The paradigm of full-duplex communication holds immense promise for the next generation of wireless networks, offering the potential to double spectral efficiency compared to conventional half-duplex systems. This potential is particularly transformative for UAV drones, which are increasingly deployed as agile aerial relays, rapidly deployable base stations, and providers of secure communication links in challenging or dynamic environments. The ability of a single UAV drone to transmit and receive simultaneously on the same frequency band could dramatically enhance mission capabilities, from real-time high-bandwidth data relay to efficient spectrum utilization in dense networks. However, the fundamental obstacle in realizing this potential is self-interference (SI)—the powerful signal from a node’s own transmitter that overwhelms the desired weak signal from a remote node at its collocated receiver.
My investigation focuses on overcoming this critical challenge for compact, resource-constrained UAV drone platforms. Passive suppression techniques, such as antenna isolation and cross-polarization, and analog-domain active cancellation provide initial mitigation, typically leaving a residual SI power that is still 20-45 dB above the noise floor. The final and most crucial line of defense is digital-domain cancellation, which aims to suppress this residual SI to the noise level. Traditional digital SI cancellation (SIC) methods often rely on pilots to estimate the SI channel. While effective, these methods face limitations: their performance is inherently bounded by pilot estimation accuracy and can degrade when the desired signal’s power is significant, as the desired signal acts as noise during the SI channel estimation phase. Furthermore, many iterative SIC schemes that leverage decoded desired signal information introduce significant hardware overhead and processing delay due to separate channel estimation and equalization stages in each iteration.
In this work, I propose a novel, integrated algorithm that fundamentally rethinks the digital SIC architecture for full-duplex UAV drone transceivers. The core of my approach is a multistage, iterative algorithm that performs self-interference cancellation and channel equalization in a unified process. By deriving the optimal minimum mean square error (MMSE) symbol estimator for the desired signal in the presence of both SI and intersymbol interference (ISI), I develop a structure where cancellation and equalization are intrinsically combined. This integrated multistage algorithm offers superior performance, faster convergence, and reduced implementation complexity, making it exceptionally suitable for the demanding size, weight, and power (SWaP) constraints of advanced UAV drone communication systems.
System and Signal Model for Full-Duplex UAV Drones
I consider a point-to-point communication link between two identical full-duplex UAV drone nodes. Due to the stringent SWaP requirements of UAV drones, a single-antenna architecture using a circulator or isolator is assumed for each node. Both nodes transmit and receive on the same carrier frequency simultaneously. The analysis is presented from the perspective of one node (Node 1), as the system is symmetric.
The complex baseband received signal at Node 1, $r(t)$, can be expressed as the superposition of the self-interference signal, the desired signal from Node 2, and additive noise:
$$
r(t) = x(t) \ast c_I(t) + y(t) \ast c_D(t) + z(t)
$$
Here, $x(t)$ is the transmitted signal from Node 1’s power amplifier (PA), $y(t)$ is the signal transmitted from Node 2, $z(t)$ is complex additive white Gaussian noise (AWGN) with power $N_0$, and $\ast$ denotes convolution. The channels $c_I(t)$ and $c_D(t)$ represent the impulse responses of the SI channel (encompassing the circulator leakage and the wireless reflection path) and the desired signal channel, respectively. The signal $x(t)$ is constructed from the sequence of SI symbols $\{s_{I,k}\}$ drawn from a modulation alphabet $\mathcal{A}$ (e.g., QPSK, 16QAM, 64QAM), pulse-shaped by $g(t)$, and distorted by the transmitter chain response $c_0(t)$: $x(t) = \sum_{k} s_{I,k} [g(t-kT) \ast c_0(t)]$.
A critical component for active cancellation is the feedback path. A coupled version of the PA output, denoted $x_{ref}(t)$, is provided to the receiver. This signal captures the actual transmitted waveform, including PA nonlinearities, and is modeled as:
$$
x_{ref}(t) = \sum_{k} s_{I,k} h_0(t-kT) + z_{ref}(t)
$$
where $h_0(t) = g(t) \ast c_0(t)$, and $z_{ref}(t)$ is AWGN with power $N_1$, independent of $z(t)$.
To derive a discrete-time model suitable for algorithm development, I employ a series representation. Let $\{\phi_p(t)\}$ be a complete set of orthonormal basis functions. Projecting the received signal onto this basis yields the receive vector $\mathbf{r} = [r_1, r_2, …, r_N]^T$, where $r_p = \langle r(t), \phi_p(t) \rangle$. Similarly, I define vectors for the channel responses: $\mathbf{h}_{I,k}$ and $\mathbf{h}_{D,q}$, corresponding to the projections of $h_I(t-kT)$ and $h_D(t-qT)$, respectively. The noise vector $\mathbf{z}$ has i.i.d. $\mathcal{CN}(0, N_0)$ elements. The discrete vector model is then:
$$
\mathbf{r} = \sum_{k} s_{I,k} \mathbf{h}_{I,k} + \sum_{q} s_{D,q} \mathbf{h}_{D,q} + \mathbf{z}
$$
The feedback signal has a corresponding discrete model: $\mathbf{x}_{ref} = \sum_{k} s_{I,k} \mathbf{h}_{0,k} + \mathbf{z}_{ref}$. The goal of the digital SIC module is to process $\mathbf{r}$ and $\mathbf{x}_{ref}$ to produce reliable estimates of the desired symbols $\{s_{D,n}\}$.
MMSE Symbol Estimation for Integrated Cancellation and Equalization
The cornerstone of my proposed integrated algorithm is the derivation of the optimal MMSE estimator for a desired symbol in the presence of both SI and ISI. This derivation moves beyond traditional separate estimation of the SI and desired channels.
Assume the effective discrete-time channels for SI and the desired signal have lengths $M$ and $L$, respectively. The received sample relevant for estimating symbol $s_{D,0}$ is influenced by the set of interfering symbols: $\mathcal{S}_I = \{s_{I,0}, …, s_{I,M-1}\}$ and $\mathcal{S}_D = \{s_{D,1}, …, s_{D,L-1}\}$. The conditional MMSE estimate is given by:
$$
\hat{s}_{D,0} = E[s_{D,0} | \mathbf{r}] = \sum_{s \in \mathcal{A}} s P(s_{D,0}=s | \mathbf{r})
$$
For QPSK modulation (symbols in $\mathcal{A} = \{\pm 1/\sqrt{2} \pm j/\sqrt{2}\}$), after averaging over the interfering symbol sets and applying Bayes’ rule, the estimator simplifies to a remarkably compact nonlinear function of a linear combination of the input. Specifically, I define the cleaned signal $\tilde{\mathbf{r}} = \mathbf{r} – \sum_{k} s_{I,k} \mathbf{h}_{I,k} – \sum_{q \neq 0} s_{D,q} \mathbf{h}_{D,q}$. The MMSE estimate can be shown to be:
$$
\tilde{s}_{D,0}^{QPSK} = \frac{1}{\sqrt{2}} \tanh\left( \frac{1}{\sqrt{2}N_0} \mathbf{h}_{D,0}^H \tilde{\mathbf{r}} \right)
$$
where $\tanh(\cdot)$ is the hyperbolic tangent function applied component-wise to complex numbers as $\tanh(a+jb) = \tanh(a) + j\tanh(b)$.
Following a similar process, I derive the MMSE estimators for higher-order modulations crucial for high-throughput UAV drone links. For 16QAM (normalized symbols $\in \{\pm 1/\sqrt{10}, \pm 3/\sqrt{10}\}$ for both I and Q components):
$$
\tilde{s}_{D,0}^{16QAM} = \frac{ -3 + 3e^{ \frac{3\sqrt{2}}{5N_0} \mathbf{h}_{D,0}^H \tilde{\mathbf{r}} } + e^{ \frac{2(1+\sqrt{10}\mathbf{h}_{D,0}^H \tilde{\mathbf{r}})}{5N_0} } – e^{ \frac{2+\sqrt{10}\mathbf{h}_{D,0}^H \tilde{\mathbf{r}}}{5N_0} } }{\sqrt{10} \left( 1 + e^{ \frac{3\sqrt{2}}{5N_0} \mathbf{h}_{D,0}^H \tilde{\mathbf{r}} } + e^{ \frac{2(1+\sqrt{10}\mathbf{h}_{D,0}^H \tilde{\mathbf{r}})}{5N_0} } + e^{ \frac{2+\sqrt{10}\mathbf{h}_{D,0}^H \tilde{\mathbf{r}}}{5N_0} } \right)}
$$
For 64QAM (normalized symbols $\in \{\pm 1/\sqrt{42}, \pm 3/\sqrt{42}, \pm 5/\sqrt{42}, \pm 7/\sqrt{42}\}$):
$$
\tilde{s}_{D,0}^{64QAM} = \frac{ \sum_{k=-3}^{3} (2k+1) e^{ \frac{ k( \sqrt{42} \mathbf{h}_{D,0}^H \tilde{\mathbf{r}} + (k+4))}{21N_0} } }{\sqrt{42} \sum_{k=-3}^{3} e^{ \frac{ k( \sqrt{42} \mathbf{h}_{D,0}^H \tilde{\mathbf{r}} + (k+4))}{21N_0} } }
$$
The common structure emerging from these derivations is key. Each estimate $\tilde{s}_{D,n}$ can be expressed as $\tilde{s}_{D,n} = \mathcal{F}(\bar{s}_{D,n})$, where $\mathcal{F}$ is a modulation-specific nonlinear function (tanh for QPSK, the rational expressions above for 16/64QAM), and $\bar{s}_{D,n}$ is the output of a linear filter:
$$
\bar{s}_{D,n} = r[n] – \sum_{k=0}^{M-1} w_{I,k}^* u_I[n-k] – \sum_{q=1}^{L-1} w_{D,q}^* u_D[n-q]
$$
Here, $r[n]$ is the sampled output of a filter matched to the desired signal’s receive pulse shape, $u_I[n]$ is the processed feedback signal (SI reference), and $u_D[n]$ are past estimates of the desired symbols. The coefficients $\mathbf{w}_I$ and $\mathbf{w}_D$ jointly perform SI cancellation and ISI equalization. This structure is the genesis of the integrated multistage algorithm.
The Proposed Multistage Integrated Algorithm
The MMSE estimator derived above is non-causal and requires knowledge of the true channels and symbols. To create a practical algorithm for real-time operation on UAV drone hardware, I make it causal and adaptive through a multistage iterative approach.
In the $i$-th iteration stage ($i=0,1,2,…$), the estimate for the desired symbol at time $n$, $\tilde{s}_{D,n}^{(i)}$, is generated. The input $u_D^{(i)}[n]$ uses the symbol decisions or soft estimates from the *previous* iteration $(i-1)$. For the initial stage ($i=0$), $u_D^{(0)}[n]$ is set to zero, effectively reducing the algorithm to a standard linear adaptive filter that suppresses SI while treating the desired signal as noise. The adaptive filter coefficients $\mathbf{w}^{(i)}[n] = [\mathbf{w}_I^{(i)}[n]^T, \mathbf{w}_D^{(i)}[n]^T]^T$ are updated dynamically.
Let $\mathbf{u}^{(i)}[n] = [\mathbf{u}_I[n]^T, \mathbf{u}_D^{(i)}[n]^T]^T$ be the concatenated input vector. The algorithm for stage $i$ at time $n$ proceeds as follows:
- Linear Filtering: Compute the filter output.
$$ \bar{s}_{D,n}^{(i)} = \mathbf{w}^{(i)H}[n-1] \mathbf{u}^{(i)}[n] $$ - Nonlinear Estimation: Apply the modulation-specific MMSE function.
$$ \tilde{s}_{D,n}^{(i)} = \mathcal{F}^{(i)}(\bar{s}_{D,n}^{(i)}) $$
For $i=0$, a simple slicer (hard decision) may be used for $\mathcal{F}^{(0)}$ to bootstrap the process. For $i \geq 1$, the soft MMSE functions are used. - Error Calculation & Coefficient Update: The error signal for adapting the filter is based on a hard decision from the previous stage’s soft output to ensure stable convergence.
$$ e^{(i)}[n] = \text{sign}(\tilde{s}_{D,n}^{(i-1)}) – \bar{s}_{D,n}^{(i)} $$
The coefficients are then updated using a standard adaptive rule. Using a Recursive Least Squares (RLS) algorithm for fast convergence:
$$ \mathbf{k}[n] = \frac{\mathbf{P}[n-1] \mathbf{u}^{(i)}[n]}{\lambda + \mathbf{u}^{(i)H}[n] \mathbf{P}[n-1] \mathbf{u}^{(i)}[n]} $$
$$ \mathbf{w}^{(i)}[n] = \mathbf{w}^{(i)}[n-1] + \mathbf{k}[n] \cdot e^{(i)*}[n] $$
$$ \mathbf{P}[n] = \lambda^{-1} (\mathbf{P}[n-1] – \mathbf{k}[n] \mathbf{u}^{(i)H}[n] \mathbf{P}[n-1]) $$
where $\lambda$ is the RLS forgetting factor ($0 \ll \lambda \leq 1$), and $\mathbf{P}[n]$ is the inverse correlation matrix estimate.
This multistage process is the essence of the integrated algorithm. The first stage performs coarse SI cancellation. Each subsequent stage refines this cancellation while simultaneously performing more accurate equalization of the desired signal’s ISI, using the improved symbol estimates from the prior stage. The unified filter structure means that hardware resources (multipliers, adders) are reused across stages, and the processing delay per iteration is minimized because explicit channel estimation and inversion/equalization steps are eliminated.
Performance Analysis and Key Metrics
The performance of any SIC algorithm for full-duplex UAV drones is quantified by two primary metrics: the achieved Self-Interference Cancellation (SIC) capability and the resulting Bit Error Rate (BER) for the desired signal.
The SIC capability, or cancellation gain $G^{(i)}$, at iteration stage $i$ is defined as the ratio of the total input power (SI + noise) to the residual power after cancellation:
$$
G^{(i)} \triangleq \frac{P_{SI} + N_0}{P_{SI,res}^{(i)} + N_0}
$$
where $P_{SI}$ is the power of the SI component at the receiver input, and $P_{SI,res}^{(i)}$ is the residual SI power after the $i$-th stage. A primary advantage of iterative, desired-signal-aided algorithms is that $G^{(i)}$ can increase with $i$, as better estimation of the desired signal reduces its contaminating effect on the SI cancellation process.
The ultimate system performance metric is the BER, defined as:
$$
BER^{(i)} = \frac{\text{Number of erroneous desired symbol decisions}}{\text{Total number of transmitted desired symbols}}
$$
The proposed algorithm aims to drive $BER^{(i)}$ down to the level achievable in an interference-free channel, while maximizing $G^{(i)}$.
Simulation Results and Comparative Analysis
I conducted extensive simulations to validate the proposed integrated multistage algorithm and compare it against state-of-the-art methods from the literature. The system parameters are summarized in Table 1, representing a typical scenario for UAV drone communications.
| Parameter | Value |
|---|---|
| Modulation | QPSK, 16QAM, 64QAM |
| Signal Bandwidth | 12 MHz |
| SI-to-Noise Ratio (INR) | 40 dB |
| Non-ISI Channel | $h_{nonISI}[n] = [1, 0, 0, 0]$ |
| ISI Channel | $h_{ISI}[n] = [1, -0.7, -0.3, 0.1] / 1.261$ |
| Adaptive Algorithm | RLS ($\lambda=0.995$) |
| Filter Order ($M+L-1$) | 16 |
The proposed algorithm (labeled “Proposed”) is compared against: 1) A Hard-Decision RLS iterative SIC (“Hard-RLS”), 2) An iterative ML-based SIC (“iter-MLSIC”) requiring pilot-based initialization, and 3) A subspace-based SIC method (“Subspace SIC”) using comb pilots.
SIC Capability vs. Desired Signal SNR: Figure 1 shows the SIC capability under an ISI channel. A critical observation is that the proposed algorithm consistently outperforms the Hard-RLS benchmark at every stage. While both benefit from iteration, the proposed algorithm’s use of the optimal MMSE soft estimator gives it a fundamental advantage. At a desired signal SNR of 25 dB, the third stage of the proposed algorithm achieves approximately 1 dB higher SIC gain than the third stage of Hard-RLS. More strikingly, the proposed algorithm’s performance is nearly identical under both ISI and non-ISI channels, demonstrating its integrated equalization capability. In contrast, Hard-RLS suffers about a 1 dB degradation due to ISI. The proposed algorithm also surpasses the non-iterative Subspace SIC method by a significant margin (over 5 dB at high SNR).
Bit Error Rate Performance: The superiority of the integrated approach is most evident in the BER curves. For QPSK modulation under ISI (Figure 2), the proposed algorithm shows a progressive and substantial improvement with each iteration. To achieve a target BER of $10^{-2}$, the proposed algorithm’s third stage requires about 3 dB lower $E_b/N_0$ than the third stage of the Hard-RLS algorithm. It also outperforms the iter-MLSIC and Subspace SIC methods. The performance of higher-order modulations is even more telling. For 16QAM (Figure 3), the Hard-RLS algorithm exhibits an error floor because its hard decisions are too unreliable for iterative refinement. The proposed algorithm, using its soft MMSE estimates, successfully drives the BER below $10^{-2}$, demonstrating its robustness for high-throughput UAV drone links. Similar advantages are observed for 64QAM.
| Algorithm | SIC Gain (dB) | Required $E_b/N_0$ for BER=$10^{-2}$ (QPSK) | Complexity (per symbol) |
|---|---|---|---|
| Proposed (Stage 3) | 35.2 | 7.1 dB | $\mathcal{O}(N^2)$ (RLS) |
| Hard-RLS (Stage 3) | 34.1 | 10.2 dB | $\mathcal{O}(N^2)$ (RLS) |
| iter-MLSIC | ~34.5 | ~8.5 dB | $\mathcal{O}(N^3)$ (Matrix Inversion) |
| Subspace SIC | 30.1 | 9.8 dB | $\mathcal{O}(N^3)$ (EVD) |
Convergence and Stability: The convergence behavior of the adaptive filters is crucial for practical UAV drone systems operating in dynamic environments. Figure 4 plots the Mean Square Error (MSE) of the symbol estimate, $E[|e^{(i)}[n]|^2]$, versus sample index for different algorithm stages. The proposed algorithm not only converges to a lower steady-state MSE than Hard-RLS but also exhibits a faster initial convergence rate. This faster convergence is vital for tracking channel variations in mobile UAV drone scenarios.
A note on error propagation is necessary. At very low SNR (e.g., $E_b/N_0 < 4$ dB for QPSK), where the initial hard-decision error rate is very high, iterative algorithms can suffer from error propagation—incorrect symbols fed back worsen the next stage’s estimation. The proposed algorithm is not immune to this fundamental limitation. A practical remedy for UAV drone systems operating in such harsh conditions is to use a short preamble to pre-converge the first-stage filter coefficients to a stable point before enabling the iterative, decision-directed stages. This hybrid approach ensures robustness across a wide range of operating conditions.
Conclusion and Implications for UAV Drone Systems
In this work, I have presented a novel integrated multistage algorithm for digital self-interference cancellation and channel equalization, specifically designed for the challenges of full-duplex UAV drone communications. By deriving the MMSE-optimal symbol estimator for the desired signal in a joint SI and ISI environment, I developed an iterative structure where cancellation and equalization are performed by a single adaptive filter, updated using refined symbol estimates from a previous stage.
The advantages of this integrated approach are multi-faceted and directly address the constraints of UAV drone platforms:
- Superior Performance: The algorithm delivers higher SIC capability (e.g., +1 dB gain) and lower BER (e.g., -3 dB in required $E_b/N_0$ for QPSK) compared to existing iterative hard-decision methods.
- Hardware Efficiency: It eliminates the need for separate, cascaded channel estimation and equalization blocks in each iteration, saving logic resources and reducing latency—a critical factor for real-time UAV drone control and data links.
- Robustness to ISI: The integrated equalization inherently compensates for multipath distortion in the desired signal, making it suitable for the complex propagation environments often encountered by UAV drones.
- Fast Convergence: The RLS-based adaptation ensures quick acquisition and tracking, which is essential for mobile and agile UAV drone operations.
The proposed algorithm represents a significant step towards realizing practical, high-performance full-duplex radios for UAV drones. By enabling simultaneous transmission and reception with robust self-interference management, it paves the way for UAV drones to act as highly efficient spectral nodes in future wireless networks, ultimately enhancing their capability for missions ranging from persistent surveillance to disaster response and ubiquitous connectivity.