RB Granularity Precoding Optimization

• Resource Block granularity precoding optimization is the design of beamforming variables at the RB level to reduce fronthaul load and align with frequency-selective channel characteristics.
• It jointly optimizes RB assignment, power control, and compression—using methods like RB-WMMSE and transformer-based TVQ-VAE—to enhance system sum rate and reliability.
• The approach balances reduced signaling complexity with increased centralized processing overhead, addressing trade-offs such as latency, power consumption, and interference control.

Resource Block (RB) granularity precoding optimization denotes the design of precoding or beamforming variables at the level of an RB rather than at every subcarrier, with the optimization often coupled to RB assignment, power control, compression, or waveform shaping. In the cited literature, the topic appears in several distinct but related forms: RB-wise downlink precoding matrices computed by a centralized CPU for cell-free networks and then compressed over a bandwidth-limited fronthaul (Zhang, 5 Sep 2025); robust per-RB beamforming and assignment for multi-antenna URLLC-OFDMA in a smart factory (Cheng et al., 2021); structured sparse precoder formulations in which active frequency units are represented by nonzero precoder blocks and can be interpreted at RB/PRB granularity (Wei et al., 2023); and fixed orthogonal precoders over OFDM that target inter-user interference between adjacent RB allocations under strict bandlimiting (Said et al., 9 Jan 2025).

1. System models and problem scope

In the cell-free formulation, the system is a cell-free mobile network with a centralized CPU and distributed APs. The CPU has global CSI and computes downlink precoding matrices for the APs. Rather than optimizing and sending a separate precoder for every subcarrier, the method groups subcarriers into RBs and designs one precoder per RB, motivated by the fact that adjacent subcarriers inside an RB are correlated and that fronthaul payload is therefore reduced substantially (Zhang, 5 Sep 2025).

In the URLLC-OFDMA smart-factory setting, the system is a smart factory downlink where a central controller with $N_t$ transmit antennas serves $K$ single-antenna robots over an OFDMA frame structure with $M$ RBs and $N$ OFDM symbols; each RB corresponds to 12 subcarriers $\times$ 1 OFDM symbol. The RB-level decision variables are explicit: a binary assignment indicator $\phi_{mnk}\in\{0,1\}$ specifies whether RB $(m,n)$ is assigned to robot $k$, and a beamforming vector $\mathbf{w}_{mnk}\in\mathbb{C}^{N_t}$ is used on that RB if it is assigned (Cheng et al., 2021).

In multistage OFDM-MIMO resource programming, the frequency-domain allocation variable $\beta_{knt}$ is defined per subcarrier rather than per explicit RB. However, the same source states that, if one interprets each frequency unit as an RB/PRB rather than a single subcarrier, the same weighted group-sparsity mechanism would select RBs in time. In that reading, RB activity is revealed by whether the corresponding precoder block is zero or nonzero (Wei et al., 2023).

At the waveform level, OFDM-based 4G/5G MTC studies treat RBs as the units across which transport blocks are carried and separated in time and frequency. These works emphasize that strict band-limiting can improve separation between different resource allocations without wasting guard bands, but may also lengthen the effective impulse response and create time-domain leakage, especially when adjacent users operate at different power levels and delays are fractional rather than integer-aligned (Said et al., 9 Jan 2025).

2. Compression-aware RB-wise precoding in centralized architectures

A central line of work formulates RB-granularity precoding as a joint communication-and-compression problem. In the reviewed RB-based method, the original problem is posed as a stochastic, nonconvex program whose goal is to jointly optimize the precoder and account for the distortion introduced by later compression. A lower bound is derived, and the stochastic formulation is transformed into a deterministic RB-granularity precoding optimization problem and a separate matrix compression problem. For the deterministic problem, the stationary point lies in the column space of the corresponding RB frequency-domain channel, so the RB precoder can be written as a linear combination of subcarrier-wise channel responses inside that RB. The RB-level optimization is solved using an RB-WMMSE procedure, an iterative algorithm based on the Weighted Minimum Mean Square Error framework, adapted to RBs and frequency-dependent weights so that the global sum rate is maximized (Zhang, 5 Sep 2025).

This formulation gives RB granularity a specific operational meaning. First, lower fronthaul load is obtained because RB-level transmission greatly reduces the number of matrices that must be sent to APs compared with per-subcarrier precoding transmission. Second, better alignment with channel structure is obtained because RBs match the natural coherence of frequency-selective fading, so one optimized precoder can represent multiple correlated subcarriers. The broader lesson stated in the same source is that compression-aware precoding optimization is better than post hoc compression of unoptimized matrices.

After RB precoding is optimized, the matrices are compressed using a Transformer-based vector-quantized variational autoencoder (TVQ-VAE). The RB-wise precoding matrices are stacked as

$K$0

and encoded to a latent

$K$1

The dimensionality reduction path is described as

$K$2

With codebook $K$3, each token is quantized according to

$K$4

The codec includes a Transformer encoder to capture global dependencies across antennas and frequencies, a vector quantization bottleneck with a learned codebook, a decoder to reconstruct the precoding matrix, and an entropy model with autoregressive probability estimation plus arithmetic coding to produce near-entropy-rate bitstreams.

Rate adaptation is built into the codec through hierarchical quantization / progressive refinement. With $K$5 refinement stages,

$K$6

$K$7

The expected code length is modeled as

$K$8

and the total rate is

$K$9

The decoder reconstructs

$M$0

with matrix error measured by

$M$1

Training uses the rate–distortion objective

$M$2

with optional system-level alignment, for example a term penalizing sum-rate loss.

The same source reports two specific comparisons. Relative to the traditional RB-granularity precoding algorithm, the RB-WMMSE algorithm can improve sum rate by up to 101\%. When compression distortion is included, the proposed TVQ-VAE can improve sum rate by up to 106\% compared with traditional autoencoder-based compression without the optimization stage. At the same time, the design is presented as a bandwidth-versus-latency balance: RB granularity lowers bandwidth, learned compression reduces bandwidth further, but RB-WMMSE is iterative and nontrivial in large systems, TVQ-VAE adds Transformer self-attention complexity, entropy coding introduces serial latency, and codebook lookup and nearest-neighbor search add overhead.

3. Robust RB assignment, beamforming, and power control under URLLC constraints

In robust URLLC-OFDMA, RB-granularity precoding optimization is formulated as a joint problem of RB assignment, beamforming / precoding, and power control, with the objective of minimizing total transmit power at the central controller while guaranteeing each robot’s required number of information bits, deadline, reliability, and robustness to imperfect CSI (Cheng et al., 2021).

For robot $M$3 on RB $M$4, the received signal is

$M$5

with imperfect CSI modeled by

$M$6

The worst-case SNR is

$M$7

Using the finite-blocklength normal approximation, the worst-case received bits are

$M$8

where

$M$9

and the approximation $N$0 is used.

The original optimization problem is a mixed-integer, non-convex, robust optimization problem: $N$1 subject to

$N$2

$N$3

$N$4

A key structural simplification is obtained from the independence of each robot’s beamformer design once the RB assignment is fixed. With a slack-variable reformulation and fixed beamformer power $N$5, the optimal robust beamformer has the closed form

$N$6

and the corresponding worst-case SNR becomes

$N$7

Thus, robust beamforming reduces to maximum-ratio transmission along the estimated channel direction, and only the scalar power remains as an optimization variable. Defining

$N$8

the problem becomes an equivalent power-control problem.

The RB mapping is then treated via sparsity. Binary assignment variables are relaxed to $N$9, and for each RB the vector

$\times$0

must satisfy

$\times$1

Instead of reweighted $\times$2, the paper uses a non-convex penalty (NCP) based on

$\times$3

combined with successive convex approximation. The iterative algorithm solves the convex subproblem, updates $\times$4, updates $\times$5, and increases the penalty factor according to

$\times$6

Stopping is based on simultaneous convergence of the objective and the penalty.

The reported performance conclusions are specific. The NCP approach is superior to the well-known reweighted $\times$7 method in terms of optimized power consumption, convergence rate, and robustness to channel realizations. As packet error probability $\times$8 increases, the required power decreases monotonically. Increasing the number of transmit antennas greatly reduces transmit power, and the antenna count has the strongest impact among the tested factors. Larger channel uncertainty raises the required power, but the sensitivity to uncertainty diminishes when $\times$9 is larger. Looser latency constraints reduce power, and shortening delay can sometimes be offset by improving CSI accuracy, indicating a tradeoff between time constraint and channel knowledge quality.

4. Structural sparsity and multistage full-domain formulations

A different line of work reformulates joint time/frequency/space/power scheduling as a precoding-centric optimization problem. Its target metric is the 3GPP-style experience rate

$\phi_{mnk}\in\{0,1\}$0

where $\phi_{mnk}\in\{0,1\}$1 is the payload size of user $\phi_{mnk}\in\{0,1\}$2 and $\phi_{mnk}\in\{0,1\}$3 is the total number of time slots needed to completely deliver that payload, including both scheduled and unscheduled slots. The original optimization is a multistage MINLP with binary time-domain indicators $\phi_{mnk}\in\{0,1\}$4 and frequency-domain indicators $\phi_{mnk}\in\{0,1\}$5. The key step is to absorb the frequency allocation into a sparse precoder by defining

$\phi_{mnk}\in\{0,1\}$6

so that the effective active frequency units are determined by whether the precoder block is zero or nonzero (Wei et al., 2023).

The resulting SINR is

$\phi_{mnk}\in\{0,1\}$7

and the user-wise service-completion structure is encoded by a large stacked precoder matrix. To represent the last nonzero service slot, the operator

$\phi_{mnk}\in\{0,1\}$8

is approximated by a weighted $\phi_{mnk}\in\{0,1\}$9-norm: $(m,n)$0 with nondecreasing weights $(m,n)$1. For user $(m,n)$2,

$(m,n)$3

This yields a weighted sparse precoding objective in which experience-rate maximization becomes equivalent to minimizing the maximum weighted group-sparsity measure across users.

The nonconvex rate/SINR constraints are handled through auxiliary variables $(m,n)$4, difference-of-convex reformulation, and first-order Taylor linearization around the current iterate. The final convexified problem is a sequence of conic programs. The initialization stage solves a feasibility problem P7, which is itself a convex SOCP; if infeasible, $(m,n)$5 is increased until feasible. The iterative update then solves the convexified problem P6, updates $(m,n)$6 and $(m,n)$7, and repeats until convergence.

The reported computational message is that the method avoids exponential search over binary scheduling and assignment variables. The proposed algorithm is the FDRP algorithm (Full-Domain Resource Programming). It is said to converge in only a few iterations, typically within about 10, and each iteration solves one conic program. In simulation, the design achieves the highest experience rate among the listed baselines, shows a fairness advantage over sum-rate baselines by allocating more resources to weak-channel or large-payload users, and exhibits fast convergence. For RB-granularity interpretation, the source explicitly states that the formulation is subcarrier-level rather than explicit RB-level, but that the same machinery would naturally apply if each frequency unit were a PRB/RB instead of an individual subcarrier. This suggests a direct conceptual bridge from subcarrier-wise structural sparsity to RB-wise precoding optimization.

5. Basis-transform precoding for adjacent-RB interference control

RB-granularity precoding optimization also appears as a waveform-basis design problem. In OFDM-based 4G/5G systems, information is transmitted as a sequence of RBs, and transport blocks are carried over a fixed number of physical RBs. Under strict frequency confinement, sharp filters can provide good separation between different resource allocations without wasting guard bands, but the same operation can elongate the overall system impulse response and accentuate inter-symbol interference. In multi-user MTC-like scenarios, this is particularly problematic when adjacent users operate at different power levels, because high-power user signals can leak in time into low-power user allocations (Said et al., 9 Jan 2025).

Without precoding, OFDM modulation is written as

$(m,n)$8

Introducing an orthogonal precoder $(m,n)$9 and the effective basis $k$0 gives

$k$1

For a stream of $k$2 OFDM symbols,

$k$3

The central impairment is residual inter-user interference caused by fractional delay leakage. A channel with non-integer delay taps $k$4 and gains $k$5 acting on a strictly bandlimited waveform is represented as

$k$6

so the channel matrix is no longer banded and energy leaks across many symbol intervals. With pathwise Doppler–delay decomposition,

$k$7

where $k$8 is diagonal and $k$9 is the Toeplitz delay operator with

$\mathbf{w}_{mnk}\in\mathbb{C}^{N_t}$0

The inter-symbol/inter-block leakage transfer matrix is

$\mathbf{w}_{mnk}\in\mathbb{C}^{N_t}$1

which in the quasi-static pure-delay case reduces to

$\mathbf{w}_{mnk}\in\mathbb{C}^{N_t}$2

The paper studies the resulting ISI energy via a tail-energy metric

$\mathbf{w}_{mnk}\in\mathbb{C}^{N_t}$3

and the bound

$\mathbf{w}_{mnk}\in\mathbb{C}^{N_t}$4

A tighter upper bound is stated in terms of DPSS eigenvalues: $\mathbf{w}_{mnk}\in\mathbb{C}^{N_t}$5 The key implication stated in the source is that leakage scales with $\mathbf{w}_{mnk}\in\mathbb{C}^{N_t}$6, so sequences with $\mathbf{w}_{mnk}\in\mathbb{C}^{N_t}$7 close to 1 are well concentrated.

Three precoding cases are compared. No precoding (plain OFDM) uses

$\mathbf{w}_{mnk}\in\mathbb{C}^{N_t}$8

DFT precoding / SC-FDMA-like uses

$\mathbf{w}_{mnk}\in\mathbb{C}^{N_t}$9

DPSS precoding uses

$\beta_{knt}$0

where $\beta_{knt}$1 are DPSSs and the chosen bandwidth is $\beta_{knt}$2, giving effective basis $\beta_{knt}$3. The stated design idea is to replace the OFDM subcarrier basis with sequences that are optimally concentrated in a strict frequency interval so that, when a sharply bandlimited filter is imposed, the waveform suffers less tail growth and therefore less leakage across RB boundaries.

The reported empirical rule is that only a small fraction of edge or high-order components need to be disabled to gain large leakage reduction; specifically, turning off only about $\beta_{knt}$4 of edge waveform components can significantly reduce ISI. The simulations further indicate that, under fractional delays, SER can saturate at an error floor due to inter-user leakage; as resource utilization $\beta_{knt}$5 decreases, DPSS precoding significantly suppresses the error floor, especially when an adjacent user is $\beta_{knt}$6 dB stronger. The trade-off is explicit: perfect confinement still requires sacrificing a small number of edge modes or a small fraction of resources $\beta_{knt}$7.

6. Trade-offs, clarifications, and broader significance

Across these formulations, RB granularity is linked to different bottlenecks. In cell-free and C-RAN-like systems, it is used to reduce fronthaul overhead by transmitting one precoder per RB rather than per subcarrier, then compressing those RB-level matrices aggressively while preserving system sum-rate (Zhang, 5 Sep 2025). In URLLC-OFDMA, it is the natural granularity for enforcing deadline-driven assignment, finite-blocklength reliability, and robust power-efficient transmission (Cheng et al., 2021). In multistage sparse formulations, it becomes a latent granularity represented by zero or nonzero precoder blocks, making it possible to replace binary assignment variables with structured sparsity and a sequence of SOCPs (Wei et al., 2023). In OFDM waveform design, it is the granularity at which strict spectral separation must be balanced against time-domain leakage under fractional delays and power imbalance (Said et al., 9 Jan 2025).

Several common misunderstandings are addressed by the literature itself. One is that RB-granularity design is merely a coarse version of per-subcarrier optimization. The compression-aware cell-free formulation instead aligns the optimization granularity and the compression granularity, and this alignment is identified as the key reason the method is practical for centralized cell-free systems. A second is that RB-level optimization always requires explicit binary RB indicators. The structural-sparsity formulation shows that RB or subcarrier activity can be encoded implicitly by the sparsity pattern of the precoder matrix. A third is that strict frequency confinement automatically guarantees clean RB separation. The OFDM leakage analysis shows the opposite under fractional delays: the channel matrix is no longer banded, and neighboring symbols or RBs can interfere even with prefixing.

The principal trade-off is consistent across the surveyed directions. RB-level aggregation can reduce signaling or scheduling complexity, and learned or structured processing can further improve fronthaul efficiency, power efficiency, or temporal completion behavior. The cost is additional centralized processing: iterative RB-WMMSE, Transformer self-attention, entropy coding, nearest-neighbor search, successive convex approximation, or conic programming. This suggests that RB-granularity precoding optimization is best understood not as a single algorithmic template but as a family of designs in which the chosen frequency granularity is matched to the dominant system constraint—fronthaul budget, finite-blocklength reliability, multistage completion time, or adjacent-allocation leakage—and the precoder is optimized together with the mechanism that most strongly limits system performance.