Multiuser-MISO Precoding under Channel Phase Uncertainty in Satellite Communication Systems

in IEEE Open Journal of Vehicular Technology (2022)

Linear and symbol-level precoding in satellite communications have received increasing research attention thanks to their ability to tackle inter-beam interference, allowing the use of spectral resources ... [more ▼]

Linear and symbol-level precoding in satellite communications have received increasing research attention thanks to their ability to tackle inter-beam interference, allowing the use of spectral resources more efficiently. However, there are still challenges and open questions regarding the implementation of practical precoding systems taking the phase uncertainties in estimating the channel state information into account. This work assesses the impact of phase variations and uncertainties inherent to the satellite communication system operating a precoded forward link. Specifically, we address the inability to measure at the user terminal, the absolute phase rotation introduced by the channel, and the transponder local oscillator phase noise effects on the precoding operations considering the use of frequency division multiplexing in the forward-uplink transmission. We formally demonstrate that the system performance for linear and non-linear precoding operations is not affected by the uncertainty in the phase measurements at the user terminal. Additionally, we show that using a single frequency reference for all the local oscillators at the transponder does not avoid the phase variations related to the frequency division multiplexing in the forward-uplink. This work demonstrates that these phase variations would not affect the system performance for an ideal zero-delay precoding loop. However, this is not feasible in practical scenarios, where the phase noise of the frequency reference at the transponder and the loop delay determine the impact on the system performance. We validate our results by simulations considering three frequency references with different stability levels in a typical GEO satellite system. Our results suggest that practical implementations of multiuser-MISO precoding systems must include a differential phase synchronization loop to compensate for this performance degradation. [less ▲]

Design Optimization for Low-Complexity FPGA Implementation of Symbol-Level Multiuser Precoding

in IEEE Access (2021), 9

This paper proposes and validates a low-complexity FPGA design for symbol-level precoding (SLP) in multiuser multiple-input single-output (MISO) downlink communication systems. In the optimal case, the ... [more ▼]

This paper proposes and validates a low-complexity FPGA design for symbol-level precoding (SLP) in multiuser multiple-input single-output (MISO) downlink communication systems. In the optimal case, the symbol-level precoded transmit signal is obtained as the solution to an optimization problem tailored for a given set of users’ data symbols. This symbol-by-symbol design, however, imposes excessive computational complexity on the system. To alleviate this issue, we aim to reduce the per-symbol complexity of the SLP scheme by developing an approximate yet computationally-efficient closed-form solution. The proposed solution allows us to achieve a high symbol throughput in real-time implementations. To develop the FPGA design, we express the proposed solution in an algorithmic way and translate it to hardware description language (HDL). We then optimize the processing to accelerate the performance and generate the corresponding intellectual property (IP) core. We provide the synthesis report for the generated IP core, including performance and resource utilization estimates and interface descriptions. To validate our design, we simulate an uncoded transmission over a downlink multiuser channel using the LabVIEW software, where the SLP IP core is implemented as a clock-driven logic (CDL) unit. Our simulation results show that a throughput of 100 Mega symbols per second per user can be achieved via the proposed SLP design. We further use the MATLAB software to produce numerical results for the conventional zero-forcing (ZF) and the optimal SLP techniques as benchmarks for comparison. Thereby, it is shown that the proposed FPGA implementation of SLP offers an improvement of up to 50 percent in power efficiency compared to the ZF precoding. Remarkably, it enjoys the same per-symbol complexity order as that of the ZF technique. We also evaluate the loss of the real-time SLP design, introduced by the algebraic approximations and arithmetic inaccuracies, with respect to the optimal scheme. [less ▲]

Enhanced Signal Space Design for Multiuser MIMO Interference Channels

Doctoral thesis (2021)

Multiuser precoding techniques are critical to handle the co-channel interference, also known as multiuser interference (MUI), in the downlink of multiuser multi-antenna wireless systems. The convention ... [more ▼]

Multiuser precoding techniques are critical to handle the co-channel interference, also known as multiuser interference (MUI), in the downlink of multiuser multi-antenna wireless systems. The convention in designing multiuser precoding schemes has been to treat the MUI as an undesired received signal component. Consequently, the design attempts to suppress the MUI by exploiting the channel state information (CSI), regardless of the instantaneous users’ data symbols. In contrast, it has been shown that the MUI may not always be undesired or destructive as it is possible to exploit the constructive part of the interference or even converting the interfering components into constructive interference (CI) by instantaneously exploiting the users’ intended data symbols. As a result, the MUI can be transformed into a useful source of power that constructively contributes to the users’ received signals. This observation has turned the viewpoint on multiuser precoding from conventional approaches towards more sophisticated designs that further exploit the data information (DI) in addition to the CSI, referred to as symbol-level precoding (SLP). The SLP schemes can improve the multiuser system’s overall performance in terms of various metrics, such as power efficiency, symbol error rate, and received signal power. However, such improvement comes with several practical challenges, for example, the need for setting the modulation scheme in advance, increased computational complexity at the transmitter, and sensitivity to CSI and other system uncertainties. The main goal of this thesis is to address these challenges in the design of an SLP scheme. The existing design formulations for the CI-based SLP problem consider a specific signal constellation; therefore, the design needs to set the modulation scheme in advance. In this thesis, we first elaborate on optimal and relaxed approaches to exploit the CI in a novel systematic way. This study enables us to develop a generic framework for the SLP design problem, which can be used for modulation schemes with constellations of any given shape and order. Depending on the design criterion, the proposed framework can offer significant gains in the power consumption at the transmitter side or the received signal power and the symbol error rate at the receiver side without increasing the complexity, compared to the state-of-the-art schemes. Next, to address the high computational complexity issue, we simplify the design process and propose approximate yet computationally-efficient solutions performing relatively close to the optimal design. We further propose an optimized accelerated FPGA design that allows the real-time implementation of our SLP technique in high-throughput communications systems. Remarkably, the accelerated design enjoys the same per-symbol complexity order as that of the zero-forcing (ZF) precoding scheme. Next, we address the problem of robust SLP design under system uncertainties. In particular, we focus on two sources of uncertainty, namely, the channel and the design process. The related problems are tackled by adopting worst-case and stochastic design approaches and appropriately redefining the precoding optimization problem. The resulting robust schemes can effectively deal with system uncertainties while preserving reliability and power efficiency in the multiuser communications system, at the cost of a slightly increased complexity. Finally, we broaden our scope to new technologies such as millimeter wave (mmWave) communications and massive multiple-input multiple-output (MIMO) systems and revisit the SLP problem for low-cost energy-efficient transmitter architectures. The precoding design problem is more challenging particularly in such scenarios as the related hardware restrictions impose additional (often intractable) constraints on the problem. The restrictions are typically due to the use of finite-resolution analog-to-digital converters (DAC) or analog components such as switches and/or phase shifters. Two well-known design strategies are considered in this thesis, namely, quantized (finite-alphabet) precoding and hybrid analog-digital precoding. We tackle the related problems through adopting efficient design mechanisms and optimization algorithms, which are novel for the SLP schemes. The proposed techniques are shown to improve the system’s energy efficiency compared to the state-of-the-art. [less ▲]

One-Bit Quantized Constructive Interference Based Precoding for Massive Multiuser MIMO Downlink

in One-Bit Quantized Constructive Interference Based Precoding for Massive Multiuser MIMO Downlink (2020, July 27)

We propose a one-bit symbol-level precoding method for massive multiuser multiple-input multiple-output (MU-MIMO) downlink systems using the idea of constructive interference (CI). In particular, we adopt ... [more ▼]

We propose a one-bit symbol-level precoding method for massive multiuser multiple-input multiple-output (MU-MIMO) downlink systems using the idea of constructive interference (CI). In particular, we adopt a max-min fair design criterion which aims to maximize the minimum instantaneous received signal-to-noise ratio (SNR) among the user equipments (UEs), while ensuring a CI constraint for each UE and under the restriction that the output of the precoder is a vector of binary elements. This design problem is an NP-hard binary quadratic programming due to the one-bit constraints on the elements of the precoder’s output vector, and hence, is difficult to solve. In this paper, we tackle this difficulty by reformulating the problem, in several steps, into an equivalent continuous-domain biconvex form. Our final biconvex reformulation is obtained via an exact penalty approach and can efficiently be solved using a standard block coordinate ascent algorithm. We show through simulation results that the proposed design outperforms the existing schemes in terms of (uncoded) bit error rate. It is further shown via numerical analysis that our solution algorithm is computationally-efficient as it needs only a few tens of iterations to converge in most practical scenarios. [less ▲]

Robust SINR-Constrained Symbol-Level Multiuser Precoding With Imperfect Channel Knowledge

in IEEE Transactions on Signal Processing (2020), 68(1), 1837-1852

In this paper, we address robust design of symbol-level precoding (SLP) for the downlink of multiuser multiple-input single-output wireless channels, when imperfect channel state information (CSI) is ... [more ▼]

In this paper, we address robust design of symbol-level precoding (SLP) for the downlink of multiuser multiple-input single-output wireless channels, when imperfect channel state information (CSI) is available at the transmitter. In particular, we consider a well known model for the CSI imperfection, namely, stochastic Gaussian-distributed uncertainty. Our design objective is to minimize the total (per-symbol) transmission power subject to constructive interference (CI) constraints as well as the users’ quality-of-service requirements in terms of signal-to-interference-plus-noise ratio. Assuming stochastic channel uncertainties, we first define probabilistic CI constraints in order to achieve robustness to statistically known CSI errors. Since these probabilistic constraints are difficult to handle, we resort to their convex approximations in the form of tractable (deterministic) robust constraints. Three convex approximations are obtained based on different conservatism levels, among which one is introduced as a benchmark for comparison. We show that each of our proposed approximations is tighter than the other under specific robustness settings, while both of them always outperform the benchmark. Using the proposed CI constraints, we formulate the robust SLP optimization problem as a second-order cone program. Extensive simulation results are provided to validate our analytic discussions and to make comparisons with conventional block-level robust precoding schemes. We show that the robust design of symbol-level precoder leads to an improved performance in terms of energy efficiency at the cost of increasing the computational complexity by an order of the number of users in the large system limit, compared to its non-robust counterpart. [less ▲]

An Approximate Solution for Symbol-Level Multiuser Precoding Using Support Recovery

in IEEE International Workshop on Signal Processing Advances in Wireless Communications (SPAWC), Cannes 2-5 July 2019 (2019, August 29)

In this paper, we propose a low-complexity method to approximately solve the SINR-constrained optimization problem of symbol-level precoding (SLP). First, assuming a generic modulation scheme, the ... [more ▼]

In this paper, we propose a low-complexity method to approximately solve the SINR-constrained optimization problem of symbol-level precoding (SLP). First, assuming a generic modulation scheme, the precoding optimization problem is recast as a standard non-negative least squares (NNLS). Then, we improve an existing closed-form SLP (CF-SLP) scheme using the conditions for nearly perfect recovery of the optimal solution support, followed by solving a reduced system of linear equations. We show through simulation results that in comparison with the CF-SLP method, the improved approximate solution of this paper, referred to as ICF-SLP, significantly enhances the performance with a negligible increase in complexity. We also provide comparisons with a fast-converging iterative NNLS algorithm, where it is shown that the ICF-SLP method is comparable in performance to the iterative algorithm with a limited maximum number of iterations. Analytic discussions on the complexities of different methods are provided, verifying the computational efficiency of the proposed method. Our results further indicate that the ICF-SLP scheme performs quite close to the optimal SLP, particularly in the large system regime. [less ▲]

Power Minimizer Symbol-Level Precoding: A Closed-Form Sub-Optimal Solution

in IEEE Signal Processing Letters (2018), 25(11), 1730-1734

In this letter, we study the optimal solution of multiuser symbol-level precoding (SLP) for minimization of the total transmit power under given signal-to-interference-plus noise ratio (SINR) constraints ... [more ▼]

In this letter, we study the optimal solution of multiuser symbol-level precoding (SLP) for minimization of the total transmit power under given signal-to-interference-plus noise ratio (SINR) constraints. Adopting the distance preserving constructive interference regions (DPCIR), we first derive a simplified reformulation of the problem. Then, we analyze the structure of the optimal solution using the Karush-Kuhn-Tucker (KKT) optimality conditions. This leads us to obtain a closed-form sub-optimal SLP solution (CF-SLP) for the original problem. Meanwhile, we obtain the necessary and sufficient condition under which the power minimizer SLP is equivalent to the conventional zero-forcing beamforming (ZFBF). Simulation results show that CF-SLP provides significant gains over ZFBF, while performing quite close to the optimal SLP in scenarios with rather small number of users. The results further indicate that the CF-SLP method has a reduction of order 1000 in computational time compared to the optimal solution. [less ▲]

Symbol-Level Precoding Design for Max-Min SINR in Multiuser MISO Broadcast Channels

in International Workshop on Signal Processing Advances in Wireless Communications (SPAWC), Kalamata 25-28 June 2018 (2018, August 27)

In this paper, we address the symbol level precoding (SLP) design problem under max-min SINR criterion in the downlink of multiuser multiple-input single-output (MISO) channels. First, we show that the ... [more ▼]

In this paper, we address the symbol level precoding (SLP) design problem under max-min SINR criterion in the downlink of multiuser multiple-input single-output (MISO) channels. First, we show that the distance preserving constructive interference regions (DPCIR) are always polyhedral angles (shifted pointed cones) for any given constellation point with unbounded decision region. Then we prove that any signal in a given unbounded DPCIR has a norm larger than the norm of the corresponding vertex if and only if the convex hull of the constellation contains the origin. Using these properties, we show that the power of the noiseless received signal lying on an unbounded DPCIR is an strictly increasing function of two parameters. This allows us to reformulate the originally non-convex SLP max-min SINR as a convex optimization problem. We discuss the loss due to our proposed convex reformulation and provide some simulation results. [less ▲]

Symbol vs Block Level Precoding in Multi-beam Satellite Systems

in Symbol vs Block Level Precoding in Multi-beam Satellite Systems (2018)

Precoding techniques for multi-beam satellite systems have received a considerable attention in recent years as a tool to mitigate the interference among the beams, and hence increasing the throughput ... [more ▼]

Precoding techniques for multi-beam satellite systems have received a considerable attention in recent years as a tool to mitigate the interference among the beams, and hence increasing the throughput. Our goal is to compare two main categories of precoding schemes, namely, the conventional linear block level precoding and the symbol level precoding. Focusing on power minimization problem with signal to interference plus noise ratio (SINR) constraints, symbol level precoding (SLP) has significant gains with respect to the zero forcing (ZF). However, the lower transmit power is achieved with a price: A higher computational complexity. Therefore, several sub-optimal SLP techniques have been proposed in the literature to overcome the complexity. While ZF has the lowest complexity among the techniques chosen in this paper, it is not an optimal linear block level precoder as far as power minimization is concerned. Therefore, in order to have a more complete picture, one needs also to consider optimal block level precoders. Our results indicate that in order to have a fair comparison, one needs to consider two different scenarios, namely, low and high SINR threshold regimes. While for low SINRs the optimal linear block level precoding scheme may provide a good solution with reasonable complexity, for high SINR threshold, the SLP techniques become more attractive. Our results also indicate that the performance of SLP highly depends on the chosen constellation space, and therefore a final conclusion can be achieved only after appropriately optimizing the constellation set. [less ▲]