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Efficient Transmit Waveform Design for MIMO-OFDM DFRC Systems with 1-Bit DACS
Chenfei Huang, Mingjie Shao, Ya-Feng Liu
TL;DR
Efficient MIMO-OFDM DFRC waveform design with 1-bit DACs remains underexplored, despite the large discrete optimization across subcarriers. The paper formulates an angular-FIM objective with CI-based communication constraints and develops an alternating time- and frequency-domain ADMM method. Simulations report improved convergence and DFRC performance over a beampattern-based benchmark.
Problem
Efficient MIMO-OFDM DFRC waveform design with 1-bit DACs remains underexplored, and optimizing transmit symbols across subcarriers creates a large-scale discrete problem.
Source: §1 · p. 1Method
An inexact ADMM alternates time- and frequency-domain updates to maximize target angular FIM trace subject to CI-based SEP constraints and a time-domain 1-bit transmit alphabet.
Source: §1 · p. 1Results
The proposed method shows improved convergence behavior and DFRC performance compared with the beampattern-based benchmark.
Source: §1 · p. 1Takeaways & Limitations
Retaining CI constraints in both domain subproblems is intended to promote feasible intermediate iterates and improve ADMM convergence.
Source: §1 · p. 1The design uses target parameter estimates, obtainable from an initial sensing or estimation stage or predicted from previous observations in tracking scenarios.
Source: §2.2 · p. 2
Abstract
from arXiv · showhide
This paper studies efficient waveform design for MIMO-OFDM dual-functional radar-communication (DFRC) systems with 1-bit digital-to-analog converters (DACs), which remains underexplored in the literature. We formulate the DFRC waveform design problem by maximizing the trace of the target angular Fisher information matrix (FIM), subject to symbol-error probability constraints realized via constructive interference (CI) and a time-domain 1-bit transmit alphabet constraint. The resulting problem is a large-scale nonlinear integer programming problem. We develop an inexact alternating direction method of multipliers (ADMM) algorithm with alternating time- and frequency-domain updates. The proposed scheme enables subcarrier-wise optimization in the frequency domain and closed-form primal and dual updates in the time domain. In particular, the CI constraints are deliberately retained in both the time- and frequency-domain subproblems to promote the feasibility of intermediate iterates and improve the convergence behavior of ADMM. Simulation results demonstrate promising DFRC performance.
1. INTRODUCTION
MIMO-OFDM offers spatial and frequency-domain flexibility for DFRC, while growing antenna counts raise hardware complexity and power consumption. Efficient waveform design with 1-bit DACs remains underexplored because optimizing symbols across subcarriers creates a large discrete problem.
Motivation
- MIMO-OFDM combines MIMO spatial degrees of freedom with flexible frequency-domain design for communication and range-Doppler sensing.Prior MIMO-DFRC work has balanced communication and sensing through waveform or beamformer design, and MIMO-OFDM studies have considered joint transmit and receive designs.Source: §1 · p. 1
- Increasing antenna counts raise MIMO-DFRC hardware complexity and power consumption.Low-resolution DACs, particularly 1-bit DACs, offer a power-efficient solution in massive MIMO communications and have attracted attention in DFRC [18].Source: §1 · p. 1
Research gap
- Waveform design with 1-bit DACs in MIMO-OFDM DFRC remains underexplored, while joint optimization across subcarriers creates a large-scale discrete problem.This paper focuses on that design setting.Source: §1 · p. 1
Contribution
- The proposed inexact ADMM maximizes target angular FIM trace subject to CI-based SEP constraints and a time-domain 1-bit alphabet, alternating time- and frequency-domain updates.Subcarrier-wise frequency-domain optimization and closed-form time-domain primal and dual updates support efficient implementation; retaining CI constraints in both subproblems is intended to promote feasible intermediate iterates and improve convergence. Simulations report improved convergence and DFRC performance over the beampattern-based benchmark.Source: §1 · p. 1
2. SYSTEM MODEL AND PROBLEM FORMULATION
The section models a MIMO-OFDM DFRC link with 1-bit transmission, communication constraints expressed through constructive interference, and target-angle sensing measured by angular FIM trace. It then formulates a constrained waveform problem whose frequency- and time-domain variables are coupled by the DFT relation.
System model
- The system has a multi-antenna base station serving single-antenna users and far-field targets, with a 1-bit DAC pair per transmit antenna and OFDM frequency- and time-domain signals related by an IDFT.Each transmit frame spans OFDM symbols and subcarriers; the time-domain transmit samples obey a finite alphabet imposed by the 1-bit DACs.Source: §2 · p. 1, §2.1 · pp. 1–2
2.1. Communication Model and Design Metric
- For PSK communication symbols, symbol-level constructive interference pushes noiseless received signals into their decision regions, with constraints providing a sufficient condition for per-user, per-subcarrier SEP no greater than ε_c.The frequency-domain CI constraints can also be expressed in the time domain.Source: §2.1 · p. 2
2.2. Sensing Model and Design Metric
- The sensing model uses the received radar echo and target reflection, angle, delay, and Doppler parameters to form the Fisher information matrix blocks.Target parameter estimates may come from an initial sensing or estimation stage or be predicted from previous observations in target-tracking scenarios.Source: §2.2 · p. 2
- The sensing objective maximizes angular FIM trace, equivalent to minimizing a tractable lower bound on the CRB; its quadratic-form matrix depends on target angles and reflection powers, not delays, Dopplers, or reflection phases.The matrix is constructed using estimates of target angles and reflection powers.Source: §2.2 · p. 2
2.3. Problem Formulation
- The waveform problem maximizes the sensing metric subject to CI constraints and the time-domain 1-bit transmit-signal constraint.Source: §2.3 · p. 2
- The problem separates into independent subproblems across OFDM symbols.Each per-symbol formulation retains the DFT relation between frequency- and time-domain variables.Source: §2.3 · p. 3
- Within each subproblem, the objective and CI constraints separate across frequency-domain subcarriers, while the 1-bit constraint applies elementwise to time-domain samples and the DFT relation couples the domains.Source: §2.3 · p. 3
3. ALGORITHMIC DESIGN
The inexact ADMM alternates frequency- and time-domain updates while enforcing consistency through the DFT relation; retaining time-domain CI constraints promotes feasible intermediate iterates. [p06, p12]
3. ALGORITHMIC DESIGN
- Retaining CI constraints in the time-domain subproblem promotes feasibility of intermediate iterates, alongside the frequency-domain CI constraints.The authors compare this design with conventional ADMM that imposes CI constraints only in the frequency domain.Source: §3 · p. 3
3.1. Time-Domain Update for xT
- The time-domain update dualizes CI constraints and uses projected subgradient ascent, with an entrywise minimizer over the 1-bit alphabet for each fixed multiplier.The dual ascent is inexact and limited to at most Iℓ inner iterations before recovering the time-domain update.Source: §3.1 · p. 3
3.2. Frequency-Domain Update for xF
- The frequency-domain update separates into Ns independent Nt-dimensional quadratic programs, solved inexactly by accelerated projected gradient on the dual problems.Choosing ρ(ℓ) > ζmax(Q) makes the corresponding problem strictly convex.Source: §3.2 · p. 3
3.3. Implementation and Complexity Analysis
- The ADMM penalty parameter is updated adaptively, with ρmax > 2ζmax(Q) prescribed.The implementation monitors the primal residual and time-domain CI constraint violation; per-iteration complexity is O(IℓNsNt (log Ns + K) + √κℓNsK2 log(1/ϵℓ) + NsNtK(Nt + K)).Source: §3.3 · p. 4
4. NUMERICAL RESULTS
Across the tested settings, the proposed ADMM converges faster with smaller CI violations than its variant without time-domain CI, and its sensing–communication tradeoff outperforms Beampattern-MSE while approaching the unquantized benchmark.
4. NUMERICAL RESULTS
- Simulations use 8 transmit and receive antennas, 10 OFDM symbols, 32 subcarriers, 2 users, and 3 targets.The system uses QPSK with an SEP requirement of 1×10^-4.Source: §4 · p. 4
4.1. Convergence Behavior
- The proposed ADMM converges rapidly, while the variant without time-domain CI converges more slowly and has larger CI violations.Convergence is evaluated using the primal residual and time-domain CI constraint violation.Source: Figure 1 · p. 4, §4.1 · p. 4
4.2. Sensing–Communication Performance
- Across achieved SERs, the proposed design outperforms Beampattern-MSE and closely approaches the unquantized benchmark.Results average 100 independent system realizations.Source: Figure 2 · p. 4, §4.2 · p. 4