision analogto-digital converter (ADC), time-domain equalization, inter-symbol-interference (ISI) channel. Y.-S. Jeon, H. Do, and N. Lee are with the

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Section: A Related Workmentioning

confidence: 99%

Section: A Quantized Bcjr (Q-bcjr)mentioning

confidence: 99%

Section: A Quantized Bcjr (Q-bcjr)mentioning

confidence: 99%

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Soft-Output Detection Methods for Sparse Millimeter-Wave MIMO Systems With Low-Precision ADCs

Jeon

Hong

et al. 2019

IEEE Trans. Commun.

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“…As a result, for an MIMO system, the number of messages that need to be tracked is reduced to per subcarrier. After a few simple algebraic manipulations, (27) can be rewritten as follows (31) If is large, the term in the denominator of (31) may be neglected, then we have (32) Likewise, can be approximated by , then (22) and (28) …”

Section: Complexity Reduction Using the First-order Approximation mentioning

confidence: 99%

Low-Complexity Iterative Detection for Large-Scale Multiuser MIMO-OFDM Systems Using Approximate Message Passing

Kuang

et al. 2014

IEEE J. Sel. Top. Signal Process.

222

115

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One of the challenges in the design of large-scale multiuser MIMO-OFDM systems is developing low-complexity detection algorithms. To achieve this goal, we leverage message passing algorithms over the factor graph that represents the multiuser MIMO-OFDM systems and approximate the original discrete messages with continuous Gaussian messages through the use of the minimum Kullback-Leibler (KL) divergence criterion. Several signal processing techniques are then proposed to achieve near-optimal performance at low complexity. First, the principle of expectation propagation is employed to compute the approximate Gaussian messages, where the symbol belief is approximated by a Gaussian distribution and then the approximate message is calculated from the Gaussian approximate belief. In addition, the approximate symbol belief can be computed by the a posteriori probabilities fed back from channel decoders, which reduces the complexity dramatically. Second, the first-order approximation of the message is utilized to further simplify the message updating, leading to an algorithm that is equivalent to the AMP algorithm proposed by Donoho et al. Finally, the message updating is further simplified using the central-limit theorem. Compared with the single tree search sphere decoder (STS-SD) and the iterative (turbo) minimum mean-square error based soft interference cancellation (MMSE-SIC) in the literature through extensive simulations, the proposed message passing algorithms can achieve a near-optimal performance while the complexity is decreased by tens of times for a 64 64 MIMO system. In addition, it is shown that the proposed message passing algorithms exhibit desirable tradeoffs between performance and complexity for a low-dimensional MIMO system.

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“…In particular, iterative equalizers based on soft-decision equalization (SDE) [7], a belief-propagation (BP) detector [8], and iterative soft-decision interference cancellation (ISDIC) [9] have been developed for MIMO-ISI channels. For a received block, these equalizers iteratively execute the equalization process by transforming the outputs from the previous equalization procedures into a priori information for the future equalization procedures.…”

Section: Introductionmentioning

confidence: 99%

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

Park

Choi

2015

IEEE Trans. Signal Process.

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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. Index TermsMIMO systems, frequency-selective fading, ISI, Kalman filtering, Kalman smoothing, iterative equalizer, a priori information nulling.

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Belief Propagation over SISO/MIMO Frequency Selective Fading Channels

Cited by 18 publications

References 11 publications

Soft-Output Detection Methods for Sparse Millimeter-Wave MIMO Systems With Low-Precision ADCs

Soft-Output Detection Methods for Sparse Millimeter-Wave MIMO Systems With Low-Precision ADCs

Low-Complexity Iterative Detection for Large-Scale Multiuser MIMO-OFDM Systems Using Approximate Message Passing

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

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