Symbol-Level Multiuser MISO Precoding for Multi-level Adaptive Modulation

I. INTRODUCTION

• Symbol-level precoding designs the transmitted signal using both channels and user symbols, manipulating multiuser interference constructively at the cost of greater transmitter complexity.The signal must be recalculated and switched on a symbol rather than codeword basis.Source: §I · p. 2
• The paper extends the connection between symbol-level precoding and PHY-layer multicasting with phase constraints to generic multi-level modulations.Earlier multicast-based symbol-level precoding was developed for MPSK.Source: §I · pp. 3–4
• The proposed algorithm minimizes power under per-user SINR or goodput constraints while adapting modulation in a multi-level system.The stated extension covers generic multi-level modulations, including MQAM.Source: §I · pp. 3–4

II. SYSTEM AND SIGNAL MODELS

• The model assumes quasi-static channels known at the base station through CSI feedback and fixed over each frame.The frame contains a common pilot-and-signaling preamble followed by useful payload symbols.Source: §II · pp. 4–5
• The system model selects each user’s modulation from its requested rate and SINR thresholds, holds it for a frame, and precodes useful symbols individually.Users receive their modulation selection in the frame preamble.Source: §II · pp. 4, 6

A. Power constraints for user-level and symbol-level precodings

• Symbol-level precoding enforces the power constraint for each symbol-vector transmission, unlike user-level precoding’s coherence-time average constraint.For user-level precoding, the text expresses the average using the fixed precoding matrix and uncorrelated symbols over the coherence time.Source: A. Power constraints for user-level… · p. 7

III. CONSTRUCTIVE INTERFERENCE DEFINITION

• Interference can help outer and outermost multi-level symbols move deeper into their detection regions, while its constructive contribution is limited for inner symbols.The precoding strategy uses the detection regions of the adopted modulation rather than treating all interference as harmful.Source: §III · pp. 7–8

A. PHY-layer Multicasting Preliminaries

• PHY-layer multicasting power minimization imposes SINR targets for each user and can be solved using semidefinite relaxation.The SINR targets are represented by the vector ζ.Source: A. PHY-layer Multicasting Preliminaries · p. 8

B. Symbol-level Precoding Through Multicasting

• The constraints are tailored to ensure each user receives its symbol with correct amplitude and phase, with the desired amplitude combining long-term SINR and short-term symbol-amplitude factors.The text assumes the symbol set has unit average power.Source: B. Symbol-level Precoding Through… · p. 10
• Theorem 1 establishes that symbol-level power minimization under SINR constraints is equivalent to PHY-layer multicasting over an effective channel with phase constraints.The formulation absorbs each symbol phase into the user channel and designs the transmitted signal directly rather than as a precoding matrix times the symbol vector.Source: B. Symbol-level Precoding Through… · pp. 10–11
• The equivalent channel combines the fixed channel with current input symbols, so it changes with the symbol index and can be modeled as random fast fading.The symbol-level formulation constrains both signal amplitude and phase, unlike conventional multicasting’s power-domain constraints.Source: B. Symbol-level Precoding Through… · pp. 11–12

C. Constructive Interference Power Minimization (CIPM) for Multi-level Modulation

• The generic formulation minimizes transmit power under symbol-level SINR constraints, using modulation-specific constraints to construct the equivalent channel and calculate the transmit signal.The text identifies this problem’s connection to directional modulation.Source: C. Constructive Interference Power… · pp. 12–13
• Theorem 2 gives the Lagrangian for the power-minimization problem, and its solution is found by solving the equations obtained from its derivatives.The derivatives are taken with respect to the transmit vector and the constraint multipliers.Source: C. Constructive Interference Power… · pp. 12–13

V. SYMBOL-LEVEL PRECODING WITH MULTI-LEVEL MODULATION

• Symbol-level constraints C1 and C2 are specialized to the detection regions of each modulation and constellation point, with the same rationale applicable to other modulation types.The section presents typical practical modulations as examples.Source: §V · p. 13

A. MQAM

• For MQAM, inner symbols must be received at the exact constellation point, while outer and outermost symbols need only remain in their correct detection regions.The 16-QAM figure labels these classes as inner (1), outer (2), and outermost (3).Source: A. MQAM · pp. 14–15, Figure 3 · p. 14
• The MQAM constraints C1 and C2 can be defined by applying the same rationale to any MQAM constellation.Source: A. MQAM · pp. 13, 15
• Outermost points have more flexible detection regions, but this flexibility is expected to matter less at higher constellation orders, where multicast characterization supplies most performance gain.For outermost symbols, the in-phase and quadrature constraints are inequalities.Source: A. MQAM · p. 15

• The equivalent-channel distribution is derived from the symbol-power and phase PMFs together with the channel-power distribution.The passages describe the symbol phases and amplitudes and formulate the equivalent-channel PDF for generic channels.Source: §VI · pp. 15–16
• For Rayleigh fading, channel power follows a Gamma distribution, which is used to express the equivalent-channel power distribution.Source: §VI · p. 16
• The simulated and derived PDFs for the equivalent channel (27) match, while Fig. 5 compares actual and equivalent channel power distributions.The passage reports the match for Fig. 4 and identifies Fig. 5 as showing the power-distribution difference.Source: §VI · p. 17
• Equivalent-channel construction preserves channel-phase uniformity and induces no inter-user channel correlation; users with identical channel distributions and modulation have identical equivalent-channel distributions.Source: §VI · p. 17

• Prior power-minimization work commonly used SINR constraints because Gaussian coding gives a direct connection between SINR and throughput rate.Source: §VII · p. 17
• Under adaptive multi-level symbol-level precoding, effective throughput or goodput depends on both the assigned modulation and achieved SINR, so the conventional average-SINR-to-rate connection does not hold.The modulation sets the upper bound on supported rate, while achieved SINR determines the operating point on the SER curve.Source: §VII · pp. 17–18
• The objective is to minimize total consumed power across all symbol vectors in a frame, subject to goodput constraints for each user.The formulation builds on symbol-level power minimization and goodput targets.Source: §VII · p. 18

A. Power Minimization with Goodput Constraints

• With modulation known, power minimization is formulated per symbol vector, and the received-power constraint is stricter because it applies per symbol rather than on average.Source: A. Power Minimization with Goodput… · pp. 18–19
• The algorithm selects the lowest modulation that can achieve each user’s target goodput.Source: A. Power Minimization with Goodput… · p. 19
• After fixing modulation, the algorithm converts each goodput target to a required SER and then to an average SINR using the analytical SER–SINR relationship.For MQAM, required SINR is expressed as a function of SER.Source: A. Power Minimization with Goodput… · p. 19

VIII. NUMERICAL RESULTS

• CIPM outperforms optimal user-level beamforming in average transmit power at every target SINR; PHY-layer multicasting provides a theoretical lower bound.The comparison uses power minimization under SINR constraints.Source: ACRONYMS, AND THEIR RELATED EQUATIONS… · p. 21

ACRONYMS, AND THEIR RELATED EQUATIONS AND ALGORITHMS

• 2.5-3.2 dB power savings over OB persist at 16/32/64-QAM, while the 32-to-64-QAM transmit-power gap is 0.1 dB.The paper says savings decrease with modulation order, especially from 16-QAM to 32-QAM.Source: ACRONYMS, AND THEIR RELATED EQUATIONS… · pp. 21–22
• CIPM outperforms OB in energy efficiency at all target SINR values, with the metric accounting for both goodput and power consumption.Source: ACRONYMS, AND THEIR RELATED EQUATIONS… · p. 22
• As system size grows, CIPM's average transmit power decreases while OB's increases, attributed to constructive interference exploitation and a greater chance of outer-constellation symbols.The paper contrasts this with OB sending more interfering streams as system size increases, which leads to poor energy efficiency.Source: ACRONYMS, AND THEIR RELATED EQUATIONS… · pp. 22–23
• Transmit power rises with user count for both CIPM and OB, but CIPM's advantage grows and is greatest at full loading, K = Nt.At low user counts relative to antenna count, users are almost orthogonal and the methods perform closely.Source: ACRONYMS, AND THEIR RELATED EQUATIONS… · p. 23
• For the 2 × 2 QPSK example, OB's average frame transmit power is 2.2 dB higher than CIPM's, with symbol-combination differences ranging from 0.4 dB to 4.1 dB.The maximum difference occurs at combinations 3 and 14.Source: ACRONYMS, AND THEIR RELATED EQUATIONS… · p. 23

RELAXED APPROACH (INEQUALITY CONSTRAINT) FROM TRANSMIT POWER PERSPECTIVE

• With relaxed inequality constraints, transmit power increases with modulation order because higher-order modulation requires higher target SINR.The corresponding energy efficiency also decreases with modulation order; the gains from inequalities diminish as detection regions become more restricted.Source: RELAXED APPROACH (INEQUALITY… · p. 24

A. Complexity

• The number of possible precoding calculations depends on user count, each user's modulation order, and frame length N.Source: A. Complexity · p. 25
• For small systems, precoding vectors can be computed in advance for all symbol combinations and stored in a lookup table; for larger systems, optimization can be solved per combination.Each symbol combination is calculated once and stored to avoid recalculating the same values.Source: A. Complexity · pp. 25–26
• OB has lower overall runtime than CIPM, but a single CIPM optimization becomes less complex than OB as system size increases.Symbol-level runtime depends on the modulation combinations and number of users; the authors note that cloud RAN can absorb computational complexity.Source: A. Complexity · p. 25

IX. CONCLUSIONS

• In the 2 × 2 scenario, symbol-level precoding reduces transmit power by 2.2 dB versus conventional user-level precoding, and the gain increases with system size.The paper connects the approach to PHY-layer multicasting with phase constraints for generic modulation.Source: §IX · p. 26

Symbol Level Precoding

• Figure 15 presents a detailed block diagram of symbol-level precoding.Source: Figure 15 · p. 39