This paper proposes a novel downlink precoding method for a cell-free massive multiple-input multiple-output (CF-mMIMO) network, requiring no channel state information sharing between the access points via fronthaul links. By drawing analogies between a CF-mMIMO network and an artificial neural network, the proposed algorithm borrows the idea of backpropagation to train the precoders and the combiners through over-the-air ping-pong signaling between the access points and user equipments. It utilizes manifolds optimization to meet the per-AP power constraint and is named as distributed quasi-neural network precoding on manifold (DQNPM). The DQNPM algorithm can accommodate a large category of objective functions for fully distributed implementation. Numerical simulations show that our method outperforms the state-of-the-art approaches, and is robust against pilot contamination.

This paper proposes a novel algorithm, named a quasi-neural network-based decoder (QNN-decoder), for a single-carrier communication system. The algorithm is designed for an inter-symbol-interference (ISI) channel that a trellis diagram can model. According to the trellis diagram, a quasi-neural network (QNN) is built to acquire the likelihoods of the received samples enabling the subsequent decoding. The QNN-decoder differs from artificial neural network (ANN) based algorithms, such as the online learning trellis diagram (OLTD), as it doesn’t rely on data but instead utilizes the physical system model. This means the QNN-decoder can use a much shorter pilot to train its network via backpropagation than OLTD. Meanwhile, the QNN-decoder doesn’t require explicit channel state information (CSI) or statistics of interference and noise. Instead, it can efficiently suppress non-Gaussian interference by learning the CSI and interference and noise statistics. Simulation results verify the QNN-decoder outperforms the state-of-the-art methods and approaches the performance limits provided by the conventional Viterbi with perfect CSI in Gaussian noise only. The QNN-detector outperforms the conventional Viterbi and OLTD with non-Gaussian interference. A few redundant nodes make the QNN-decoder robust to channel length uncertainty, and it may be easily extended to a multi-antenna system for even greater interference suppression.

This paper presents a quasi-neural network (Quasi-NN) approach for parametric channel estimation in multi-input multi-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. A unified Quasi-NN framework is proposed for both the single-user (SU) and the multi-user (MU) scenarios, enabling the joint estimation of the direction of arrival, direction of departure, time delay, complex gain, and the number of multipaths. The artificial neural network-like structure of the Quasi-NN allows the application of the backpropagation algorithm while requiring only real-time pilot signals for online network training. Furthermore, considering the issue of high pilot overhead in MU MIMO-OFDM systems, we develop a location assisted Quasi-NN (LA-QNN) that utilizes a location-parameter database to reduce the pilot overhead while maintaining accurate channel estimation. Simulation results show that the proposed Quasi-NN approaches the Cramér Rao bound, and the proposed LA-QNN scheme provides a better balance between channel estimation performance and pilot overhead in the MU scenario.

The sixth-generation (6G) communication networks target peak data rates exceeding 1Tbps, necessitating base stations (BS) to support up to 100 simultaneous data streams. However, sparse pilot allocation to accommodate such streams poses challenges for users’ channel estimation. This paper presents channel estimation considerate precoding (CECP), where BS precoders prioritize facilitating channel estimation alongside maximizing system throughput. To address the computational complexity of 6G large-scale multi-input multi-output (MIMO) systems, we propose a computationally-efficient space-time block diagonal channel shortening (ST-BDCS) precoding scheme. By leveraging the sparse Toeplitz property of orthogonal frequency division multiplexing (OFDM) channels, this time-domain precoding design effectively mitigates multi-user interference in the downlink and shortens the effective channel’s temporal length. Consequently, users can estimate the channels using sparse pilots. To enable fast implementation, we develop a generalized complex-valued Toeplitz matrix QR decomposition algorithm applicable to various space-time signal processing problems. Simulation results demonstrate that the ST-BDCS precoding method approximates the spectral efficiency performance of conventional subcarrier-by-subcarrier precoding schemes. However, it offers the advantages of accurate effective channel estimation for users and significantly reduced computational complexity for the BS.

The construction of a Golay complementary sequence (GCS) set with small number of constituent sequences and flexible length has long been an open problem. Compared with the 2-phase GCS pairs, more possible lengths were founded in literatures by extending the phase and the number of con-stituent sequences. For both mathematical theory and engineering applications, it is desirable to keep the number of constituent sequences as small as possible. In this work, we construct a 4-phase GCS set of 23+ [log2$r$sequences of arbitrary length$n$, where the 1013-base expansion of$n$has$r$nonzero digits. Specifically, the 4-phase GCS octets (sets of eight sequences) cover all the lengths no greater than 1013.

Sequences with low aperiodic autocorrelation side-lobes have been extensively researched in literatures. With sufficiently low integrated sidelobe level (ISL), their power spectrums are asymptotically flat over the whole frequency domain. However, for the beam sweeping in the massive multi-input multi-output (MIMO) broadcast channels, the flat spectrum should be constrained in a passband with tunable bandwidth to achieve the flexible tradeoffs between the beamforming gain and the beam sweeping time. Motivated by this application, we construct a family of sequences termed the generalized step-chirp (GSC) sequence with a closed-form expression, where some parameters can be tuned to adjust the bandwidth flexibly. In addition to the application in beam sweeping, some GSC sequences are closely connected with Mow's unified construction of sequences with perfect periodic autocorrelations, and may have a coarser phase resolution than the Mow sequence while their ISLs are comparable.

This paper proposes a Quasi-neural network-based detection algorithm, namely QNN-detector, for a single-carrier communication system in an inter-symbol interference (ISI) channel, which can be modeled by a trellis diagram. According to the trellis diagram, a quasi-neural network (QNN) is built to acquire the normalized likelihoods to enable the subsequent detection or decoding. The QNN can accommodate non-Gaussian interferences through ingeniously designing its hidden layers. Unlike the artificial neural network (ANN) based algorithms, which are data-driven, the QNN-detector relies on the physical system model and only needs a short pilot sequence for training. Moreover, it requires neither explicit channel state information (CSI) nor statistics of interference and noise. Simulation results illustrate that in a channel under white Gaussian noise, the QNN-detector significantly outperforms the ANN-based algorithms in that its network training requires a far shorter pilot sequence, and can approach the performance limits provided by the Viterbi detector with perfect CSI. The simulations also show that in the presence of non-Gaussian interferences, the QNN-detector can learn the distribution of the interferences and therefore suppress them effectively, while the conventional Viterbi detector fails to.

Using one-bit analog-to-digital converters (ADCs) can drastically reduce the cost and energy consumption of a wideband large array system. But it brings about challenges to the signal processing aspect of the system. This letter focuses on the estimation of a frequency-selective single-input multi-output (SIMO) channel from the received pilot signals quantized by one-bit ADCs. We first parameterize the channel by the complex gains, angles-of-arrival (AoAs), and time-delays of the multipath. We then show that a recently-developed modeling tool called quasi neural network (Quasi-NN) can be employed to model the log-likelihood function of the one-bit measurements via artfully designing the network, including its structure and the activation functions. By “training” the network, the maximum likelihood (ML) estimates of the channel parameters are obtained automatically, so is the channel state information (CSI). To expedite the network training, we employ a gradient-based method called the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm, which turns out to be much faster than the alternatives, including the widely used gradient descent algorithm with momentum acceleration.

Motivated by the recent application of two-dimensional Golay complementary arrays (2-D GCA) in uniform rectangular array (URA) -based omnidirectional precoding for the next generation of cellular communications, we propose in this paper new constructions of GCA pairs and GCA quads, which allow for more possible sizes. These constructions are facilitated by four identities over a commutative ring, of which two are established results of quaternions and octonions and the others are novel. We prove that the size of a 4-phase GCA pair is possible if the product of the array sizes in all dimensions is a 4-phase Golay number with an additional constraint on the factorization of the product. For 2-phase 2-D GCA quads, all sizes no greater than$78\times 78$can be covered. For 4-phase GCA quads, all the positive integers within 1000 can be covered for the size in one dimension. Besides producing GCAs that can accommodate to antenna arrays of various sizes, this study also yields new Hadamard matrices of sizes previously unavailable.

It is well-known that dirty paper coding (DPC)-based transceiver can achieve the sum capacity of a multi-input multi-output (MIMO) broadcast channel. In this paper, we study DPC-based hybrid precoding to maximize the sum-rate of a massive MIMO (mMIMO) downlink broadcast channel, subject to the constant modulus constraint of the analog phase shifter network (PSN). Using the duality between a massive MIMO broadcast channel (mMIMO-BC) and a massive MIMO multiple access channel (mMIMO-MAC), we propose to first optimize the transmitters and the hybrid receiver for the mMIMO-MAC, before obtaining the hybrid precoder of mMIMO-BC according to the MAC-BC duality. The algorithm is also extended for mMIMO orthogonal frequency division multiplexing (OFDM) systems over broadband frequency-selectivity channels. Numerical results show that the proposed DPC-based hybrid precoding can significantly outperform the existing linear counterpart, especially in the case of numerous users. In simulations based on the 5G new radio (5G-NR) standard, the relative gain of the proposed scheme appears prominent, which suggests that the DPC can be a worthy candidate for the future generation of wireless communications.

Cell-free massive multiple-input multiple-output (MIMO) can resolve the inter-cell interference issue in cellular networks through cooperative beamforming of the distributed access points (APs). This paper focuses on an uplink cell-free massive MIMO network and investigates novel methods to train the central processing unit (CPU), the APs, and the users in the network. To reduce the communication burden posed on the fronthaul, each AP applies receive beamforming to compress the vector signals into scalar ones before passing them to the CPU for centralized processing. By drawing analogies between an uplink cell-free network and a quasi-neural network and borrowing the idea of backpropagation algorithm, we propose a novel scheme named the distributed learning for uplink cell-free massive MIMO beamforming (DLCB), which can achieve the multi-AP cooperation without explicit estimation of their channel state information (CSI). The DLCB has low computational complexity and is applicable to various objective functions, such as the minimum mean squared error criterion and the maximum sum rate criterion. Extensive simulations verify that the proposed scheme achieves superior performance over the state-of-the-art methods.

The wireless in-band full-duplex (IBFD) technology can in theory double the system capacity over the conventional frequency division duplex (FDD) or time-division duplex (TDD) alternatives. But the strong self-interference of the IBFD can cause excessive quantization noise at the output of the analog-to-digital converters (ADCs), which hampers its real implementation. Fortunately, the reconfigurable intelligent surface (RIS) can reconfigure the wireless channels by dynamically adjusting the reflection coefficients, which makes it a promising solution to self-interference mitigation (SIM) for the IBFD system. This paper considers a RIS-assisted IBFD (RAIBFD) system where a full-duplex base station (BS), assisted by a co-located RIS, receives and transmits signals on the same frequency band simultaneously. We propose to jointly design the DL precoding matrix and the RIS coefficients to mitigate the strong self-interference before the ADCs of finite bit resolutions. To gauge the performance of the proposed RAIBFD system, we also consider an idealistic RIS-assisted IBFD (I-RAIBFD) system with ADCs of infinite bit resolutions and RIS-assisted FDD (RAFDD) system, and take them as performance benchmarks. The effectiveness of the proposed RAIBFD system is verified by simulation studies, even if the phases of the RIS have only finite resolutions.

This paper studies distributed optimization of an uplink cell-free Massive MIMO (CF-mMIMO) network. By observing some interesting analogies between the CF network and an artificial neural network (ANN), we propose to relate the uplink CF network to a so-called quasi-neural network. Borrowing the idea of the back-propagation (BP) algorithm, we propose a novel scheme to optimize the central processing unit (CPU) and the access points (APs) of the network. The proposed scheme can achieve multi-AP cooperation using only the pilot sequences, but without the channel state information (CSI). To reduce the required throughput of the fronthaul, we let each AP beamform the received vector signals into scalar ones before passing them to the CPU. The effectiveness of the proposed scheme is verified by the simulations.

A large number of Internet of Things (IoT) devices have been interconnected for information collection and exchange. The data are only meaningful if it is captured at the expected location (i.e., the IoT devices or sensors are not removed accidentally or intentionally). This article presents a new algorithm, which cooperatively locates multiple IoT devices deployed in a 3-D space based on pairwise Euclidean distance measurements. When the distance measurement noises are negligible, a new feasibility problem of rank-3 variables is formulated. We solve the problem using the difference-of-convex (DC) programming to preserve the rank-3 constraints, rather than relaxing the constraints, using semidefinite relaxation (SDR). When the distance measurements are corrupted by additive noises and nonlight-of-sight (NLOS) propagation, a maximum-likelihood estimation (MLE) problem is formulated and transformed to a DC program solved with the rank-3 constraints preserved. Simulation results indicate that the proposed approach can achieve satisfactory accuracy results with a low complexity and strong robustness to the irregular topology, poor connectivity, and measurement errors, as compared to existing SDR-based alternatives.

This paper studies machine learning-assisted optimal receivers for a communication system with memory, which can be modelled by a trellis diagram. The prerequisite of the optimal receiver is to obtain the likelihoods of the received samples under different state transitions. We propose to learn the trellis diagram real-time using an artificial neural network (ANN) trained by a pilot sequence. This approach, termed as the online learning trellis diagram (OLTD), requires neither the channel state information (CSI) nor statistics of the noise, and can be incorporated into the classic Viterbi and the BCJR algorithm. In a channel with non-Gaussian noise, the OLTD method can significantly outperform the model-based methods that use Gaussian assumption. It requires much less training overhead than the state-of-the-art ANN-assisted methods. As an illustrative example, the OLTD-based BCJR is applied to a Bluetooth low energy (BLE) receiver trained only by a 256-sample pilot sequence. Moreover, the OLTD-based BCJR can accommodate for turbo equalization. As an interesting by-product, we propose an enhancement to the BLE standard by introducing a bit interleaver to its physical layer; the resultant improvement of the receiver sensitivity can make it a better fit for some Internet of Things (IoT) communications.

Unmanned Aerial Vehicle (UAV)-based streaming media transmission may become unstable when the bit rate generated by the source load exceeds the channel capacity owing to the UAV location and speed change. The change of the location can affect the network connection, leading to reduced transmission rate; the change of the flying speed can increase the video payload due to more I-frames. To improve the transmission reliability, in this paper we design a Client-Server-Ground&User (C-S-G&U) framework, and propose an algorithm of splitting-merging stream (SMS) for multi-link concurrent transmission. We also establish multiple transport links and configure the routing rules for the cross-layer design. The multi-link transmission can achieve higher throughput and significantly smaller end-to-end delay than a single-link especially in a heavy load situation. The audio and video data are packaged into the payload by the Real-time Transport Protocol (RTP) before being transmitted over the User Datagram Protocol (UDP). The forward error correction (FEC) algorithm is implemented to promote the reliability of the UDP transmission, and an encryption algorithm to enhance security. In addition, we propose a Quality of Service (QoS) strategy so that the server and the user can control the UAV to adapt its transmission mode dynamically, according to the load, delay, and packet loss. Our design has been implemented on an engineering platform, whose efficacy has been verified through comprehensive experiments.

This paper studies a distributed scheme for a multi-input multi-output (MIMO) relay network, where the transmit nodes are subject to the nonlinear instantaneous power constraints. We introduce a novel perspective of regarding a relay network as a so-termed quasi-neural network by drawing its striking analogies with a (four-layer) artificial neural network (ANN). We propose a nonlinear amplify-and-forward (NAF) scheme inspired by the back-propagation (BP) algorithm, namely the NAF-BP, to optimize the transceivers to maximize the output signal-to-interference-plus-noise ratio (SINR) of the data streams. The NAF-BP algorithm can be implemented in a distributed manner with no channel state information (CSI) and no data exchange between the relay nodes. The NAF-BP can also coordinate the distributed relay nodes to form a virtual array to suppress interferences from unknown directions. Extensive simulations verify the effectiveness of the proposed scheme.

The estimation of velocity, angle-of-arrival (AOA), and range of a target has been researched for decades, as it finds wide applications in radar and wireless communications. In recent years, this classic problem has gained renewed interest with the advent of 5G internet of things (IoT) technologies, owing to the numerous emerging localization-related applications. This paper studies the joint estimation of velocity, AOA, and range (JEVAR) of a target in a multipath environment. To solve the JEVAR problem, we propose a novel scheme, which has the target transmit a pair of conjugate Zadoff-Chu (ZC) sequences and has the multi-antenna receiver conduct maximum likelihood (ML) estimation. The simulations verify the effectiveness of the proposed scheme by showing that its performance can approach the Cramer-Rao bound (CRB).

To have a global time clock is important for many latency-sensitive wireless network applications, including the industrial Internet-of-Things, the distributed time division multi-access (TDMA) scheduling and network localization. As the unknown propagation delays between the distributed nodes presents a challenge to network time synchronization, this paper proposes to eliminate the impact of the propagation delays upon network clock synchronization via having all the nodes broadcast beacons to their one-hop neighbors. For a performance benchmark, we first consider a simplistic scenario where the time-stamp information broadcasted from all the nodes can be gathered by a central node, and propose a centralized algorithm to estimate (and henceforth to compensate) not only the time offsets but the skewness of the nodes' clocks against a virtual global consensus. Despite its optimum performance, the benchmark algorithm requires some major overhead to aggregate all the information at a central node. To reduce the overhead, we propose a distributed algorithm, in which the nodes use only the time-stamp information of its own and of its one-hop neighbors to reach consensus through rounds of beacon broadcasting. Simulation results verify the effectiveness of both algorithms. We find that the sprawling area of the network does not affect the synchronization performance.

Direction-of-arrival (DOA) estimation is one of the most demanding tasks for the millimeter wave (mmWave) communication of massive multiple-input multiple-output (MIMO) systems with the hybrid beamforming (HBF) architecture. In this letter, we focus on the optimization of the HBF matrix for receiving pilots to enhance the DOA estimation performance. Motivated by the fact that many existing DOA estimation algorithms can achieve the Cramér-Rao bound (CRB), we formulate the HBF optimization problem aiming at minimizing the CRB with the prior knowledge of the rough DOA range. Then, to tackle the problem with intractable non-convex constraints introduced by the analog beamformers, we propose an efficient manifold optimization (MO) based algorithm. Simulation results demonstrate the significant improvement of the proposed CRB-MO algorithm over the conventional HBF algorithms and provide insights for the HBF design in the beam training stage for practical applications.

This paper proposes a novel scheme for mitigating strong interferences, which is applicable to various wireless scenarios, including full-duplex wireless communications and uncoordinated heterogeneous networks. As strong interferences can saturate the receiver’s analog-to-digital converters (ADC), they need to be mitigated both before and after the ADCs, i.e., via hybrid processing. The key idea of the proposed scheme, namely the Hybrid Interference Mitigation using Analog Prewhitening (HIMAP), is to insert an$M$-input$M$-output analog phase shifter network (PSN) between the receive antennas and the ADCs to spatially prewhiten the interferences, which requires no signal information but only an estimate of the covariance matrix. After interference mitigation by the PSN prewhitener, the preamble can be synchronized, the signal channel response can be estimated, and thus a minimum mean squared error (MMSE) beamformer can be applied in the digital domain to further mitigate the residual interferences. The simulation results verify that the HIMAP scheme can suppress interferences 80dB stronger than the signal by using off-the-shelf phase shifters (PS) of 6-bit resolution.

Clock synchronization has been a challenging task in the design of wireless networks because the synchronization accuracy suffers from uncertain transmission delay and/or packet loss due to poor wireless channel conditions. To address this problem, this paper develops robust clock synchronization schemes based on the matrix completion theory to improve the accuracy in presence of random transmission delay and packet loss. We propose a matrix completion-based maximum likelihood estimator (MC-MLE) to estimate the clock offset and clock skew under Gaussian transmission delay model. Thanks to the denoise feature of matrix completion, the proposed schemes outperform the maximum likelihood estimator (MLE) in the presence of packet loss and random transmission delay. That is, the proposed schemes are closer to the Cramer-Rao lower bound (CRLB) than the MLE when the timestamp packets are randomly corrupted. The robustness and accuracy of the proposed schemes are validated by numerical results.

For the millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems, hybrid beamforming has been proposed to reap the great gain of the large number of antennas with a limited number of radio frequency (RF) chains. The hybrid beamforming relies on a phase shifter network (PSN) in the RF domain to steer the signal power along the desired direction (or subspace). However, the RF circuits connecting the antennas and the RF chains can introduce distinct phase deviations, which need to be calibrated for efficient hybrid beamforming designs. This paper develops a novel approach to the estimation and calibration of the PSN in mmWave massive MIMO communication systems. To this end, we formulate the calibration problem as an optimization program with the constant modulus constraint. An efficient iterative algorithm is then proposed to estimate the phase deviations to be calibrated. We also derive the Cramer-Rao lower bound (CRLB) of the phase estimates. The numerical results validate the efficiency of our approach by showing that the algorithm yields estimates whose mean squared errors (MSE) are close to the CRLB.

In public channels, common signals are required to transmit omnidirectionally to ensure cell-wide coverage. In this paper, we focus on omnidirectional beamforming for common signal transmission in a massive multiple-input multiple-output (MIMO) system equipped with a uniform rectangular array (URA). We first model the omnidirectional transmission as a feasibility optimization problem in a matrix form. By counting the number of equality constraints and the degrees of freedom of the matrix variable, we conjecture that it takes at least three beamforming vectors to achieve constant-power signal transmission at any direction for a URA with more than two rows/columns. We then propose an efficient iterative rank-reduction algorithm, which can obtain three beamforming vectors that can generate a perfectly flat radiation beampattern, but cannot reduce further for a URA with more than two rows/columns. That is, the algorithm numerically verifies the conjecture. The numerical results validate the superior performance of the proposed scheme over the existing alternatives.

In a mobile ad-hoc network (MANET), concurrent transmission enabled via interference alignment or transmit and receive beamforming between$K$transmitters and$K$receivers can result in a significant increase in the network’s sum throughput. However, to achieve this high sum-throughput each of the$K$receivers must: 1) determine the presence of its desired transmitter; 2) correct the frequency and timing offset of the desired transmitter; 3) estimate the channel from the desired transmitter; and 4) estimate either the channel from each of the$K-1$interfering transmitters or the covariance matrix of the interferences. In this paper, we address the challenges associated with enabling concurrent links within a MANET. By exploiting the unique properties of Zadoff–Chu (ZC) sequences, we propose a practical mechanism for all receivers to achieve the required synchronization and channel estimations concurrently. We also propose a constant false alarm rate detection algorithm to detect the presence of the ZC sequences in a high-interference environment in the absence of frequency and timing lock. Simulation results verified the great performance of our approach in sequence detection, the carrier offset, timing offset, channel estimate and covariance estimates, in both frequency flat channels and frequency selective channels.

This paper presents an in-depth analysis of the zero forcing (ZF) and minimum mean squared error (MMSE) equalizers applied to wireless multiinput multioutput (MIMO) systems with no fewer receive than transmit antennas. In spite of much prior work on this subject, we reveal several new and surprising analytical results in terms of output signal-to-noise ratio (SNR), uncoded error and outage probabilities, diversity-multiplexing (D-M) gain tradeoff and coding gain. Contrary to the common perception that ZF and MMSE are asymptotically equivalent at high SNR, we show that the output SNR of the MMSE equalizer (conditioned on the channel realization) is$\rho_{\rm mmse} = \rho_{\rm zf}+\eta_{\ssr snr}$, where$\rho_{\rm zf}$is the output SNR of the ZF equalizer and that the gap$\eta_{\ssr snr}$is statistically independent of$\rho_{\rm zf}$and is a nondecreasing function of input SNR. Furthermore, as${\ssr snr}\ura{} \infty$,$\eta_{\ssr snr}$converges with probability one to a scaled${\cal F}$random variable. It is also shown that at the output of the MMSE equalizer, the interference-to-noise ratio (INR) is tightly upper bounded by${{\eta_{\ssr snr}}\over {\rho_{\rm zf}}}$. Using the decomposition of the output SNR of MMSE, we can approximate its uncoded error, as well as outage probabilities through a numerical integral which accurately reflects the respective SNR gains of the MMSE equalizer relative to its ZF counterpart. The$\epsilon$-outage capacities of the two equalizers, however, coincide in the asymptotically high SNR regime. We also provide the solution to a long-standing open problem: applying optimal detection ordering does not improve the D-M tradeoff of the vertical Bell Labs layered Space-Time (V-BLAST) architecture. It is shown that optimal ordering yields a SNR gain of$10\log_{10}N$dB in the ZF-V-BLAST architecture (where$N$is the number of transmit antennas) whereas for the MMSE-V-BLAST architecture, the SNR gain due to ordered detection is even better and significantly so.

The large gain promised by the multi-input multioutput (MIMO) technology comes with a cost. In particular, multiple analog radio frequency (RF) chains, which are expensive and power consuming, are required at both the transmitter and receiver sides. On the other hand, the antennas connecting to the RF chains are less expensive. Hence, one engineering compromise is to implement more antennas than RF chains and to use only a subset of them based on some antenna selection (AS) algorithm. An interesting question therefore arises: given a RF chain limited MIMO system, what is the fundamental performance gain by adding more antennas? In this two-part paper, we answer this question by using the diversity-multiplexing (D-M) gain tradeoff metric. Consider a Rayleigh fading channel with Mt) antennas and Lt(Lt⩽ Mt) RF chains at the transmitter while Mrantennas and Lr(Lr⩽ Mr) RF chains at the receiver. We obtain the fundamental D-M tradeoff as a function of Mt, Mr, and min(Lr, Lt). Referring to the special case where Lt= Mt) and Lr= Mras the RF unlimited system (or full system) and RF limited system (or pruned system) otherwise, we prove that the pruned system with optimal channel-dependent AS has the same D-M tradeoff as the full system if the multiplexing gain is less than some integer threshold P, while it suffers from some diversity gain loss for multiplexing gains larger than P. In particular, if min(Lr, Lt) = K = min(Mr, Mt), then P = K, i.e. the D-M tradeoffs of the pruned system and the full system are the same. Moreover, this result can be extended to more general fading channels such as Nakagami channel. A fast and D-M tradeoff-optimal AS algorithm is proposed as a byproduct of our analysis. Index Terms?Antenna selection, diversity gain, fast algorithm, MIMO, Nakagami fading, outage probability, Rayleigh fading, spatial multiplexing gain, tradeoff.

The V-BLAST (vertical Bell Labs layered Space- Time) architecture involves independent coding/decoding per antenna (layer) with equal rate and power per antenna and a fixed order of nulling/canceling decoding but is known to suffer from poor performance; for example, in a multi-input multioutput (MIMO) Rayleigh fading channel with Mt transmit and Mr receive antennas (Mr⩾ Mt), the diversity-multiplexing gain (D-M) tradeoff is just (Mr- Mt+1)(1 - r/Mt) for r ε [0,Mt]. There are two remedies available, namely, (i) channel-dependent ordered decoding at the receiver and (ii) allocation of rates and powers across the transmit antennas. However, the former doesn't improve the D-M tradeoff curve and while the latter does (with maximum diversity gain Mr and maximum multiplexing gain Mt), its tradeoff curve is still significantly inferior compared to the D-M tradeoff curve of the optimum (unconstrained) MIMO architecture. In this two-part paper, it is shown that a dramatically better D-M tradeoff and error (e.g. outage) probability can be obtained if the two remedies, i.e., ordered BLAST decoding and rate/power allocation, are judiciously combined. Indeed, a framework is developed for jointly designing channel-dependent ordered decoding at the receiver and decoding order-dependent rate/power allocation at the transmitter. The framework encompasses a large class of new spatial multiplexing architectures (SMAs). In this part, an upper bound to the D-M tradeoff for this class is obtained and found to be quite close to the optimal D-M tradeoff of the MIMO channel. Two special SMAs are proposed corresponding to two different decoding orderings. One is called the Norm ordering Rate Tailored SMA (NRT-SMA), and the other is called the Greedy ordering Rate Tailored SMA (GRT-SMA).

The study of the class of new spatial multiplexing architectures (SMAs) is continued. As introduced in Part I of this paper, the SMAs consist of joint design of rate and power allocation to the spatially-multiplexed substreams at the transmitter and ordered nulling/canceling detection/decoding at the receiver. This was studied in Part I under the diversitymultiplexing tradeoff framework. Here the more detailed and practical problem of allocating rates and powers across the transmit antennas is investigated to minimize the overall system (uncoded or outage) error probability. Since the layer gains are unavailable to the transmitter, the rates and powers must be allocated based on the statistics of the layer gains. However, the channel dependent ordering rules make the precise distributions of the layer gains complicated or intractable. To solve this problem, a simple, yet effective, four-parameter hyperbola model is proposed to closely approximate the error probability of each layer. With this approximation, the computation of rate and power allocation according to the criterion of minimizing the maximal error probability of all the substreams is given. Simulation results validate the superior performance of the proposed SMAs, especially that of the Greedy ordering Rate Tailored SMA (GRT-SMA). Although the rate and power allocation method is obtained under the assumption of iid Rayleigh fading channel, the proposed SMAs also work well in other types of fading channels (such as in correlated and Rician channels).

The decision feedback detector (DFD) can achieve the high spectral efficiency of a MIMO channel in that it converts the MIMO channel into multiple parallel layers, through which independently coded data substreams may be spatially multiplexed and be transmitted over the same time and frequency slot. Because of independent coding/decoding, the DFD may apply arbitrarily ordered detection. In this paper, we analyze the effect of detection ordering on the diversity gain per layer of the DFD in a MIMO Rayleigh-fading channel. For a MIMO channel withMttransmit andMr(MrgesMt) receive antennas, we derive an upper bound to the diversity gain per layer for any detection ordering, i.e.,Diles (Mr-i+ 1)(Mt-i+ 1) for 1 lesilesMt. We show that the DFD using the so-called greedy ordering rule can achieve the diversity gain upper bound. We further study the diversity-multiplexing (D-M) gain tradeoff of DFD in a pruned MIMO channel whereLt(Ltles Mt) transmit andLr(LtlesLrlesMr) receive antennas are selected out of the full system. It is shown that the D-M tradeoff of DFD in an optimally pruned channel isddfd,opt(r) = (Mr-Lt+ 1)(Mt-Lt+ 1)(1 -r/Lt). Such a tradeoff-optimally pruned system can be obtained by a fast antenna selection algorithm. This result has interesting implications to the multi-access communications with user selection. The theoretical analysis is validated by the numerical examples.

The diversity-multiplexing (D-M) gain tradeoff is a popular benchmark for measuring the performance of multi-input multi-output (MIMO) systems. This paper studies the fundamental D-M gain tradeoff of a pruned MIMO system where Lttransmit and Lrreceive antennas are selected out of the full system with Mttransmit and Mrreceive antennas (Lt≤ Mtand Lr≤ Mr). It is shown that a MIMO system with the optimal antenna selection (AS) has the same D-M tradeoff as the full system if the multiplexing gain is less than some threshold P, although it suffers from some diversity gain loss for the multiplexing gain larger than P. On the other hand, this paper quantifies, in terms of the D-M tradeoff, the gain of introducing additional transmit/receive antennas without increasing the number of RF chains and coding complexity. We also propose a fast and D-M tradeoff-optimal AS algorithm as a byproduct of our analysis.

In this paper, we present an asymptotic analysis of the V-BLAST scheme at high signal-to-noise ratio (SNR) region. We consider point-to-point MIMO communications over an i.i.d. Rayleigh flat fading channel with n transmitting antennas and m (m /spl ges/ n) receiving antennas. Both the zero-forcing V-BLAST (ZF-V-BLAST) and minimum mean-squared-error V-BLAST (MMSE-V-BLAST) are analyzed with respect to their diversity gains and BER performances. We show that the diversity gain of V-BLAST, including ZF-V-BLAST and MMSE-V-BLAST, with optimal ordering is m - n + 1, i.e. applying the optimal ordering technique does not improve the diversity gain. Contrary to the common perception that the MMSE and ZF estimators have asymptotically the same post-processing SNR for high input SNR, we show that the difference between the post-processing SNRs of the two estimators does not vanish for high SNR. We also quantify the remarkable BER performance advantage of the MMSE-V-BLAST over the ZF-V-BLAST for high SNR.

Assuming the availability of the channel state information at the transmitter (CSIT) and receiver (CSIR), we consider the joint optimal transceiver design for multi-input multi-output (MIMO) communication systems. Using our recently developed generalized triangular decomposition (GTD), we propose a scheme, which we refer to as adaptable channel decomposition (ACD), to decompose a MIMO channel into multiple subchannels with prescribed capacities, or equivalently, signal-to-interference-and-noise ratios (SINR). We also determine the subchannel capacity region such that the channel decomposition is capacity lossless. This scheme is particularly relevant to the applications where independent data streams with different quality-of-services (QoS) share the same MIMO channel.

We present a multi-input multi-output (MIMO) transceiver design that combines the geometric mean decomposition (GMD) with either the conventional zero-forcing VBLAST decoder (ZF-VBLAST), or the zero-forcing dirty paper precoder (ZF-DP). Our approach decomposes a MIMO channel into multiple identical subchannels, which obviates the need of bit allocation and simplifies the design of modulation/demodulation and coding/decoding schemes. Moreover, we prove that our scheme is asymptotically optimal for high signal-to-noise ratio (SNR) in terms of both the channel throughput and the bit-error-rate (BER) performance.

The amplitude estimation of a signal whose waveform is known (up to an unknown scaling factor) in the presence of interference and noise is of interest in several applications including using the emerging quadrupole resonance (QR) technology for explosive detection. In such applications a sensor array is often deployed for interference suppression. This paper considers the complex amplitude estimation of a known waveform signal whose array response is also known a priori. We study a practical scenario where the interference and noise is both spatially and temporally correlated. We model the interference and noise vector as a multichannel autoregressive (AR) random process. A cyclic iterative ML (IML) method is presented. We show that in most cases the IML method is superior to its simple ML counterpart that ignores the temporal correlation of the interference and noise.