The concept of subnetworks has been recently identified as a key component of 6 G, enabling mission-critical services with hyper-reliability. In this paper, we address the challenges posed by both inter-subnetwork interference and external interference in hyper-dense and dynamic industrial environments. We focus on in-factory subnetworks for industrial wireless control applications and propose an advanced frequency-power resource allocation scheme using Gradient Descent-based Resource Allocation (GDRA). The proposed GDRA scheme efficiently mitigates interference while optimizing resource allocation. We evaluate the performance of the proposed scheme and compare it with state-of-the-art approaches, demonstrating significant improvements in spectral efficiency and reliability.

This paper proposes a novel mixed panel architecture for channel state information (CSI) acquisition from uplink (UL) channel training in hybrid analog-digital beamforming systems with partially-connected structures in time-division duplex massive multiple-input multiple-output networks. The proposed architecture combines a few fully-digital (FD) panels with a large number of subarray-based panels for UL pilot reception, addressing CSI acquisition challenges while balancing performance and power efficiency. We then develop a unified method that can utilize measurements from both panel types to estimate the required CSI for analog precoder design. In particular, by recognizing that the dominant eigenvector of the panel covariance matrix is crucial for analog precoding, we propose an orthogonal matching pursuit-type algorithm to estimate it by exploiting channel sparsity in the angular domain. Additionally, we introduce a data-driven technique to optimize analog combiners for subarray-based panels during UL pilot reception. Numerical experiments demonstrate that our proposed method approaches the performance of an all-FD-panel architecture for UL pilot training while maintaining the low complexity of all-subarray-based-panel structures

Localization services for wireless devices play an increasingly important role in our daily lives and a plethora of emerging services and applications already rely on precise position information. Widely used on-device positioning methods, such as the global positioning system, enable accurate outdoor positioning and provide the users with full control over what services and applications are allowed to access their location information. In order to provide accurate positioning indoors or in cluttered urban scenarios without line-of-sight satellite connectivity, powerful off-device positioning systems, which process channel state information (CSI) measured at the infrastructure base stations or access points with deep neural networks, have emerged recently. Such off-device wireless positioning systems inherently link a user’s data transmission with its localization, since accurate CSI measurements are necessary for reliable wireless communication—this not only prevents the users from controlling who can access this information but also enables virtually everyone in the device’s range to estimate its location, resulting in serious privacy and security concerns. We therefore propose on-device attacks against off-device wireless positioning systems in multi-antenna orthogonal frequency-division multiplexing systems while remaining standard compliant and minimizing the impact on quality-of-service, and we demonstrate their efficacy using real-world measured datasets for cellular outdoor and wireless LAN indoor scenarios. We also investigate defenses to counter such attack mechanisms, and we discuss the limitations and implications on protecting location privacy in existing and future wireless communication systems.

Ising problem is an NP-hard combinatorial op-timization problem. Recently, networks of mutually coupled, nonlinear, self-sustaining oscillators known as Oscillator Ising Machines (OIMs) were shown to heuristically solve Ising prob-lems. The phases of the oscillators in OIMs can be modeled as systems of Ordinary Differential Equations (ODEs) known as Generalized Kuramoto (Gen-K) models. In this paper, we solve Gen-K Ode systems efficiently using cleverly designed fixed point operations. To demonstrate this idea, we fabricated a prototype chip containing 33 spins with programmable all-to-all connectivity. We test this design using Multi-Input Multi-Output decoding problems, and show that the OIM emulator achieves near-optimal Symbol Error Rates (SER).

Over the last several years, Oscillator Ising Machines (OIMs) have been shown to heuristically solve NP-hard combinatorial optimization (CO) problems, most notably MAX-CUT. In this paper, we show that OIMs are capable of solving Multi-User Multiple-Input-Multiple-Output (MU-MIMO) detection, an important real-world problem in telecommunications, achieving near-optimal Symbol Error Rates (SERs). Our results are obtained using CPU- and GPU-based simulation; the latter features a parallelizable event-based algorithm for the generalized Kuramoto equations that reduces OIM simulation times by about 6× without losing accuracy. We also find that good SER results are obtained if 6 or more bits are used to quantize the Ising problem's coupling weights. We provide runtime, throughput and energy consumption comparisons of different implementations and algorithms for MU-MIMO detection, including an OIM emulator chip we had reported earlier. Our results provide useful guidance for designing analog OIM ICs tailored for MU-MIMO detection.

This is the second part of a two-part paper that focuses on link-adaptation (LA) and physical layer (PHY) abstraction for multi-user MIMO (MU-MIMO) systems with non-linear receivers. The first part proposes a new metric, called bit-metric decoding rate (BMDR) for a detector, as being the equivalent of post-equalization signal-to-interference-noise ratio (SINR) for non-linear receivers. Since this BMDR does not have a closed form expression, a machine-learning based approach to estimate it effectively is presented. In this part, the concepts developed in the first part are utilized to develop novel algorithms for LA, dynamic detector selection from a list of available detectors, and PHY abstraction in MU-MIMO systems with arbitrary receivers. Extensive simulation results that substantiate the efficacy of the proposed algorithms are presented.

LA is one of the most important aspects of wireless communications where the MCS used by the transmitter is adapted to the channel conditions in order to meet a certain target error-rate. In a SU-SISO system with out-of-cell interference, LA is performed by computing the post-equalization SINR at the receiver. The same technique can be employed in MU-MIMO receivers that use linear detectors. Another important use of post-equalization SINR is for PHY abstraction, where several PHY blocks like the channel encoder, the detector, and the channel decoder are replaced by an abstraction model in order to speed up system-level simulations. However, for MU-MIMO systems with non-linear receivers, there is no known equivalent of post-equalization SINR which makes both LA and PHY abstraction extremely challenging. This important issue is addressed in this two-part paper. In this part, a metric called the BMDR of a detector, which is the proposed equivalent of post-equalization SINR, is presented. Since BMDR does not have a closed form expression that would enable its instantaneous calculation, a machine-learning approach to predict it is presented along with extensive simulation results.

In orthogonal frequency division multiplexing (OFDM)-based wireless communication systems, the bit error rate (BER) performance is heavily dependent on the accuracy of channel estimation. It is important for a good channel estimator to be capable of handling the changes in the wireless channel conditions that occur due to the mobility of the users. In recent years, the focus has been on developing complex neural network (NN)-based channel estimators that enable an error performance close to that of a genie-aided channel estimator. This work considers the other alternative which is to have a simple channel estimator but a more complex NN-based demapper for the generation of soft information for each transmitted bit. In particular, the problem of reversing the adverse effects of an imperfect channel estimator is addressed, and a convolutional self-attention-based neural demapper that significantly outperforms the baseline is proposed.

The problem of estimating a high-dimensional sparse vector θ ∈ ℝnfrom an observation in i.i.d. Gaussian noise is considered. An empirical Bayes shrinkage estimator, derived using a Bernoulli-Gaussian prior, is analyzed and compared with the well-known soft-thresholding estimator using squared-error loss as a measure of performance. We obtain concentration inequalities for the Stein's unbiased risk estimate and the loss function of both estimators. Depending on the underlying θ, either the proposed empirical Bayes (eBayes) estimator or soft-thresholding may have smaller loss. We consider a hybrid estimator that attempts to pick the better of the soft-thresholding estimator and the eBayes estimator by comparing their risk estimates. It is shown that: i) the loss of the hybrid estimator concentrates on the minimum of the losses of the two competing estimators, and ii) the risk of the hybrid estimator is within order 1/√n of the minimum of the two risks. Simulation results are provided to support the theoretical results.

This paper considers the problem of estimating a high-dimensional vector of parameters Θ ∈ Rn from a noisy observation. The noise vector is independent identically distributed Gaussian with known variance. For a squared-error loss function, the James-Stein (JS) estimator is known to dominate the simple maximum-likelihood (ML) estimator when the dimension n exceeds two. The JS-estimator shrinks the observed vector toward the origin, and the risk reduction over the ML-estimator is greatest for Θ that lie close to the origin. JS-estimators can be generalized to shrink the data toward any target subspace. Such estimators also dominate the ML-estimator, but the risk reduction is significant only when Θ lies close to the subspace. This leads to the question: in the absence of prior information about Θ, how do we design estimators that give significant risk reduction over the ML-estimator for a wide range of Θ? In this paper, we propose shrinkage estimators that attempt to infer the structure of Θ from the observed data in order to construct a good attracting subspace. In particular, the components of the observed vector are separated into clusters, and the elements in each cluster shrunk toward a common attractor. The number of clusters and the attractor for each cluster are determined from the observed vector. We provide concentration results for the squared-error loss and convergence results for the risk of the proposed estimators. The results show that the estimators give significant risk reduction over the ML-estimator for a wide range of Θ, particularly for large n. Simulation results are provided to support the theoretical claims.

This paper considers the problem of estimating a high-dimensional vector θ ∈ ℝnfrom a noisy one-time observation. The noise vector is assumed to be i.i.d. Gaussian with known variance. For the squared-error loss function, the James-Stein (JS) estimator is known to dominate the simple maximum-likelihood (ML) estimator when the dimension n exceeds two. The JS-estimator shrinks the observed vector towards the origin, and the risk reduction over the ML-estimator is greatest for θ that lie close to the origin. JS-estimators can be generalized to shrink the data towards any target subspace. Such estimators also dominate the ML-estimator, but the risk reduction is significant only when θ lies close to the subspace. This leads to the question: in the absence of prior information about θ, how do we design estimators that give significant risk reduction over the ML-estimator for a wide range of θ? In this paper, we attempt to infer the structure of θ from the observed data in order to construct a good attracting subspace for the shrinkage estimator. We provide concentration results for the squared-error loss and convergence results for the risk of the proposed estimators, as well as simulation results to support the claims. The estimators give significant risk reduction over the ML-estimator for a wide range of θ, particularly for large n.

It is well known that the interference alignment (IA) based transmission scheme proposed by Jafar and Shamai achieves the 4M over 3 sum-degrees of freedom (DoF) of the twotransmitter, two-receiver multiple-input multiple-output (MIMO) X-Network with M antennas at each node, referred to as the (2 × 2, M) X-Network. The Jafar-Shamai scheme assumes the availability of “global” channel-state-information at the transmitter (CSIT). “Local” CSIT based transmission schemes that couple IA with space-time block codes (STBC) in order to achieve the sum-DoF of the (2 × 2, M) X-Network are known specifically for M = 2; 3; 4. Further, these schemes have been proven to guarantee a diversity gain of M when finite-sized input constellations are employed. In this paper, an explicit transmission scheme that achieves the 4M over 3 sum-DoF of the (2 × 2, M) X-Network, for arbitrary M, is presented. The proposed scheme needs only local CSIT unlike the Jafar-Shamai scheme. In addition, it is shown analytically that the proposed scheme guarantees a diversity gain of M + 1 when finite-sized input constellations are employed.

In this paper, a new method is proposed to obtain full-diversity, rate-2 (rate of two complex symbols per channel use) space-time block codes (STBCs) that are full-rate for multiple input double output (MIDO) systems. Using this method, rate-2 STBCs for 4 × 2, 6 × 2, 8 × 2, and 12 × 2 systems are constructed and these STBCs are fast ML-decodable, have large coding gains, and STBC-schemes consisting of these STBCs have a non-vanishing determinant (NVD) so that they are DMT-optimal for their respective MIDO systems. It is also shown that the Srinath-Rajan code for the 4 × 2 system, which has the lowest ML-decoding complexity among known rate-2 STBCs for the 4 × 2 MIDO system with a large coding gain for 4-/16-QAM, has the same algebraic structure as the STBC constructed in this paper for the 4 × 2 system. This also settles in positive a previous conjecture that the STBC-scheme that is based on the Srinath-Rajan code has the NVD property and hence is DMT-optimal for the 4 × 2 system.

Perfect space-time block codes (STBCs) are based on four design criteria - full-rateness, non-vanishing determinant, cubic shaping and uniform average transmitted energy per antenna per time slot. Cubic shaping and transmission at uniform average energy per antenna per time slot are important from the perspective of energy efficiency of STBCs. The shaping criterion demands that the generator matrix of the lattice from which each layer of the perfect STBC is carved be unitary. In this paper, it is shown that unitariness is not a necessary requirement for energy efficiency in the context of space-time coding with finite input constellations, and an alternative criterion is provided that enables one to obtain full-rate (rate of ntcomplex symbols per channel use for an nttransmit antenna system) STBCs with larger normalized minimum determinants than the perfect STBCs. Further, two such STBCs, one each for 4 and 6 transmit antennas, are presented and they are shown to have larger normalized minimum determinants than the comparable perfect STBCs which hitherto had the best known normalized minimum determinants.

In this paper, a new method is proposed to obtain full-diversity, rate-2 (rate of 2 complex symbols per channel use) space-time block codes (STBCs) that are full-rate for multiple input, double output (MIDO) systems. Using this method, rate-2 STBCs for 4×2, 6×2, 8×2 and 12×2 systems are constructed and these STBCs are fast ML-decodable, have large coding gains, and STBC-schemes consisting of these STBCs have a non-vanishing determinant (NVD) so that they are DMT-optimal for their respective MIDO systems.

A space-time block code (STBC) is said to be multigroup decodable if the information symbols encoded by it can be partitioned into two or more groups such that each group of symbols can be maximum-likelihood (ML) decoded independently of the other symbol groups. In this paper, we show that the upper triangular matrix R encountered during the sphere decoding of a linear dispersion STBC can be rank-deficient even when the rate of the code is less than the minimum of the number of transmit and receive antennas. We then show that all known families of high-rate (rate greater than 1) multigroup decodable codes have rank-deficient R matrix even when the rate is less than the number of transmit and receive antennas, and this rank-deficiency problem arises only in asymmetric MIMO systems when the number of receive antennas is strictly less than the number of transmit antennas. Unlike the codes with full-rank R matrix, the complexity of the sphere decoding-based ML decoder for STBCs with rank-deficient R matrix is polynomial in the constellation size, and hence is high. We derive the ML sphere decoding complexity of most of the known high-rate multigroup decodable codes, and show that for each code, the complexity is a decreasing function of the number of receive antennas.

For any nt transmit, nr receive antenna ( nt×nr) multiple-input multiple-output (MIMO) system in a quasi-static Rayleigh fading environment, it was shown by Elia that linear space-time block code schemes (LSTBC schemes) that have the nonvanishing determinant (NVD) property are diversity-multiplexing gain tradeoff (DMT)-optimal for arbitrary values of nr if they have a code rate of nt complex dimensions per channel use. However, for asymmetric MIMO systems (where ), with the exception of a few LSTBC schemes, it is unknown whether general LSTBC schemes with NVD and a code rate of nr complex dimensions per channel use are DMT optimal. In this paper, an enhanced sufficient criterion for any STBC scheme to be DMT optimal is obtained, and using this criterion, it is established that any LSTBC scheme with NVD and a code rate of min{nt,nr} complex dimensions per channel use is DMT optimal. This result settles the DMT optimality of several well-known, low-ML-decoding-complexity LSTBC schemes for certain asymmetric MIMO systems.

Perfect space-time block codes (STBCs) are based on four design criteria-full-rateness, nonvanishing determinant, cubic shaping, and uniform average transmitted energy per antenna per time slot. Cubic shaping and transmission at uniform average energy per antenna per time slot are important from the perspective of energy efficiency of STBCs. The shaping criterion demands that the generator matrix of the lattice from which each layer of the perfect STBC is carved be unitary. In this paper, it is shown that unitariness is not a necessary requirement for energy efficiency in the context of space-time coding with finite input constellations, and an alternative criterion is provided that enables one to obtain full-rate (rate of nt complex symbols per channel use for an nt transmit antenna system) STBCs with larger normalized minimum determinants than the perfect STBCs. Further, two such STBCs, one each for 4 and 6 transmit antennas, are presented and they are shown to have larger normalized minimum determinants than the comparable perfect STBCs which hitherto had the best-known normalized minimum determinants.

A Space-Time Block Code (STBC) is said to be multigroup ML decodable if the information symbols encoded by it can be partitioned into two or more groups, such that each group of symbols can be ML decoded independently of the other symbol groups. In this paper, we show that the upper triangular matrix R encountered during the sphere decoding of a linear dispersion STBC can be rank-deficient even when the rate of the code is less than the minimum of the number of transmit and receive antennas. We then show that all known families of high rate (rate greater than 1) multigroup ML decodable codes have rank-deficient R matrix, even when the rate is less than the number of transmit and receive antennas, and this rank-deficiency problem arises only when the number of receive antennas is strictly less than the number of transmit antennas. Unlike the codes with full-rank R matrix, the average sphere decoding complexity of the STBCs whose R matrix is rank-deficient is polynomial in the constellation size, and hence is high. We derive the sphere decoding complexity of most of the known high rate multigroup ML decodable codes, and show that for each code, the complexity is a decreasing function of the number of receive antennas.

For an nttransmit, nrreceive antenna (nt× nr) MIMO system with quasi-static Rayleigh fading, it was shown by Elia et al. that space-time block code-schemes (STBC-schemes) which have the non-vanishing determinant (NVD) property and are based on minimal-delay STBCs (STBC block length equals nt) with a symbol rate of ntcomplex symbols per channel use (rate-ntSTBC) are diversity-multiplexing gain tradeoff (DMT)-optimal for arbitrary values of nr. Further, explicit linear STBC-schemes (LSTBC-schemes) with the NVD property were also constructed. However, for asymmetric MIMO systems (where nrt), with the exception of the Alamouti code-scheme for the 2×1 system and rate-1, diagonal STBC-schemes with NVD for an nt×1 system, no known minimal-delay, rate-nrLSTBC-scheme has been shown to be DMT-optimal. In this paper, we first obtain an enhanced sufficient criterion for an STBC-scheme to be DMT optimal and using this result, we show that for certain asymmetric MIMO systems, many well-known LSTBC-schemes which have low ML-decoding complexity are DMT-optimal, a fact that was unknown hitherto.

Precoding for multiple-input, multiple-output (MIMO) antenna systems is considered with perfect channel knowledge available at both the transmitter and the receiver. For 2 transmit antennas and QAM constellations, a precoder that is approximately optimal (with respect to the minimum Euclidean distance between points in the received signal space) among real-valued precoders based on the singular value decomposition (SVD) of the channel is proposed. The proposed precoder is obtainable easily for arbitrary QAM constellations, unlike the known complex-valued optimal precoder by Collin et al. for 2 transmit antennas which is in existence for 4-QAM alone and is extremely hard to obtain for larger QAM constellations. The proposed precoding scheme is extended to higher number of transmit antennas on the lines of the E-dminprecoder for 4-QAM by Vrigneau et al.. The proposed precoder has an ML-decoding complexity of O(√M) as against the E-dminprecoder's complexity of O(M√M) (M = 4). Compared with the recently proposed X- and Y - precoders, the error performance of the proposed precoder is significantly better. The proposed precoder provides full-diversity for QAM constellations and this is supported by simulation plots of the word error probability for 2 × 2, 4 × 4 and 8 × 8 systems.

The Generalized Distributive Law (GDL) is a message passing algorithm which can efficiently solve a certain class of computational problems, and includes as special cases the Viterbi's algorithm, the BCJR algorithm, the Fast-Fourier Transform, Turbo and LDPC decoding algorithms. In this paper GDL based maximum-likelihood (ML) decoding of Space-Time Block Codes (STBCs) is introduced and a sufficient condition for an STBC to admit low GDL decoding complexity is given. Fast-decoding and multigroup decoding are the two algorithms used in the literature to ML decode STBCs with low complexity. An algorithm which exploits the advantages of both these two is called Conditional ML (CML) decoding. It is shown in this paper that the GDL decoding complexity of any STBC is upper bounded by its CML decoding complexity, and that there exist codes for which the GDL complexity is strictly less than the CML complexity. Explicit examples of two such families of STBCs is given in this paper. Thus the CML is in general suboptimal in reducing the ML decoding complexity of a code, and one should design codes with low GDL complexity rather than low CML complexity.

It is well known that the space-time block codes (STBCs) from complex orthogonal designs (CODs) are single-symbol decodable/symbol-by-symbol decodable (SSD). The weight matrices of the square CODs are all unitary and obtainable from the unitary matrix representations of Clifford Algebras when the number of transmit antennasnis a power of 2. The rate of the square CODs forn= 2ahas been shown to be [(a+1)/(2a)] complex symbols per channel use. However, SSD codes having unitary-weight matrices need not be CODs, an example being the minimum-decoding-complexity STBCs from quasi-orthogonal designs. In this paper, an achievable upper bound on the rate of any unitary-weight SSD code is derived to be [(a)/(2a-1)] complex symbols per channel use for 2aantennas, and this upper bound is larger than that of the CODs. By way of code construction, the interrelationship between the weight matrices of unitary-weight SSD codes is studied. Also, the coding gain of all unitary-weight SSD codes is proved to be the same for QAM constellations and conditions that are necessary for unitary-weight SSD codes to achieve full transmit diversity and optimum coding gain are presented.

For annttransmit,nrreceive antenna system (nt×nrsystem), a full-rate space time block code (STBC) transmits at leastnmin=min(nt,nr) complex symbols per channel use. The well-known Golden code is an example of a full-rate, full-diversity STBC for two transmit antennas. Its ML-decoding complexity is of the order ofM2.5for squareM-QAM. The Silver code for two transmit antennas has all the desirable properties of the Golden code except its coding gain, but offers lower ML-decoding complexity of the order ofM2. Importantly, the slight loss in coding gain is negligible compared to the advantage it offers in terms of lowering the ML-decoding complexity. For higher number of transmit antennas, the best known codes are the Perfect codes, which are full-rate, full-diversity, information lossless codes (fornr≥nt) but have a high ML-decoding complexity of the order ofMntnmin(for nrrwith reduced ML-decoding complexity of the order of Mnt(nmin-3/4)-0.5 is presented. The codes constructed are also information lossless fornr≥nt, like the Perfect codes, and allow higher mutual information than the comparable punctured Perfect codes fornrnt. These codes are referred to as the generalized Silver codes, since they enjoy the same desirable properties as the comparable Perfect codes (except possibly the coding gain) with lower ML-decoding complexity, analogous to the Silver code and the Golden code for two transmit antennas. Simulation results of the symbol error rates for four and eight transmit antennas show that the generalized Silver codes match the punctured Perfect codes in error performance while offering lower ML- decoding complexity.

For an nttransmit, nrreceive antenna system (nt× nrsystem), a fall-rate space time block code (STBC) transmits nmin= min(nt, nr) complex symbols per channel use and in general, has an ML-decoding complexity of the order of Mntnmin(considering square designs), where M is the constellation size. In this paper, a scheme to obtain a fullrate STBC for 2atransmit antennas and any nτ, with reduced ML-decoding complexity of the order of Mnt(nmin-3/4)-0.5, is presented. The well known Silver code for 2 transmit antennas is a special case of the proposed scheme. Further, it is shown that the codes constructed using the scheme have higher ergodic capacity than the well known punctured Perfect codes for nrt. Simulation results of the symbol error rates are shown for 8 × 2 systems, where the comparison of the proposed code is with the punctured Perfect code for 8 transmit antennas. The proposed code matches the punctured Perfect code in error performance, while having reduced ML-decoding complexity and higher ergodic capacity.

For an nttransmit, nrreceive antenna system (nt× nrsystem), a full-rate space time block code (STBC) transmits min(nt, nr) complex symbols per channel use. In this paper, a scheme to obtain a full-rate STBC for 4 transmit antennas and any nr, with reduced ML-decoding complexity is presented. The weight matrices of the proposed STBC are obtained from the unitary matrix representations of a Clifford Algebra. By puncturing the symbols of the STBC, full rate designs can be obtained for nrr, the proposed design offers the least ML-decoding complexity among known codes. The proposed design is comparable in error performance to the well known Perfect code for 4 transmit antennas while offering lower ML-decoding complexity. Further, when nr< 4, the proposed design has higher ergodic capacity than the punctured Perfect code. Simulation results which corroborate these claims are presented.

This paper proposes a full-rate, full-diversity space-time block code (STBC) with low maximum likelihood (ML) decoding complexity and high coding gain for the 4 transmit antenna, 2 receive antenna (4 times 2) multiple-input multiple-output (MIMO) system that employs 4/16-QAM. For such a system, the best code known is the DjABBA code and recently, Biglieri, Hong and Viterbo have proposed another STBC (BHV code) for 4-QAM which has lower ML-decoding complexity than the DjABBA code but does not have full-diversity like the DjABBA code. The code proposed in this paper has the same ML-decoding complexity as the BHV code for any squareM-QAM but has full- diversity for 4- and 16-QAM. Compared with the DjABBA code, the proposed code has lower ML-decoding complexity for squareM-QAM constellation, higher coding gain for 4- and 16-QAM, and hence a better codeword error rate (CER) performance. Simulation results confirming this are presented.

A Space-Time Block Code (STBC) in K-variables is said to be g-Group ML-Decodable (GMLD) if its Maximum-Likelihood (ML) decoding metric can be written as a sum of g independent terms, with each term being a function of a subset of the K variables. In this paper, a construction method to obtain high-rate, 2-GMLD STBCs for 2mtransmit antennas, m ≫ 1, is presented. The rate of the STBC obtained for 2mtransmit antennas is 2m−2+ 1/2mcomplex symbols per channel use. The design method is illustrated for the case of 4 and 8 transmit antennas. The code obtained for 4 transmit antennas is equivalent to the rate-5/4 Quasi-Orthogonal design (QOD) proposed by Yuen, Guan and Tjung.

This paper presents a low-ML-decoding-complexity, full-rate, full-diversity space-time block code (STBC) for a 2 transmit antenna, 2 receive antenna multiple-input multiple- output (MIMO) system, with coding gain equal to that of the best and well known Golden code for any QAM constellation. Recently, two codes have been proposed (by Paredes, Gershman and Alkhansari and by Sezginer and Sari), which enjoy a lower decoding complexity relative to the Golden code, but have lesser coding gain. The 2 times 2 STBC presented in this paper has lesser decoding complexity for non-square QAM constellations, compared with that of the Golden code, while having the same decoding complexity for square QAM constellations. Compared with the Paredes-Gershman-Alkhansari and Sezginer-Sari codes, the proposed code has the same decoding complexity for non-rectangular QAM constellations. Simulation results, which compare the codeword error rate (CER) performance, are presented.