Joint Channel & Data Detection

• JCDE is a unified receiver architecture that concurrently estimates channel coefficients and data symbols from the same observations.
• It employs various algorithmic methods such as GLRT, message passing, and optimization-based relaxations to handle bilinear models with sparsity and coding constraints.
• JCDE techniques significantly improve SNR and error rates in systems like massive MIMO and grant-free mMTC, and they pave the way for hybrid, learning-based designs.

Searching arXiv for the papers on arXiv and topic context. Joint Channel and Data Detection (JCDE) denotes a receiver architecture in which channel inference and symbol or bit inference are performed jointly from the same received observations, instead of following the conventional pipeline of pilot-based channel estimation, coherent detection, and optional decoding as separate blocks. In the literature, closely related labels include joint channel estimation and data detection (JCD or JED), joint activity detection, channel estimation, and data decoding in grant-free access, and joint channel estimation, detection, and decoding (JCDD) when coding constraints are explicitly embedded. Across multihop OFDM, massive MIMO, cell-free systems, grant-free mMTC, near-field XL-MIMO, FTN signaling, and URLLC, the unifying feature is a single probabilistic or optimization problem over a bilinear observation model such as $\mathbf{Y} = \mathbf{H}\mathbf{X} + \mathbf{N}$, often augmented by sparsity, decoder, or activity variables (Min et al., 2012, Alshamary et al., 2016, Bian et al., 2021, Sun et al., 2024).

1. Definition, scope, and nomenclature

JCDE replaces the separated receiver architecture by a unified inference step in which the channel matrix and the transmitted data are treated as coupled unknowns. In the GLRT formulation for massive MIMO uplink, this appears as a mixed optimization over continuous channel variables and discrete constellation variables; in Bayesian formulations it appears as posterior inference over $p(\mathbf{H},\mathbf{X}\mid\mathbf{Y})$ or extensions such as $p(\mathbf{H},\mathbf{X},\mathbf{u}\mid\mathbf{Y})$ when user activity is also unknown (Alshamary et al., 2016, Bian et al., 2021).

The terminology varies with the surrounding communication task. In cell-free massive MU-MIMO, the term JED is used for a MAP receiver that jointly estimates the channel and payload symbols while exploiting channel sparsity and QAM boundedness (Song et al., 2021). In grant-free mMTC, the same core idea expands to joint activity detection, channel estimation, and data decoding, because user activity induces a common sparsity pattern across pilot and data observations (Bian et al., 2021). In coded short-packet MIMO, JCDD adds bit-to-symbol mapping and LDPC code constraints to the same joint optimization (Sun et al., 2024).

The literature does not treat JCDE as synonymous with blind operation. Blind or semi-blind joint processing is one important branch, including bilinear expectation propagation for cell-free massive MIMO (Karataev et al., 2023), but pilot-aided formulations are equally central. Representative examples include non-orthogonal pilot-based near-field XL-MIMO JCDE (Arai et al., 2024), superimposed-pilot-aided FTN JCEDD (Keykhosravi et al., 21 Mar 2025), and pilot-assisted JCDD for URLLC (Sun et al., 2024).

2. Mathematical formulations

A standard starting point is the block-fading matrix model

$\mathbf{Y} = \mathbf{H}\mathbf{X} + \mathbf{N},$

with $\mathbf{H}$ unknown over a coherence block and $\mathbf{X}$ containing known pilots, unknown data, or both. In the noncoherent massive-MIMO GLRT formulation, the joint problem is

$$(\hat{\mathbf{H}},\hat{\mathbf{X}}) = \arg\min_{\mathbf{H},\ \mathbf{X}\in\Omega^{M\times T}} \|\mathbf{Y}-\mathbf{H}\mathbf{X}\|_F^2,$$

which can be reduced by eliminating $\mathbf{H}$ through least squares, yielding a discrete optimization in $\mathbf{X}$ based on a projection residual (Alshamary et al., 2016). This formulation is exact for unknown deterministic channel coefficients and leads to GLRT-optimal detection.

Bayesian JCDE instead specifies likelihood and priors explicitly. In grant-free massive random access, the posterior is factorized as

$$p(\mathbf{H},\mathbf{X}\mid\mathbf{Y}) \propto \prod_{m,t} p\!\left(y_{mt}\,\middle|\,\sum_n h_{mn}x_{nt}\right) \prod_n \Bigl[p(u_n)\prod_m p(h_{mn}\mid u_n)\prod_t p(x_{nt})\Bigr],$$

so user activity $p(\mathbf{H},\mathbf{X}\mid\mathbf{Y})$0, channel coefficients, and data symbols are inferred jointly from a common factor graph (Bian et al., 2021). In this setting, the common sparsity pattern between pilot and data phases is not incidental; it is a structural prior.

Other systems enrich the objective with application-specific regularization. In cell-free massive MU-MIMO, a MAP JED criterion combines data fidelity with a Laplace prior on the channel, leading to an $p(\mathbf{H},\mathbf{X}\mid\mathbf{Y})$1-regularized objective and a convex-hull relaxation of the QAM alphabet (Song et al., 2021). In coded URLLC, JCDD replaces unconstrained symbols by bit variables tied to modulation and LDPC parity constraints, then relaxes the parity-polytope constraints and adds a quadratic term that favors binary solutions (Sun et al., 2024). In diffusion-based JCDE, the target quantity is the joint posterior $p(\mathbf{H},\mathbf{X}\mid\mathbf{Y})$2, and approximate MAP estimation is obtained by sampling from that posterior with a score-based generative model for the channel and a discrete prior for symbols (Zilberstein et al., 2023).

3. Principal algorithmic families

The diversity of JCDE formulations has produced several distinct algorithmic families. They differ mainly in how they handle the bilinear coupling between channel and data, the discrete alphabet constraint, and structural priors such as sparsity or coding.

Family	Representative realization	Characteristic feature
GLRT search	Massive-MIMO branch-and-bound tree search	GLRT-optimal with expected polynomial complexity in coherence time (Alshamary et al., 2016)
Message passing	Bilinear-EP, BiG-AMP turbo, sequential EP	Factor-graph inference with alternating channel/data updates (Karataev et al., 2023, Bian et al., 2021, Arai et al., 2024)
Continuous relaxations	FBS-based JED, ADMM-based JCDD	Convex-hull or polytope relaxations with closed-form proximal or ADMM steps (Song et al., 2021, Sun et al., 2024)
Iterative equalization / VI	SP-aided JCEDD, variational multihop OFDM JCDE	Channel re-estimation or VI updates inside detection loops (Keykhosravi et al., 21 Mar 2025, Min et al., 2012)
Learned or hybrid inference	Diffusion, BCJRNet, SVM, DNN receivers	Learned priors or discriminative mappings for joint inference (Zilberstein et al., 2023, Tsai et al., 2020, Akın et al., 2020, Wang et al., 2019)

The GLRT branch-and-bound line is important because it shows that exact noncoherent joint processing need not be dismissed as purely exponential. For massive MIMO with fixed user number $p(\mathbf{H},\mathbf{X}\mid\mathbf{Y})$3, the expected complexity of the proposed algorithm grows polynomially in coherence time $p(\mathbf{H},\mathbf{X}\mid\mathbf{Y})$4, and the method remains GLRT-optimal for general constellations (Alshamary et al., 2016).

Message-passing methods reformulate JCDE as bilinear inference on factor graphs. In grant-free mMTC, a turbo receiver based on BiG-AMP jointly estimates channel state, user activity, and soft data symbols, while decoder extrinsic information is fed back into the joint estimator (Bian et al., 2021). In near-field XL-MIMO, sequential EP alternates channel and data updates, combines Bayesian inference with a model-based deterministic channel refinement, and uses a sub-array LMMSE filter to address beam-domain correlation caused by near-field energy leakage (Arai et al., 2024). In cell-free massive MIMO, bilinear-EP JCD is derived from an approximation of the joint a posteriori distribution whose factor-graph representation enables distributed implementation among access points and the central processing unit with polynomial complexity (Karataev et al., 2023).

Optimization-based relaxations address the discrete alphabet by continuous surrogates. Cell-free JED uses forward-backward splitting after replacing the QAM alphabet by its convex hull and adding a concave penalty that pulls the relaxed solution toward constellation corners (Song et al., 2021). JCDD for URLLC uses ADMM with closed-form updates in each iteration, then unfolds the ADMM iterations into trainable networks (Sun et al., 2024). Earlier doubly-selective multihop OFDM work used variational inference with sparse GCE-BEM coefficients, Gamma hyperpriors, and alternating channel recovery, Viterbi-based data detection, and learning of noise statistics (Min et al., 2012).

4. System-level realizations

In massive MIMO, JCDE appears in both noncoherent and pilot-limited forms. The GLRT-optimal massive-MIMO algorithm treats the channel as deterministic unknown and the symbols as drawn from a general constellation, producing an exact noncoherent benchmark (Alshamary et al., 2016). Diffusion-based JCDE revisits the same uplink setting from a generative perspective, sampling jointly over channels and symbols under a learned prior and a finite-alphabet prior, with the explicit goal of reducing pilot overhead (Zilberstein et al., 2023).

In cell-free architectures, the motivation is usually pilot scarcity under large user populations. Cell-free massive MU-MIMO JED exploits channel sparsity and QAM boundedness, and the reported outcome is reliable short-packet communication with reduced pilot overhead compared with orthogonal training (Song et al., 2021). The bilinear-EP variant extends the cell-free setting toward blind or semi-blind distributed processing, emphasizing local low-complexity computations at the APs and explicit modeling of channel-data interplay (Karataev et al., 2023).

Grant-free access adds user activity as a latent variable. In massive random access, the key structural fact is that the same sparse set of active users governs both pilot and data blocks, so separate activity detection and channel estimation discard information that can be recovered by a joint posterior (Bian et al., 2021). In asynchronous mMTC, the problem expands further: continuous-valued user delays are estimated in an outer EM loop, while an AMP-based inner loop performs joint user activity detection, channel estimation, and data detection after delay calibration (Shao et al., 19 Jul 2025).

Near-field XL-MIMO changes the sparsity model itself. Because energy leaks across beams under spherical-wave propagation, the channel is not strictly sparse in the DFT beam domain; it is angle-distance sparse and beam-domain cluster-sparse. The XL-MIMO JCDE framework therefore uses a two-stage compressed-sensing initializer in the polar domain and then refines the channel through EP plus a deterministic near-field model update (Arai et al., 2024).

Doubly-selective channels motivate another branch. Multihop OFDM JCDE uses a composite multihop channel matrix and a GCE-BEM with a large oversampling factor to induce delay-Doppler sparsity, then applies variational inference without requiring known channel orders, Doppler frequencies, or noise powers (Min et al., 2012). FTN signaling over doubly-selective channels instead uses superimposed pilots and a BEM-based time-variation model; the joint extension, JCEDD, re-estimates the channel in every turbo iteration rather than treating it as fixed (Keykhosravi et al., 21 Mar 2025).

5. Learning-based and hybrid JCDE

Learning-based JCDE spans both discriminative receivers and hybrid model-driven designs. One early discriminative example is the SVM-based receiver that combines pilot-based channel estimation, data demodulation, and decoding in one joint operation. Two variants are considered: one SVM classifier for the entire codeword class and one SVM per information bit. The reported behavior is that the SVM-based receiver performs very closely to the maximum likelihood decoder, outperforms conventional blockwise receivers, and can be trained on 1-bit ADC outputs while remaining close to conventional receivers using 32-bit ADC outputs (Akın et al., 2020).

A hybrid model-based alternative is the BCJR receiver for joint symbol detection and channel decoding over ISI channels. Its trellis jointly encodes code memory and channel memory, so the BCJR recursion operates on a single joint state rather than a separated equalizer-plus-decoder stack. With perfect CSI, the joint BCJR receiver achieves a 2.3 dB gain over separate block design, and a dedicated neural network that replaces channel-model-based branch-metric computation yields a further 1.0 dB gain under CSI uncertainty (Tsai et al., 2020).

Deep neural receivers for joint MIMO detection and channel decoding also fit this line. A seven-hidden-layer DNN is trained to map received MIMO signals and channel estimates directly to information bits, and it outperforms conventional model-based linear or iterative receivers for the short-code settings studied (Wang et al., 2019). In URLLC, the trainable JCDDNet-G and JCDDNet-S architectures unfold ADMM iterations derived from Gaussian and sparse mmWave MAP formulations, respectively, and the trainable JCDD receivers outperform turbo receivers with affordable computational complexities (Sun et al., 2024).

Diffusion models represent a different hybridization strategy. Rather than classifying directly, the diffusion-based massive-MIMO method samples from an approximation to the joint posterior of channels and symbols, using a learned score model for the channel prior and an exact finite-constellation prior for the symbols. The reported outcome is lower normalized mean-squared error than competing approaches and reduced pilot overhead (Zilberstein et al., 2023).

6. Performance, tradeoffs, and research directions

Performance gains reported for JCDE are often substantial when pilot budgets are tight or the propagation model is difficult. In massive MIMO, the GLRT-optimal joint algorithm yields about 5 dB SNR gain over iterative MMSE at SER $p(\mathbf{H},\mathbf{X}\mid\mathbf{Y})$5 for $p(\mathbf{H},\mathbf{X}\mid\mathbf{Y})$6, and around 6 dB gain at SER $p(\mathbf{H},\mathbf{X}\mid\mathbf{Y})$7 for $p(\mathbf{H},\mathbf{X}\mid\mathbf{Y})$8 (Alshamary et al., 2016). In grant-free mMTC, the BiG-AMP turbo receiver supports about 40 active users at BLER $p(\mathbf{H},\mathbf{X}\mid\mathbf{Y})$9, whereas the separate design supports about 20, while a lower-complexity side-information-aided receiver reduces average execution time by roughly 66–74% compared with the turbo receiver (Bian et al., 2021). In FTN over doubly-selective channels, the SP-aided JCEDD method is the primary focus because of its superior performance, and at a higher fading rate on the order of $p(\mathbf{H},\mathbf{X},\mathbf{u}\mid\mathbf{Y})$0 the reference approaches fail to track rapid channel variations (Keykhosravi et al., 21 Mar 2025).

These results also clarify two recurring misunderstandings. First, JCDE is not equivalent to zero-pilot or purely blind processing: the literature includes blind or semi-blind bilinear EP (Karataev et al., 2023), pilot-aided MAP JCDD (Sun et al., 2024), non-orthogonal-pilot XL-MIMO JCDE (Arai et al., 2024), and superimposed-pilot FTN JCEDD (Keykhosravi et al., 21 Mar 2025). Second, joint processing is not uniformly intractable: one line attains GLRT-optimality with expected polynomial complexity in coherence time (Alshamary et al., 2016), while others use polynomial-complexity EP, AMP, FBS, ADMM, or unfolded-network approximations (Karataev et al., 2023, Song et al., 2021, Sun et al., 2024).

Several research directions recur across the literature. Distributed AP/CPU implementations are explicit in bilinear-EP for cell-free systems (Karataev et al., 2023). Multi-cell and coded grant-free extensions remain important for activity-aware JCDE (Bian et al., 2021). Wideband, OFDM, downlink, and hardware-impairment extensions are repeatedly suggested for cell-free JED, diffusion-based JCDE, and trainable JCDD (Song et al., 2021, Zilberstein et al., 2023, Sun et al., 2024). Near-field and asynchronous settings indicate that future JCDE designs must also accommodate angle-distance sparsity, beam-domain leakage, and continuous-time delay calibration rather than assuming a stationary narrowband far-field model (Arai et al., 2024, Shao et al., 19 Jul 2025).

Taken together, the field shows a clear progression: from exact but carefully structured GLRT formulations, through Bayesian message passing and variational methods, to unfolded optimization and generative priors. The central problem, however, remains unchanged: infer the channel and the transmitted information from a shared observation model in which each is informative about the other.