Optimal Power Allocation and AI Receiver Design for Superimposed DMRS and Data Transmission

Sha Hu; Zhongwang Fu

cs.ITAug 13, 2026

Optimal Power Allocation and AI Receiver Design for Superimposed DMRS and Data Transmission

Authors: Sha Hu, Zhongwang Fu

Organizations: Nyquist Research Center, Huawei Technologies Sweden AB, Sweden

Abstract

In this paper, we consider transmissions with superimposed (SI) demodulation-reference-symbol (DMRS) and data in orthogonal frequency-division multiplexing (OFDM) based multiple-input multiple-output (MIMO) systems. First, we derive an analytical framework to characterize the iterative behavior between the mean-square errors (MSEs) of channel estimation (CE) and MIMO detection (MD) within an iterative CE and detection (ICED) process. This framework is subsequently utilized to optimize power allocation and pilot patterns between the DMRS and data symbols for SI-DMRS transmission. Second, we design an artificial intelligence (AI) based receiver built upon Transformer encoders for SI-DMRS transmissions, which incorporates an iterative CE and detection (ICED) structure. Simulation results demonstrate that the proposed AI-ICED receiver, combined with SI-DMRS, effectively increases spectral efficiency (SE) compared to conventional systems using non-overlapped DMRS and data symbols.

Figures & tables

Fig. 1: Example patterns of DMRS and data transmission in standard 5G-NR (top) versus with SI-DMRS (bottom). The bandwidth is 2 physical resource block (2PRB) with $N_{\text{sc}}\!=\!24$ , and two OFDM symbols are used for control channel such that $N_{\text{sym}}\!=\!12$ for the SI-DMRS case. In both cases, the transmit power per RE is normalized to unity. Under the SI-DMRS scheme, superimposing additional DMRS symbols onto data introduces no pilot overhead, however, because total transmit power is split between the DMRS and data components, both CE and MD become more challenging

Fig. 2: The equilibrium state of CE-MSE and MD-MSE based on Property 1 with ( $a\!=\!1$ , $\gamma\!=\!2$ , $N_{\text{t}}\!=\!4$ , $N\!=\!264$ , $M\!=\!24$ ).

Fig. 3: The effective MD-MSE based on MIESM mapping of $p$ and $t$ with ( $a\!=\!1$ , $\gamma\!=\!2$ , $N_{\text{t}}\!=\!4$ , $N\!=\!264$ , $M\!=\!24$ ) and $\sigma^{2}\!=\!-15$ dB.

Fig. 4: 2D contour of effective MD-MSE for joint power allocations over $(a,b)$ with ( $\gamma\!=\!2$ , $N_{\text{t}}\!=\!4$ , $N\!=\!264$ , $M\!=\!24$ ) and $\sigma^{2}\!=\!-15$ dB.

Fig. 5: The minimal effective MIESM with different configurations of $M$ , i.e., for superimposing more DMRS with data. The gains are limited even under the idea assumption that the de-nosing gain of CE linearly increases in the number of DMRS.

Fig. 6: The structure of the MIMO-OFDM system and the proposed AI-ICED receiver, along with details regarding the NN construction and configurations provided in Appendix F through I and Table III.

Fig. 7: The VWN-TPA-MoE architecture enhanced Transformer encoder design.

Fig. 8: CE-MSE over iteration stages for $4\!\times\!4$ MIMO and 16QAM modulation.

Fig. 9: BLER performance with the same configurations in Fig. 8.

Fig. 10: CE-MSE under $2\!\times\!2$ MIMO and 16-QAM across a wide SNR range.

Fig. 11: Throughput envelopes under the $2\!\times\!2$ and 16-QAM modulation.

Fig. 12: Throughput envelopes under the $4\!\times\!4$ and 16-QAM modulation.

Operation	Dense Transformer block	Proposed backbone
Latent memory width	$d_{\mathrm{model}}$	$d_{\mathrm{virtual}}=(n/m)d_{\mathrm{model}}$
Q/K/V projections	$\mathcal{O}(Ld_{\mathrm{model}}^{2})$	$\mathcal{O}\!\left(Ld_{\mathrm{model}}(r_{q}+2r)\right)$
FFN computation	$\mathcal{O}(Ld_{\mathrm{model}}d_{\mathrm{ff}})$	$\mathcal{O}(Ld_{\mathrm{model}}d_{\mathrm{ff}})$
Attention score	$\mathcal{O}(L^{2}d_{\mathrm{model}})$	$\mathcal{O}(L^{2}d_{\mathrm{model}})$

TABLE I: Dominant inference complexity per stage.

Symbol	Description	Value
$N_{\mathrm{r}}\times N_{\mathrm{t}}$	MIMO size	$2\times 2$ , $4\times 4$
$\mathcal{A}$	Modulation scheme	16QAM, 64QAM
$N_{\mathrm{sym}}$	Number of OFDM symbols carrying data	$12$
$N_{\mathrm{sc}}$	Active subcarriers	$24$
$N$	Number of REs carrying only data	$240$
$M$	Number of REs carrying both SI-DMRS and data	$48$

TABLE II: System parameters.

Modulation	$a_{1}$	$b_{1}$	$a_{2}$	$b_{2}$	$a_{3}$	$b_{3}$
QPSK	0.9810	1.0420	0.0190	4.2500	0.0000	0.0000
16-QAM	0.6053	0.2845	0.3541	1.2562	0.0406	5.3784
64-QAM	0.4076	0.0717	0.3951	0.3556	0.1973	1.8315

TABLE III: Three-term exponential MI mapping parameters.

Symbol	Description	Value
Transformer Backbone
$d_{\text{model}}$	Latent dimension	$512$
$N_{\text{head}}$	Number of attention heads	$8$
$m/n$	VWN memory / compute slots	$2/3$
$d_{\text{virtual}}$	Virtual memory width $(n/m)\cdot d_{\text{model}}$	$768$
$r_{q}/r$	TPA query rank / key-value rank	$16/16$

TABLE IV: Hyperparameter Configuration of the Proposed AI-ICED Receiver

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