Signal Shaping for Generalized Spatial Modulation and Generalized Quadrature Spatial Modulation

This paper investigates generic signal shaping methods for multiple-data-stream generalized spatial modulation (GenSM) and generalized quadrature spatial modulation (GenQSM) based on the maximizing the minimum Euclidean distance (MMED) criterion. Three cases with different channel state information at the transmitter (CSIT) are considered, including no CSIT, statistical CSIT and perfect CSIT. A unified optimization problem is formulated to find the optimal transmit vector set under size, power and sparsity constraints. We propose an optimization-based signal shaping (OBSS) approach by solving the formulated problem directly and a codebook-based signal shaping (CBSS) approach by finding sub-optimal solutions in discrete space. In the OBSS approach, we reformulate the original problem to optimize the signal constellations used for each transmit antenna combination (TAC). Both the size and entry of all signal constellations are optimized. Specifically, we suggest the use of a recursive design for size optimization. The entry optimization is formulated as a non-convex large-scale quadratically constrained quadratic programming (QCQP) problem and can be solved by existing optimization techniques with rather high complexity. To reduce the complexity, we propose the CBSS approach using a codebook generated by quadrature amplitude modulation (QAM) symbols and a low-complexity selection algorithm to choose the optimal transmit vector set. Simulation results show that the OBSS approach exhibits the optimal performance in comparison with existing benchmarks. However, the OBSS approach is impractical for large-size signal shaping and adaptive signal shaping with instantaneous CSIT due to the demand of high computational complexity. As a low-complexity approach, CBSS shows comparable performance and can be easily implemented in large-size systems.Comment: Summited to IEEE TW

Peak to Average Power Ratio Reduction for Space-Time Codes That Achieve Diversity-Multiplexing Gain Tradeoff

Zheng and Tse have shown that over a quasi-static channel, there exists a fundamental tradeoff, known as the diversity-multiplexing gain (D-MG) tradeoff. In a realistic system, to avoid inefficiently operating the power amplifier, one should consider the situation where constraints are imposed on the peak to average power ratio (PAPR) of the transmitted signal. In this paper, the D-MG tradeoff of multi-antenna systems with PAPR constraints is analyzed. For Rayleigh fading channels, we show that the D-MG tradeoff remains unchanged with any PAPR constraints larger than one. This result implies that, instead of designing codes on a case-by-case basis, as done by most existing works, there possibly exist general methodologies for designing space-time codes with low PAPR that achieve the optimal D-MG tradeoff. As an example of such methodologies, we propose a PAPR reduction method based on constellation shaping that can be applied to existing optimal space-time codes without affecting their optimality in the D-MG tradeoff. Unlike most PAPR reduction methods, the proposed method does not introduce redundancy or require side information being transmitted to the decoder. Two realizations of the proposed method are considered. The first is similar to the method proposed by Kwok except that we employ the Hermite Normal Form (HNF) decomposition instead of the Smith Normal Form (SNF) to reduce complexity. The second takes the idea of integer reversible mapping which avoids the difficulty in matrix decomposition when the number of antennas becomes large. Sphere decoding is performed to verify that the proposed PAPR reduction method does not affect the performance of optimal space-time codes.Comment: submitted to IEEE Transactions on Signal Processin

One-Bit Sigma-Delta MIMO Precoding

Coarsely quantized MIMO signalling methods have gained popularity in the recent developments of massive MIMO as they open up opportunities for massive MIMO implementation using cheap and power-efficient radio-frequency front-ends. This paper presents a new one-bit MIMO precoding approach using spatial Sigma-Delta ($\Sigma\Delta$) modulation. In previous one-bit MIMO precoding research, one mainly focuses on using optimization to tackle the difficult binary signal optimization problem that arises from the precoding design. Our approach attempts a different route. Assuming angular MIMO channels, we apply $\Sigma\Delta$ modulation---a classical concept in analog-to-digital conversion of temporal signals---in space. The resulting $\Sigma\Delta$ precoding approach has two main advantages: First, we no longer need to deal with binary optimization in $\Sigma\Delta$ precoding design. Particularly, the binary signal restriction is replaced by peak signal amplitude constraints. Second, the impact of the quantization error can be well controlled via modulator design and under appropriate operating conditions. Through symbol error probability analysis, we reveal that the very large number of antennas in massive MIMO provides favorable operating conditions for $\Sigma\Delta$ precoding. In addition, we develop a new $\Sigma\Delta$ modulation architecture that is capable of adapting the channel to achieve nearly zero quantization error for a targeted user. Furthermore, we consider multi-user $\Sigma\Delta$ precoding using the zero-forcing and symbol-level precoding schemes. These two $\Sigma\Delta$ precoding schemes perform considerably better than their direct one-bit quantized counterparts, as simulation results show

The information and wave-theoretic limits of analog beamforming

The performance of broadband millimeter-wave (mmWave) RF architectures, is generally determined by mathematical concepts such as the Shannon capacity. These systems have also to obey physical laws such as the conservation of energy and the propagation laws. Taking the physical and hardware limitations into account is crucial for characterizing the actual performance of mmWave systems under certain architecture such as analog beamforming. In this context, we consider a broadband frequency dependent array model that explicitly includes incremental time shifts instead of phase shifts between the individual antennas and incorporates a physically defined radiated power. As a consequence of this model, we present a novel joint approach for designing the optimal waveform and beamforming vector for analog beamforming. Our results show that, for sufficiently large array size, the achievable rate is mainly limited by the fundamental trade-off between the analog beamforming gain and signal bandwidth.Comment: Presented at ITA, february 201

Constant Envelope Precoding for MIMO Systems

Constant envelope (CE) precoding is an appealing transmission technique, which enables highly efficient power amplification, and is realizable with a single radio frequency (RF) chain at the multi-antenna transmitter. In this paper, we study the transceiver design for a point-to-point multiple-input multiple-output (MIMO) system with CE precoding. Both single-stream transmission (i.e., beamforming) and multi-stream transmission (i.e., spatial multiplexing) are considered. For single-stream transmission, we optimize the receive beamforming vector to minimize the symbol error rate (SER) for any given channel realization and desired constellation at the combiner output. By reformulating the problem as an equivalent quadratically constrained quadratic program (QCQP), we propose an efficient semi-definite relaxation (SDR) based algorithm to find an approximate solution. Next, for multi-stream transmission, we propose a new scheme based on antenna grouping at the transmitter and minimum mean squared error (MMSE) or zero-forcing (ZF) based beamforming at the receiver. The transmit antenna grouping and receive beamforming vectors are then jointly designed to minimize the maximum SER over all data streams. Finally, the error-rate performance of single- versus multi-stream transmission is compared via simulations under different setups.Comment: Submitted for possible journal publicatio

Antenna Current Optimization and Realizations for Far-Field Pattern Shaping

Far-field shaping of small antennas is a challenge and the realizations of non-dipole radiation of small to intermediate sized antennas are difficult. Here we examine the antenna bandwidth cost associated with such constraints, and in certain cases we design antennas that approach the bounds. Far-field shaping is in particular interesting for Internet-of-things (IoT) and Wi-Fi applications since e.g. spatial filtering can mitigate package loss through a reduction of mutual interference, and hence increase the power efficiency of the devices. Even a rather careful far-field shaping of smaller antennas can be associated with a steep reduction in the best available bandwidth. It is thus important to develop constraints that a small antenna can support. We describe a power front-to-back ratio, and a related, beam-shaping constraint that can be used in optimization for the minimum Q-factor. We show that such a non-convex Q-factor optimization can be solved with the semi-definite relaxation technique. We furthermore show that certain of the above optimized non-standard radiation patterns can be realized with a multi-position feeding strategy with a moderate loss of Q-factor: $Q_\text{antenna}\leq 1.61Q_\text{optimal}$

Compute-and-Forward Strategies for Cooperative Distributed Antenna Systems

We study a distributed antenna system where $L$ antenna terminals (ATs) are connected to a Central Processor (CP) via digital error-free links of finite capacity $R_0$, and serve $K$ user terminals (UTs). We contribute to the subject in the following ways: 1) for the uplink, we apply the "Compute and Forward" (CoF) approach and examine the corresponding system optimization at finite SNR; 2) For the downlink, we propose a novel precoding scheme nicknamed "Reverse Compute and Forward" (RCoF); 3) In both cases, we present low-complexity versions of CoF and RCoF based on standard scalar quantization at the receivers, that lead to discrete-input discrete-output symmetric memoryless channel models for which near-optimal performance can be achieved by standard single-user linear coding; 4) For the case of large $R_0$, we propose a novel "Integer Forcing Beamforming" (IFB) scheme that generalizes the popular zero-forcing beamforming and achieves sum rate performance close to the optimal Gaussian Dirty-Paper Coding. The proposed uplink and downlink system optimization focuses specifically on the ATs and UTs selection problem. We present low-complexity ATs and UTs selection schemes and demonstrate, through Monte Carlo simulation in a realistic environment with fading and shadowing, that the proposed schemes essentially eliminate the problem of rank deficiency of the system matrix and greatly mitigate the non-integer penalty affecting CoF/RCoF at high SNR. Comparison with other state-of-the art information theoretic schemes, such as "Quantize reMap and Forward" for the uplink and "Compressed Dirty Paper Coding" for the downlink, show competitive performance of the proposed approaches with significantly lower complexity.Comment: Submitted to IEEE Transactions on Information Theor

Reverse Compute and Forward: A Low-Complexity Architecture for Downlink Distributed Antenna Systems

We consider a distributed antenna system where $L$ antenna terminals (ATs) are connected to a Central Processor (CP) via digital error-free links of finite capacity $R_0$, and serve $L$ user terminals (UTs). This system model has been widely investigated both for the uplink and the downlink, which are instances of the general multiple-access relay and broadcast relay networks. In this work we focus on the downlink, and propose a novel downlink precoding scheme nicknamed "Reverse Quantized Compute and Forward" (RQCoF). For this scheme we obtain achievable rates and compare with the state of the art available in the literature. We also provide simulation results for a realistic network with fading and pathloss with $K > L$ UTs, and show that channel-based user selection produces large benefits and essentially removes the problem of rank deficiency in the system matrix.Comment: 5 pages, 3 figures, submission to the 2012 IEEE International Symposium on Information Theory (ISIT 2012

A Journey from Improper Gaussian Signaling to Asymmetric Signaling

The deviation of continuous and discrete complex random variables from the traditional proper and symmetric assumption to a generalized improper and asymmetric characterization (accounting correlation between a random entity and its complex conjugate), respectively, introduces new design freedom and various potential merits. As such, the theory of impropriety has vast applications in medicine, geology, acoustics, optics, image and pattern recognition, computer vision, and other numerous research fields with our main focus on the communication systems. The journey begins from the design of improper Gaussian signaling in the interference-limited communications and leads to a more elaborate and practically feasible asymmetric discrete modulation design. Such asymmetric shaping bridges the gap between theoretically and practically achievable limits with sophisticated transceiver and detection schemes in both coded/uncoded wireless/optical communication systems. Interestingly, introducing asymmetry and adjusting the transmission parameters according to some design criterion render optimal performance without affecting the bandwidth or power requirements of the systems. This dual-flavored article initially presents the tutorial base content covering the interplay of reality/complexity, propriety/impropriety and circularity/noncircularity and then surveys majority of the contributions in this enormous journey.Comment: IEEE COMST (Early Access

MIMO Beampattern and Waveform Design with Low Resolution DACs

Digital beamforming and waveform generation techniques in MIMO radar offer enormous advantages in terms of flexibility and performance compared to conventional radar systems based on analog implementations. To allow for such fully digital design with an efficient hardware complexity, we consider the use of low resolution digital-to-analog converters (DACs) while maintaining a separate radio-frequency chain per antenna. A sum of squared residuals (SSR) formulation for the beampattern and spectral shaping problem is solved based on the Generalized Approximate Message Passing (GAMP) algorithm. Numerical results demonstrate good performance in terms of spectral shaping as well as cross-correlation properties of the different probing waveforms even with just 2-bit resolution per antenna