## A MESSAGE-PASSING RECEIVER FOR BICM-OFDM OVER UNKNOWN CLUSTERED-SPARSE CHANNELS

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Citations: | 8 - 6 self |

### BibTeX

@MISC{Schniter_amessage-passing,

author = {Philip Schniter},

title = {A MESSAGE-PASSING RECEIVER FOR BICM-OFDM OVER UNKNOWN CLUSTERED-SPARSE CHANNELS},

year = {}

}

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### Abstract

We propose a factor-graph-based approach to joint channel-estimationand-decoding of bit-interleaved coded orthogonal frequency division multiplexing (BICM-OFDM). In contrast to existing designs, ours is capable of exploiting not only sparsity in sampled channel taps but also clustering among the large taps, behaviors which are known to manifest at larger communication bandwidths. In order to exploit these channel-tap structures, we adopt a two-state Gaussian mixture prior in conjunction with a Markov model on the hidden state. For loopy belief propagation, we exploit a “generalized approximate message passing ” algorithm recently developed in the context of compressed sensing, and show that it can be successfully coupled with soft-input soft-output decoding, as well as hidden Markov inference. ForN subcarriers andM bits per subcarrier (and any channel length L < N), our scheme has a computational complexity of onlyO(N log 2N+N2 M). Numerical experiments using IEEE 802.15.4a channels show that our scheme yields BER performance within 1 dB of the known-channel bound and 4 dB better than decoupled channel-estimation-and-decoding via LASSO. 1.

### Citations

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Citation Context ...ER: MESSAGE-PASSING RECEIVER FOR BICM-OFDM OVER UNKNOWN CLUSTERED-SPARSE CHANNELS 1463 among the nodes of the factor graph, first instincts suggest to apply the standard “sum-product algorithm” (SPA) =-=[18]-=-–[20]. Exact SPA on the JCED factor graph is computationally infeasible, however, and so it must be approximated. For this, there are many options, since many well-known iterative inference algorithms... |

2041 | Regression shrinkage and selection via the Lasso
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Citation Context ...ltipath arrivals with a particular reference lag j. Recently, there have been many attempts to apply breakthrough non-linear estimation techniques from the field of “compressive sensing” (e.g., LASSO =-=[2]-=-) to the wireless channel estimation problem [3]. These works take a decoupled approach to the problem of channel estimation and data decoding, in that pilot-symbol knowledge is first exploited for sp... |

1779 | Atomic decomposition by basis pursuit
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Citation Context ...s receiver design becomes more complicated. Recently, there have been many attempts to apply breakthrough nonlinear estimation techniques from the field of “compressive sensing” [8] (e.g., LASSO [9], =-=[10]-=-) to the wireless channel estimation problem. We refer to this approach as “compressed channel sensing” (CCS), after the recent comprehensive overview [11]. The CCS literature generally takes a decoup... |

1280 |
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Citation Context ...lock. Doing so is equivalent to feeding extrinsic soft bit estimates to a soft-input/soft-output (SISO) decoder/deinterleaver, which treats them as priors. Since SISO decoding is a well-studied topic =-=[5]-=-, we will not give details here. It suffices to say that, once the extrinsic outputs of the SISO decoder have been computed, they are reinterleaved and passed rightward from the coding/interleaving bl... |

1278 | Factor graphs and the sum-product algorithm
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Citation Context ...ESSAGE-PASSING RECEIVER FOR BICM-OFDM OVER UNKNOWN CLUSTERED-SPARSE CHANNELS 1463 among the nodes of the factor graph, first instincts suggest to apply the standard “sum-product algorithm” (SPA) [18]–=-=[20]-=-. Exact SPA on the JCED factor graph is computationally infeasible, however, and so it must be approximated. For this, there are many options, since many well-known iterative inference algorithms can ... |

702 |
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Citation Context .... Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JSTSP.2011.2169232 scheme is well known to be linear =-=[2]-=-. As the communication bandwidth increases, however, the channel taps are no longer well-modeled as Gaussian nor independent. Rather, they tend to be heavy-tailed or “sparse” in that only a few values... |

604 |
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Citation Context ... even steepest descent [24]. Moreover, because the JCED factor graph is loopy, even non-approximate SPA is not guaranteed to yield the correct output distributions, because exact inference is NP hard =-=[25]-=-. It is perhaps not surprising that, amidst this uncertainty about exact SPA and its “best” approximation, a number of different factor-graph approaches to JCED over frequency-selective channels have ... |

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Citation Context ...ops, convergence to the exact posteriors is not guaranteed [25]. That said, there exist many problems to which loopy BP [37] has been successfully applied, including inference on Markov random fields =-=[38]-=-, LDPC decoding [14], and compressed sensing [13], [15], [32], [39]–[41]. Our work not only leverages these past successes, but unites them. B. Background on GAMP An important sub-problem within our l... |

402 |
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Citation Context ...d realizations of the tap vector from channel impulse responses generated according to the method specified in the IEEE 802.15.4a “ultra-wideband” standard [16], which uses the Saleh–Valenzuela model =-=[36]-=- where denotes the number of clusters, the delay of the th cluster, the number of components per cluster, the relative component delays, the component amplitudes, and the component phases. In particul... |

198 | The effect upon channel capacity in wireless communications of perfect and imperfect knowledge of the channel
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Citation Context ... taps are often clustered together in lag . These behaviors are both a blessing and a curse: a blessing because, of all tap distributions, the independent Gaussian one is most detrimental to capacity =-=[7]-=-, but a curse because optimal channel estimation becomes nonlinear and thus receiver design becomes more complicated. Recently, there have been many attempts to apply breakthrough nonlinear estimation... |

180 |
Modern Coding Theory
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Citation Context ...OFDM OVER UNKNOWN CLUSTERED-SPARSE CHANNELS 1469 bit estimates to a soft-input/soft-output (SISO) decoder/deinterleaver, which treats them as priors. Since SISO decoding is a well-studied topic [14], =-=[43]-=- and high-performance implementations are readily available (e.g., [44]), we will not elaborate on the details here. It suffices to say that, once the extrinsic outputs of the SISO decoder have been c... |

167 | Probing the Pareto frontier for basis pursuit solutions
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Citation Context ...is the PDP,A[q]�D(spt[q])Φpt, andΦpt∈C Np×L is constructed from the pilot rows and the firstLcolumns of theN-DFT matrix. LASSO tap estimates ˆxlasso[q] were computed by the celebrated SPGL1 algorithm =-=[17]-=- usingA[q] and a genie-optimized tuning parameter. Figure 5 shows bit error rate (BER) versus the number of pilot subcarriers Np at Eb/No = 11 dB and a fixed spectral efficiency of η = 2 bpcu. In this... |

121 | Evaluation of an ultrawide-band propagation channel
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Citation Context ...h increases, however, the channel taps are no longer well-modeled as Gaussian nor independent. Rather, they tend to be heavy-tailed or “sparse” in that only a few values in have significant amplitude =-=[3]-=-–[6]. Moreover, groups of large taps are often clustered together in lag . These behaviors are both a blessing and a curse: a blessing because, of all tap distributions, the independent Gaussian one i... |

72 |
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Citation Context ... complex Gaussian random variables, resulting in the “uncorrelated Rayleigh-fading” and “uncorrelated Rician-fading” models that have dominated the wireless communications literature for many decades =-=[1]-=-. For receiver design, the Gaussian tap assumption is very convenient because the optimal estimation Manuscript received January 25, 2011; revised May 20, 2011, August 29, 2011; accepted September 07,... |

72 | Message passing algorithms for compressed sensing: I. motivation and construction
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Citation Context ...M2 prior on . Building on recent work on multiuser detection by Guo and Wang [42], as well as recent work on message passing algorithms for compressed sensing by Donoho, Maleki, Montanari, and Bayati =-=[40]-=-, [41], Rangan proposed a so-called generalized approximate message passing (GAMP) scheme that, for the sub-problem described above, admits rigorous analysis3 as [13]. The main ideas behind GAMP are t... |

67 | Unified design of iterative receivers using factor graphs
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Citation Context ...e now place our work in the context of existing factorgraph designs. Factor-graph based joint channel-estimation and decoding (JCED) was proposed more than a decade ago (see, e.g., the early overview =-=[17]-=-). To calculate the messages passed 1932-4553/$26.00 © 2011 IEEESCHNITER: MESSAGE-PASSING RECEIVER FOR BICM-OFDM OVER UNKNOWN CLUSTERED-SPARSE CHANNELS 1463 among the nodes of the factor graph, first... |

58 | Bayesian compressive sensing via belief propagation
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Citation Context ...at said, there exist many problems to which loopy BP [37] has been successfully applied, including inference on Markov random fields [38], LDPC decoding [14], and compressed sensing [13], [15], [32], =-=[39]-=-–[41]. Our work not only leverages these past successes, but unites them. B. Background on GAMP An important sub-problem within our larger bit-inference problem is the estimation of a vector of indepe... |

57 | Ultrawideband propagation channels—Theory, measurement and modeling
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Citation Context ... over the duration of one codeword. As the communication bandwidth increases, the channel taps tend to be heavy-tailed or “sparse” in that only a few values in {xj} L−1 j=0 have significant amplitude =-=[1]-=-. Moreover, groups of large taps are often clustered together in lag j. Furthermore, both sparsity and clustering can be lag-dependent, such as when the receiver’s timing-synchronization mechanism ali... |

46 |
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Citation Context ...ision multiplexing (OFDM) with bitinterleaved coded modulation (BICM), and propose a novel factorgraph-based receiver that leverages recent results in “generalized approximate message passing” (GAMP) =-=[4]-=-, soft-input/soft-output (SISO) decoding [5], and structured-sparse estimation [6]. Our receiver assumes a clustered-sparse channel-tap prior constructed using a two-state Gaussian mixture with a Mark... |

44 | Spike and Slab Variable Selection: Frequentist and Bayesian Strategies. The Annals of Statistics 33
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Citation Context ...ther non-Gaussian inference problems (see, e.g., 2 The message passing algorithm described in Section III-B can also handle non-Gaussian mixtures and/or mixtures with more than two terms. (4) (5) (6) =-=[35]-=-), and our premise here is that the GM2 model achieves a good balance between fidelity and tractability when modeling channel taps as well. To capture the big-tap clustering behavior, we employ a hidd... |

43 |
The dynamics of message passing on dense graphs, with applications to compressed sensing
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Citation Context ...xact posteriors is not guaranteed. Even so, there exist many problems to which loopy BP has been successfully applied, including LDPC decoding [5], Markov field inference [14], and compressed sensing =-=[4, 6, 15]-=-. An important sub-problem within our larger bit-inference problem is the estimation of a vector of independent non-Gaussian variables x that are linearly mixed via Φ ∈ C N×L to form z=Φx= [z0,...,zN−... |

39 | Turbo reconstruction of structured sparse signals
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Citation Context ... a novel factorgraph-based receiver that leverages recent results in “generalized approximate message passing” (GAMP) [4], soft-input/soft-output (SISO) decoding [5], and structured-sparse estimation =-=[6]-=-. Our receiver assumes a clustered-sparse channel-tap prior constructed using a two-state Gaussian mixture with a Markov model on the hidden tap state. The scheme that we propose has only O(N log 2N +... |

37 | The factor graph approach to model-based signal processing - Loeliger, Dauwels, et al. - 2007 |

36 |
Iterative tree search detection for MIMO wireless systems
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Citation Context ...are [44], with random interleaving. We focus on the case of subcarrier OFDM with 16-QAM (i.e., ) operating at a spectral efficiency of bpcu. For bit-to-symbol mapping, we used multilevel Gray-mapping =-=[45]-=-, noting recent work [46] that conjectures the optimality of Gray-mapping when BICM is used with a strong code. In some simulations, we used pilot-only subcarriers and interspersed training bits, wher... |

35 | Compressed channel sensing: a new approach to estimating sparse multipath channels
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(Show Context)
Citation Context ... j. Recently, there have been many attempts to apply breakthrough non-linear estimation techniques from the field of “compressive sensing” (e.g., LASSO [2]) to the wireless channel estimation problem =-=[3]-=-. These works take a decoupled approach to the problem of channel estimation and data decoding, in that pilot-symbol knowledge is first exploited for sparse-channel estimation, after which the channel... |

22 |
Estimation with random linear mixing, belief propagation and compressed sensing
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Citation Context ...k is an evolution of our earlier work [30], [31] that was limited to an exactly sparse channel, that did not exploit clustering, and that was based on the “relaxed belief propagation” (RBP) algorithm =-=[32]-=-, which has higher implementation complexity than GAMP. For example, the JCED scheme from [30], [31] has complexity , which grows with the channel length . Our paper is organized as follows. In Sectio... |

19 | Cluster characteristics in a MIMO indoor propagation environment
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Citation Context ...creases, however, the channel taps are no longer well-modeled as Gaussian nor independent. Rather, they tend to be heavy-tailed or “sparse” in that only a few values in have significant amplitude [3]–=-=[6]-=-. Moreover, groups of large taps are often clustered together in lag . These behaviors are both a blessing and a curse: a blessing because, of all tap distributions, the independent Gaussian one is mo... |

15 | Surface wave focusing and acoustic communications in the surf zone - Preisig, Deane - 2004 |

14 | Random sparse linear systems observed via arbitrary channels: A decoupling principle
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Citation Context ...OVER UNKNOWN CLUSTERED-SPARSE CHANNELS 1467 TABLE I GAMP ALGORITHM and the node rightward of each node “ ” represents the GM2 prior on . Building on recent work on multiuser detection by Guo and Wang =-=[42]-=-, as well as recent work on message passing algorithms for compressed sensing by Donoho, Maleki, Montanari, and Bayati [40], [41], Rangan proposed a so-called generalized approximate message passing (... |

11 |
Analysis and simulation of a digital mobile radio channel using orthogonal frequency division multiplexing
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Citation Context ...lies an N-DFT Φ to the sequence r[q] = [r0[q],...,rN−1[q]] T , yielding y[q]=[y0[q],...,yN−1[q]] T =Φr[q] forq = 1...Q. For the pulse-shaped channel responsex(τ)�(gr⋆h⋆gt)(τ), it is well known (e.g., =-=[13]-=-) that, when the support ofx(τ) is contained in[0,LT), the observation on thei th subcarrier can be written as yi[q] = si[q]zi[q]+vi[q], (1) where zi[q] ∈ C is the i th subcarrier’s gain and {vi[q]} a... |

11 | Expectation maximization as message passing
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(Show Context)
Citation Context ...roximated. For this, there are many options, since many well-known iterative inference algorithms can themselves be recognized as SPA approximations, e.g., the expectation–maximization (EM) algorithm =-=[21]-=-, particle filtering [22], variational (or “mean-field”) techniques [23], and even steepest descent [24]. Moreover, because the JCED factor graph is loopy, even non-approximate SPA is not guaranteed t... |

7 |
Matlab programs for encoding and decoding of LDPC codes over GF(2 m ).” http://www.kozintsev.net/soft.html
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Citation Context ...el state information (CSI). Setup: For all results, we used irregular LDPC codes with codeword length ∼10000 and average column weight 3, generated (and decoded) using the publicly available software =-=[16]-=-, with random interleaving. We focus on the case of N=1024 subcarriers and 16QAM (i.e., M =4) operating at a spectral efficiency of η=2 bpcu. For bit-to-symbol mapping, we used multilevel Gray-mapping... |

7 | Particle methods as message passing
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Citation Context ...e are many options, since many well-known iterative inference algorithms can themselves be recognized as SPA approximations, e.g., the expectation–maximization (EM) algorithm [21], particle filtering =-=[22]-=-, variational (or “mean-field”) techniques [23], and even steepest descent [24]. Moreover, because the JCED factor graph is loopy, even non-approximate SPA is not guaranteed to yield the correct outpu... |

5 | On communication over unknown sparse frequency-selective block-fading channels
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Citation Context ...in that pilot-symbol knowledge is first exploited for sparse-channel estimation, after which the channel estimate is used for data decoding. However, this decoupled approach is known to be suboptimal =-=[12]-=-. The considerations above motivate a joint approach to structured-sparse-channel-estimation and decoding that offers both near-optimal decoding performance and low implementation complexity. In this ... |

4 | Joint estimation and decoding for sparse channels via relaxed belief propagation
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Citation Context ...ed (i.e., independent) channel-taps or, e.g., non-sparse channels with unknown lengthL[8], with minor modifications of our assumed channel prior. Finally, we mention that this work is an evolution of =-=[11]-=-, which applied an O(NL)-complexity “relaxed belief propagation” algorithm to unclustered exactly sparse channels, and an abbreviated version of [12]. 1 2.1. The BICM-OFDM model 2. SYSTEM MODEL We con... |

4 | On variational message passing on factor graphs
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Citation Context ...tive inference algorithms can themselves be recognized as SPA approximations, e.g., the expectation–maximization (EM) algorithm [21], particle filtering [22], variational (or “mean-field”) techniques =-=[23]-=-, and even steepest descent [24]. Moreover, because the JCED factor graph is loopy, even non-approximate SPA is not guaranteed to yield the correct output distributions, because exact inference is NP ... |

3 | Factor graph based design of an OFDM-IDMA receiver performing joint data detection, channel estimation, and channel length selection
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Citation Context ... the case of clusteredsparse channels, our approach could be applied to non-sparse (i.e., Gaussian) or non-clustered (i.e., independent) channel-taps or, e.g., non-sparse channels with unknown lengthL=-=[8]-=-, with minor modifications of our assumed channel prior. Finally, we mention that this work is an evolution of [11], which applied an O(NL)-complexity “relaxed belief propagation” algorithm to unclust... |

3 |
Variational message-passing for joint channel estimation and decoding
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Citation Context ...sing that, amidst this uncertainty about exact SPA and its “best” approximation, a number of different factor-graph approaches to JCED over frequency-selective channels have been proposed (e.g., [26]–=-=[29]-=-). Our approach differs from existing factor-graph JCED designs in that it uses 1) a sparse (i.e., non-Gaussian) channel-tap prior, 2) a clustered (i.e., non-independent) channel-tap prior, and 3) a s... |

3 | Joint channel estimation and decoding using Gaussian approximation in a factor graph over multipath channel - Liu, Brunel, et al. |

3 |
Belief-propagation-based joint channel estimation and decoding for spectrally efficient communication over unknown sparse channels
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Citation Context ...hannel-taps or, e.g., non-sparse channels with unknown length [26], with minor modifications of our assumed channel prior. Finally, we mention that this work is an evolution of our earlier work [30], =-=[31]-=- that was limited to an exactly sparse channel, that did not exploit clustering, and that was based on the “relaxed belief propagation” (RBP) algorithm [32], which has higher implementation complexity... |

2 | 2D graph-based soft channel estimation for MIMO-OFDM, in - Kneivel, Shi, et al. - 2010 |

2 | Steepest descent as message passing, in
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(Show Context)
Citation Context ...emselves be recognized as SPA approximations, e.g., the expectation–maximization (EM) algorithm [21], particle filtering [22], variational (or “mean-field”) techniques [23], and even steepest descent =-=[24]-=-. Moreover, because the JCED factor graph is loopy, even non-approximate SPA is not guaranteed to yield the correct output distributions, because exact inference is NP hard [25]. It is perhaps not sur... |

2 |
Matlab Programs for Encoding and Decoding
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Citation Context ...t-input/soft-output (SISO) decoder/deinterleaver, which treats them as priors. Since SISO decoding is a well-studied topic [14], [43] and high-performance implementations are readily available (e.g., =-=[44]-=-), we will not elaborate on the details here. It suffices to say that, once the extrinsic outputs of the SISO decoder have been computed, they are re-interleaved and passed rightward from the coding/i... |

2 |
On the suitability of Gray bit mappings to outer channel codes in iteratively decoded BICM
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(Show Context)
Citation Context ...erleaving. We focus on the case of subcarrier OFDM with 16-QAM (i.e., ) operating at a spectral efficiency of bpcu. For bit-to-symbol mapping, we used multilevel Gray-mapping [45], noting recent work =-=[46]-=- that conjectures the optimality of Gray-mapping when BICM is used with a strong code. In some simulations, we used pilot-only subcarriers and interspersed training bits, whereas in others we used and... |

1 |
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Citation Context ...Propagation Although exact evaluation of the posteriors is computationally impractical for the problem sizes of interest, these posteriors can be approximately evaluated using belief propagation (BP) =-=[37]-=- on the factor graph in Fig. 4. In textbook BP, beliefs take the form of pdfs/pmfs that are propagated among nodes of the factor graph via the sum/product algorithm (SPA) [18]–[20]. 1) Say the factor ... |