Reconfigurable Intelligent Surfaces (RIS) appear as a promising solution to combat wireless channel fading and interferences. However, the elements of the RIS need to be properly oriented to boost the data transmission rate. In this work, we propose a new strategy to adaptively configure the RIS without Channel State Information (CSI). Our goal is to minimize the number of RIS configurations to be tested to find the optimal one. We formulate the problem as a stochastic shortest path problem, and use Q-Learning to solve it.

In this paper, we propose a novel low-complexity, near-optimal soft-input soft-output detector for N × M multiple-input multiple-output (MIMO) systems. Our algorithm is based on the combination of minimum mean square error decision feedback equalization (MMSE-DFE) and conditional optimization. In a round-robin fashion, one symbol is detected using exhaustive search in such a way that all N × (M - 1) submatrices of the baseband channel matrix are considered and the one with the best metric is chosen. This search over all columns of the channel matrix, which can be performed in parallel, has the advantages of improving the performance of the hard-output version of the detector, and refining the list of candidates for efficient implementation of the soft-output detector for MIMO systems with error correcting codes. In particular, it is shown that the error performance of the soft-output system is comparable to that of the list sphere decoder (LSD) but with much smaller list size, and hence smaller complexity than the latter. We also analyze the performance and complexity of the proposed algorithm and discuss different techniques to further reduce its complexity without affecting the performance. Finally, the obtained theoretical results are validated via simulations.

In this paper, we propose a novel low-complexity, near-optimal detector for multiple-input multiple-output (MIMO) systems. We consider the combination of minimum mean square error generalized decision feedback equalization (MMSE-GDFE) and conditional optimization. All submatrices of QR decomposition of regularized baseband channel matrix are considered in a round-robin fashion for detecting one symbol using exhaustive search over the constellation points. Among all possible candidates, the one with the best metric is chosen. This search over all columns of the channel matrix, which can be performed in parallel, improves the error performance of the hard-output version of the detector. Additionally, the list of candidates can be utilized for efficient implementation of the soft-output detector for MIMO systems with error correcting codes. We also discuss different techniques to further reduce the complexity of the proposed algorithm without affecting the performance. Finally, the performance of the proposed detector is analyzed and the obtained theoretical results are validated via simulations.

In this paper, we propose an efficient detector for large-scale multi-input multi-output (MIMO) systems. Our proposed detector is mainly based on conditional (or subspace) detection and partial lattice reduction (PLR) algorithm tailored to an appropriate channel ordering. The conditional detection for finding one symbol through an exhaustive search over the constellation points is considered. Then, part of the channel is reduced by the PLR technique in order to compensate for the degradation of diversity due to limiting the exhaustive search levels to one. In order to improve the error performance, all other remaining non-reduced columns are also considered for conditional detection. In the proposed detector, part of the detection complexity is transferred to the preprocessing stage where the PLR algorithm is implemented. Consequently, for quasi-static channels where the channel is constant over a long block, the cost of PLR can be negligible. The improvement over the error performance of the state-of-the-art detection schemes is investigated for some large-scale MIMO systems.

In this paper, we investigate the dependency of the diversity-multiplexing tradeoff (DMT) of lognormal channels on their dB spread for both single-input-single-output (SISO) and multiple-input-multiple-output (MIMO) channels. We tackle both the finite and the asymptotically high signal-to-noise ratio (SNR) regimes. The finite SNR DMT for a SISO lognormal channel is shown to be strongly dependent on the dB spread, [10/ln(10)]σx, where σxis the shaping parameter of the lognormal distribution. For different values of σx, the outage probability versus SNR curves on a log-log scale have different slopes and significant flooring for high values of σx. In order to capture the DMT dependency on the dB spread, the SNR gap between the outage curves of lognormal channels with different σxis derived. Moreover, the relative slopes of the outage probability curves are derived. Given that in the limiting-case of high SNR, the DMT for MIMO channels are dictated by the tail behaviour of their probability density function [1] and based on the similarities between the tail behavior of lognormal and normal random variables for very small σx≪1 dB, and lognormal and Gamma random variables for small to medium σx≤ 1.5 dB, we analyze the dependency of the high-SNR DMT for MIMO lognormal channels on σx. We show that for σx≪ 1, the lognormal fading channel behaves like a Gaussian one where the power control techniques are sufficient, whereas for medium to high values of σx, the lognormal channels act like regular multipath fading channels, and thus, diversity techniques should be utilized to improve communication reliability over such channels

In this paper, we analyze the performance of coded and uncoded spatial modulations over multi-mode fiber optic channels with the mode-dependent loss (MDL) under the maximum likelihood (ML) and zero-forcing (ZF) detection schemes. We focus on the multi-dimensional modulations that satisfy certain orthogonality criteria such as the Threaded Algebraic Space-Time (TAST) codes. In particular, we link the post-detection signal-to-noise ratio (SNR) to the orthogonality defect factor (ODF) of the equivalent channel matrix by deriving their closed-form expressions as well as characterizing their statistical properties. Using the post-detection SNR and ODF properties, we develop upper and ad-hoc tight bounds on the error probabilities, which illustrate how these “orthogonal” spatial modulations mitigate the MDL under both the ML and ZF detection schemes. The obtained properties also allow us to propose a modification to the detection algorithm such that it still achieves an essentially optimal performance but at a much smaller cost than exhaustive or tree search algorithms. The theoretical results are validated numerically and by simulations.

The heterogeneous wireless network is considered to be a cornerstone of the system architectural design of the next cellular network generations such as the fifth generation (5G) to alleviate the imminent capacity crunch. With the heterogeneity of the 5G cellular network, it is inevitable to have different statistical channel models within the same system. In this paper, we analyze the cooperative benefits of five different heterogeneous relay networks in terms of the outage probability. The system model incorporates lognormal and Rayleigh distributions to model the small-scale fading of wide-band indoor and outdoor wireless networks, respectively. We analyze the outage probability of the decode-and-forward scheme in 5 different settings depending on the nature of the indoor and the outdoor environments. Numerical quantitative comparisons among the various settings indicate that integrating indoor systems such as WiFi or LiFi into an outdoor system like cellular system can dramatically decrease the outage probability of the network.

In next generation wireless technologies such as 5 G systems, heterogeneous relay networks are crucial to connect different wireless environments. In this paper, we analyze the end-to-end outage probability of two-hop relay networks over heterogeneous wireless networks. The setup incorporates Lognormal and Rayleigh distributions to model small-scale fading of some indoor and outdoor wireless channels, respectively. We derive an analytic expression for the outage probability of the amplify-and-forward transmission scheme over two-hop heterogeneous (Rayleigh-Lognormal) relay networks. In particular, we derive closed-form expressions for lower and upper bounds on the end-to-end outage probability. Numerical results validate the tightness of the proposed bounds. We also provide quantitative comparisons of the outage performance of two-hop relay networks in Rayleigh-Lognormal environments and the outage performance of two-hop relay networks in Rayleigh-Rayleigh fading. Numerical examples show that the former has lower outage probability over the entire signal-to-noise ratio range.

We introduce a low-complexity decoder with near-optimal performance for transmission over multi-antenna systems. By using lattice basis reduction for generating almost orthogonal channel matrix, we enhance the conditional decoding technique to implement a fast yet efficient decoder. The lattice-reduction-aided conditional decoder is presented as a general detection technique over fading channels to yield significant savings in complexity while achieving close to Maximum Likelihood (ML) performance. We specifically apply the decoder for two practical schemes, uncoded multi-input multi-output (MIMO) systems and the Golden code. By employing the orthogonality defect factor as a universal measure to select a near-orthogonal channel submatrix for conditional decoding, we implement an almost optimal decoder with linear complexity over quasi-static channels for the Golden code and the four-by-four uncoded MIMO system.

We introduce a low-complexity detector with near-optimal performance for transmission over multi-antenna systems. By using lattice basis reduction for generating almost orthogonal channel submatrices, we enhance the conditional optimization technique to implement a fast yet efficient detector. The lattice-reduction-aided (LRA) conditional method is presented as a general detection technique over fading channels to yield significant saving in computational complexity while achieving close to Maximum Likelihood (ML) error performance. By employing the orthogonality defect factor as a universal measure to select a near-orthogonal channel submatrix for conditional detection, we implement efficient detectors for MIMO systems. In particular, an almost optimal decoder with linear complexity for the Golden code is presented over quasi-static channels.

The diversity-multiplexing tradeoff (DMT) of a general two-hop asynchronous cooperative network is examined for orthogonal and nonorthogonal selection decode-and-forward relaying protocols. The transmitter nodes send pulse amplitude modulation signals, in which information symbols are linearly modulated by a shaping waveform to be sent to the destination. We consider two different cases of band-limited and time-limited shaping waveforms. In each case, the DMT performance of the asynchronous and synchronous networks is compared. It is proved that in the band-limited system scenario, the asynchronism does not incur any performance loss, and the same DMT as that of the corresponding synchronous network is obtained for both protocols. In the time-limited-system scenario, the bandwidth is expanded for high values of signal-to-noise ratio. In this scenario, it is observed that only asynchronous signaling is able to exploit the extra degrees of freedom of the channel. The asynchronous network in this scenario provides better DMT performances for both protocols throughout the range of the multiplexing gain.

In this paper, we revisit the concept of fractionally spaced equalization (FSE) for broadband single-carrier amplify-and-forward (AaF) cooperative systems. Particularly, we investigate fractionally spaced frequency domain equalization (FS-FDE) for cooperative multi-relay systems. Our motivation stems from the elegant properties reported for the FSE in the point-to-point communication systems (i.e., its robustness to sampling phases and potential in achieving the optimum performance) and the scalability of the FDEs. In particular, we propose a TS/2-spaced equalizer that transforms the temporal sample sequence of the received signal to the frequency domain, applies linear/decision-feedback equalization, and returns the resulting signal back to the time domain for detection. The vital importance of using FS-FDE method in cooperative systems is disclosed in practical scenarios where the transmitted signals have nonzero roll-off components and sampling phase error may occur in relay(s) and destination terminals. Our results demonstrate that, under specific channel realizations and sampling errors, the cooperative systems with symbol spaced FDE (SS-FDE) fail to harvest the available cooperative diversity and the performance approaches to that of no relay scenario. On the other hand, the performance of cooperative system with FS-FDE method becomes independent of sampling phase errors and full benefit of cooperation is retained.

The impact of time asynchronism on the performance of compute-and-forward strategy in relay networks is considered. While the key idea in compute-and-forward is to decode a linear synchronous combination of the transmitted codewords, the relays receive random asynchronous versions of the combinations due to the distributed nature of the network. Over a symbol-asynchronous network, we show that by using a simple equalizer as a part of the signaling scheme, one can transform the asynchronous system into a synchronous one albeit with a smaller channel gain. With frame-asynchronism, we propose to use extra antennas at the relays to efficiently remove the asynchronous delays. By applying a linear filter with a delay-dependent structure before the decoder of compute-and-forward, the achievable rate is maximized at all signal-to-noise-ratios (SNRs).

The potential benefits of deploying Matrix C in mobile WiMAX applications are investigated for improving quality of service (QoS). Also, it is shown that Matrix C in the IEEE 802.16e standard is not a Golden code, as previously thought, but a threaded algebraic space-time (TAST) code.

A constant K-user interference channel in which the users are not symbol-synchronous is considered. It is shown that the asynchronism among the users facilitates aligning interfering signals at each receiver node while it does not affect the total number of degrees of freedom (DoF) of the channel. To achieve the total K/2 DoF of the channel when single antenna nodes are used, a novel interference alignment scheme is proposed wherein the alignment task is performed with the help of asynchronous delays which inherently exist among the received signals at each receiver node. When each node is equipped with M >; 1 antennas, it is argued that the same alignment scheme is sufficient to achieve the total MK/2 DoF of the medium when all links between collocated antennas experience the same asynchronous delay. The proposed alignment scheme is also extended to achieve the total DoF of X networks at the presence of the asynchronism among the nodes.

A symbol-asynchronous X network with time-invariant channel coefficients and single antenna nodes is considered. By employing the asynchronism in the design of the interference alignment, we achieve the upper bound for the total number of degrees of freedom of this network which is argued to be the same as that of the synchronous case. The asynchronism, which exists among the received signals at each receiver, results in inter-symbol-interference (ISI) among the transmitted symbols from different transmitters. This can provide the channel variation required for the vector alignment over the constant network with single antenna nodes.

The impact of symbol-asynchronism on compute-and-forward strategy in relay networks is considered. The lattice-based coding and decoding scheme presented recently by Nazer and Gastpar is applied over asynchronous distributed networks. While the key idea in compute-and-forward is to decode a linear combination of the transmitted codewords, due to distributed nature of the network, the relays receive random asynchronous versions of the combinations. It is shown that by using a simple equalizer as a part of the signaling scheme, one can transform the system to a synchronous one albeit with a smaller channel gain. The effect of asynchronism on the achievable rates is also studied, which implies a loss compared to the synchronous case. However, the resulting gap vanishes as the signal-to-noise-ratio (SNR) increases.

In multiple-input multiple-output (MIMO) systems, lattice reduction significantly improves the performance of approximate detection techniques. Taking advantage of the temporal correlation of a Rayleigh fading channel, low complexity lattice reduction is investigated in this work by adaptively updating the reduced lattice basis. We show that a careful use of previous channel realizations yields a significant saving in complexity with a minimal degradation in performance.

Perfect space-time codes (STC) are optimal codes in their original construction for multiple-input multiple-output (MIMO) systems. Based on cyclic division algebras (CDA), they are full-rate, full-diversity codes, have non-vanishing determinants (NVD) and hence achieve diversity-multiplexing tradeoff (DMT). In addition, these codes have led to optimal distributed space-time codes when applied in cooperative networks under the assumption of perfect synchronization between relays. However, they lose their diversity when delays are introduced and thus are not delay-tolerant. In this paper, using the cyclic division algebras of perfect codes, we construct new codes that maintain the same properties as perfect codes in the synchronous case. Moreover, these codes preserve their full-diversity in asynchronous transmission.

The optimal diversity-multiplexing-delay tradeoff for the multi- input multi-output (MIMO) automatic repeat request (ARQ) channel can be achieved using an incremental redundancy lattice space- time codes. The optimal tradeoff has been shown in to be achieved using a list lattice decoder for joint detection and decoding. However, such decoder suffers from high computational complexity for low-to-moderate signal-to-noise ratios, especially for large signal's dimension. In this paper, we would like to construct a more efficient decoder that is capable of achieving the optimal tradeoff with much lower complexity. We show, analytically and via simulation, that using a modified lattice sequential decoder for joint error detection and correction in the MIMO ARQ channel, the optimal tradeoff can be achieved with significant reduction in decoder complexity at a very small degradation in performance.

In this paper, the performance limit of lattice sequential decoder for coded $M\times N$ MIMO channel is analysed. We determine the rates achievable by lattice coding and sequential decoding applied to such channel. The diversity-multiplexing trade- off under lattice sequential decoding is derived as a function of its parameter---the bias term. Such parameter is critical for controlling the amount of computations required at the decoding stage. Achieving low decoding complexity requires increasing the value of the bias term. However, this is done at the expense of losing the optimal trade- off of the channel. We show how such decoder can bridge the gap between lattice decoder and low complexity decoders [e.g., minimum mean-square error successive interference cancellation (MMSE-SIC)]. We argue that, MMSE-SIC may achieve close to the maximum diversity gain of the channel $MN$ at very low multiplexing gain.

In this paper, the performance limits and computational complexity of lattice sequential decoder for coded MIMO channel are analyzed. It is shown that using nested lattice codes, the optimal diversity-multiplexing tradeoff of the channel can be achieved in the presence of such very low complexity decoder. We show that the computational complexity distribution, at high signal-to-noise ratio, is dominated by the outage probability.

Perfect Space-Time Codes (STC) are full-rate, full-diversity codes originally proposed for Multiple Input Multiple Output (MIMO) systems. Based on Cyclic Division Algebras (CDA), they have non-vanishing determinants and hence achieve the Diversity-Multiplexing Tradeoff (DMT). In addition, these codes have led to optimal distributed Space-Time Codes when applied in cooperative networks under the assumption of perfect synchronization between relays. However, they lose their diversity when delays are introduced and thus are not delay-tolerant. In this paper, using the cyclic division algebras of perfect codes, we construct new codes that maintain the same properties as perfect codes in the synchronous case. Moreover, these codes preserve their full-diversity in asynchronous transmission.

From a practical point of view, fast Maximum Likelihood Decoding (MLD) and low Peak-to-Average-Power- Ratio (PAPR) are two important design criteria for Space-Time Block Codes (STBCs). The use of the principle of conditional detection allows for having high-rate STBCs while keeping the complexity of detection at a reasonable level. Recently, we proposed a structure for a STBC with fast MLD having a rate of 3/2 complex symbols per channel use. In this paper, the PAPR criterion is included in the code design, and a modified version is proposed which has a lower PAPR.

The outage behavior of decode-and-forward (DF) relaying protocol over an asynchronous cooperative network is examined when orthogonal frequency division multiplexing (OFDM) is used to combat synchronization error among the transmitting nodes. We consider non-orthogonal selection DF (NSDF) and orthogonal selection DF (OSDF) protocols, respectively, over a single relay and a two relay cooperative network and analyze the diversity multiplexing gain tradeoff (DMT) in both scenarios. It is proved that asynchronous protocols provide diversity gains greater than or equal to the one of synchronous counterparts in the limit of code word length and throughout the range of multiplexing gain.

In this work, the multiple access channel (MAC) with asynchronous users is considered. Users are not allowed to cooperate together and do not have any channel side information. The code design criteria are first developed for this channel and a MAC coding scheme that verifies these criteria, i.e., delay tolerant code, is investigated. Simulation results confirms that the diversity of the proposed space-time codes is preserved in an asynchronous scenario.

Recently, Space-Time Block Codes (STBCs) with fast Maximum-Likelihood Decoding (MLD) have gained a lot of interest from a practical perspective. B. Rajan et.al proposed a systematic approach to build such codes from the representations of the real Clifford algebras. In the Sari-Sezginer code, another approach was proposed to build fast MLD STBC's. Indeed, the authors used the conditional detection principle and numerical optimization in order to have a large coding gain (thus full diversity) while maintaining a reduced complexity level at the receiver. In this paper we are interested in extending the principle of conditional detection to the case of four transmit antennas. We propose here a full-diversity 4×4 STBC achieving a rate of 3/2 complex symbols per channel use. To the best knowledge of the authors, the highest rate for full transmit diversity 4×4 codes with the same complexity level was reported to be 5/4 complex symbols per channel use (such codes were found independently).

The construction of distributed space-time codes for asynchronous relays is considered. A novel algebraic structure is proposed and shown to achieve full diversity for arbitrary number of relays, arbitrary input alphabets, and arbitrary delay profiles among the relays. Unlike previously proposed delay tolerant schemes, the new design has minimum length which translates into smaller decoding complexity at the same transmission rate. Full-rate and full-diversity are achieved by the new designs with or without the use of guard intervals between successive transmissions. Simulation results confirm the mathematical analysis of the proposed codes.

Distributed space-time code constructions are presented that are suitable for asynchronous cooperative networks using different cooperation strategies. The codes presented herein may be used with either an amplify-and-forward or a decode-and-forward protocol, achieving in either scenario full spatial diversity despite arbitrary timing offsets among asynchronous cooperating relays. The new designs are flexible with respect to the number of relays, input alphabet, and transmission rate.

In this paper, the selective time division multiple access (S-TDMA) strategy is studied in the downlink channel. This strategy consists in transmitting data to the user with the largest capacity. The diversity and multiplexing gains that can be achieved by this sub-optimal strategy are evaluated and then compared to the optimal gains over the broadcast channel. Codes construction is then proposed to achieve the diversity multiplexing tradeoff (DMT) of the S-TDMA. These codes are extended to the scenario of cooperating asynchronous broadcasting base stations where new codes that are suitable for this scenario are proposed and analyzed.

Distributed space-time codes over two asynchronous relays are considered. First, we show that the space-time code proposed in [1] is suitable for asynchronous transmission over two relays. Using tools from division algebra, we study the quadratic form resulting from its determinant and we prove that this code has a non-vanishing determinant over all constellations carved from Zopf[i], and thus is optimal in the sense of diversity-multiplexing tradeoff [2]. Then, we propose a delay-tolerant code based on the Golden code [3] the full-rate full-diversity information lossless space-time code proposed for the MIMO channel, and we deduce the convenient unitary matrices to obtain the modified code. Applying these matrices to other MIMO codes, namely Tirkkonen-Hottinen [4] and Sezginer-Sari code [5], we infer new delay-tolerant codes. In addition of being suitable for asynchronous relay transmission, all the new codes have the same determinants as the old ones.

We propose a new class of C-linear distributed space-time codes for cooperative networks using a decode- and-forward strategy. Our codes achieve full spatial diversity regardless of the relays' timing offsets. The proposed codes are effective and flexible, enabling use of different signal constellations, transmission rates, numbers of transmit and receive antennas, and different tradeoffs between decoder complexity and overall performance. Furthermore, we extend our framework to handle the case where relays have multiple antennas and propose few examples of the modified code construction.

We consider decode and forward strategy in the relay channel, where in the first time interval the source communicates its message to its neighboring relays, and in the second time interval, the relays form a distributed space-time code and forward the source message to the destination. In particular, we tackle the problem of overlapping code words in asynchronous distributed coded transmission. We show that the class of delay-tolerant TAST codes [1], with a small modification, can achieve full spatial diversity even when considering overlapping code words from the different asynchronous relays. Simulation results confirm our analysis.

Codes construction for cooperative diversity in ad-hoc networks is considered. In the context of decoded-and-forward strategy, a new class of distributed space-time codes is proposed. This class is tolerant to timing offsets between the different relays, which is crucial for relaying over ad-hoc networks that lack a timing reference. The proposed codes are effective and flexible, enabling use of different signaling constellations, transmission rates, numbers of transmit and receive antennas, and decoders of varying levels of complexity.

In cooperative networks using a decode-and-forward strategy, the multiple relays effectively transmit a distributed space-time code, the performance of which can be severely degraded when timing synchronization among the relays is not assured (e.g., in cases of broadcast to dispersed recipients or in networks without a shared, high-quality timing reference). Recent work by Xia and Hammons have investigated the design of distributed space-time codes that are delay tolerant, in the sense that full spatial diversity is achieved regardless of timing offsets. In general, the previously known space-time block codes belonging to the class of C-linear codes, however, which are important because they achieve full spatial diversity and admit near-optimal lattice decoding algorithms, are not delay tolerant. In this paper, we present a new family of such codes that are fully delay tolerant. The new codes generalize the threaded algebraic space-time (TAST) codes introduced by El Gamal and Damen. Like their brethren, the new distributed-TAST codes are effective and flexible, enabling use of different signaling constellations, transmission rates, numbers of transmit and receive antennas, and decoders of varying levels of complexity.

A simple and general form of threaded algebraic space–time (TAST) codes and constellations for arbitrary numbers of transmit and receive antennas and arbitrary input alphabets is given and analyzed. This new form gives revealing insights on the TAST framework, elucidates the connection between space–time constellation expansion and the peak-to-average power ratio (PAR), and establishes the equivalence between a certain class of TAST constellations and constellations derived from division algebras.

In this paper, the fundamental performance tradeoff of the delay-limited multiple-input multiple-output (MIMO) automatic retransmission request (ARQ) channel is explored. In particular, we extend the diversity-multiplexing tradeoff investigated by Zheng and Tse in standard delay-limited MIMO channels with coherent detection to the ARQ scenario. We establish the three-dimensional tradeoff between reliability (i.e., diversity), throughput (i.e., multiplexing gain), and delay (i.e., maximum number of retransmissions). This tradeoff quantifies the ARQ diversity gain obtained by leveraging the retransmission delay to enhance the reliability for a given multiplexing gain. Interestingly, ARQ diversity appears even in long-term static channels where all the retransmissions take place in the same channel state. Furthermore, by relaxing the input power constraint allowing variable power levels in different retransmissions, we show that power control can be used to dramatically increase the diversity advantage. Our analysis reveals some important insights on the benefits of ARQ in slow-fading MIMO channels. In particular, we show that 1) allowing for a sufficiently large retransmission delay results in an almost flat diversity-multiplexing tradeoff, and hence, renders operating at high multiplexing gain more advantageous; 2) MIMO ARQ channels quickly approach the ergodic limit when power control is employed. Finally, we complement our information-theoretic analysis with an incremental redundancy lattice space-time (IR-LAST) coding scheme which is shown, through a random coding argument, to achieve the optimal tradeoff(s). An integral component of the optimal IR-LAST coding scheme is a list decoder, based on the minimum mean-square error (MMSE) lattice decoding principle, for joint error detection and correction. Throughout the paper, our theoretical claims are validated by numerical results

We consider receiver design for coded transmission over linear Gaussian channels. We restrict ourselves to the class of lattice codes and formulate the joint detection and decoding problem as a closest lattice point search (CLPS). Here, a tree search framework for solving the CLPS is adopted. In our framework, the CLPS algorithm is decomposed into the preprocessing and tree search stages. The role of the preprocessing stage is to expose the tree structure in a form matched to the search stage. We argue that the forward and feedback (matrix) filters of the minimum mean-square error decision feedback equalizer (MMSE-DFE) are instrumental for solving the joint detection and decoding problem in a single search stage. It is further shown that MMSE-DFE filtering allows for solving underdetermined linear systems and using lattice reduction methods to diminish complexity, at the expense of a marginal performance loss. For the search stage, we present a generic method, based on the branch and bound (BB) algorithm, and show that it encompasses all existing sphere decoders as special cases. The proposed generic algorithm further allows for an interesting classification of tree search decoders, sheds more light on the structural properties of all known sphere decoders, and inspires the design of more efficient decoders. In particular, an efficient decoding algorithm that resembles the well-known Fano sequential decoder is identified. The excellent performance-complexity tradeoff achieved by the proposed MMSE-DFE Fano decoder is established via simulation results and analytical arguments in several multiple-input multiple-output (MIMO) and intersymbol interference (ISI) scenarios.

In this paper, we explore the fundamental performance tradeoff of the delay-limited multi-input-multi-output (MIMO) automatic retransmission request (ARQ) channel. In particular, we extend the diversity-multiplexing tradeoff investigated by Zheng and Tse in standard delay-limited MIMO channels with coherent detection to the ARQ scenario. We establish the three-dimensional tradeoff between reliability (i.e. diversity), throughput (i.e., multiplexing gain), and delay (i.e., maximum number of retransmissions). This tradeoff quantifies the ARQ diversity gain obtained by leveraging the retransmission delay to enhance the reliability for a given multiplexing gain. Interestingly, ARQ diversity appears even in long-term static channels where all the retransmissions take place in the same channel state. Furthermore, by relaxing the input power constraint allowing variable power levels in different retransmissions, we show that power control can be used to dramatically increase the diversity advantage. Our analysis reveals some important insights on the benefits of ARQ in slow fading MIMO channels. In particular, we show that: 1) allowing for a sufficiently large retransmission delay results in an almost flat diversity-multiplexing tradeoff, and hence, renders operating at high multiplexing gain more advantageous; 2) MIMO ARQ channels quickly approach the ergodic limit when power control is employed

We consider receiver design for coded transmission over linear Gaussian channels. We restrict ourselves to the class of lattice codes and formulate the joint detection and decoding problem as a closest lattice point search (CLPS). Here, a tree search framework for solving the CLPS is adopted. In our framework, the CLPS algorithm decomposes into preprocessing and tree search stages. The role of the preprocessing stage is to expose the tree structure in a form matched to the search stage. Here, it is argued that the minimum mean square error decision feedback (MMSE-DFE) frontend is instrumental for solving the joint detection and decoding problem in a single search stage. It is further shown that MMSE-DFE filtering allows for using lattice reduction methods to reduce complexity, at the expense of a marginal performance loss, and solving under-determined linear systems. For the search stage, we present a generic method, based on the branch and bound (BB) algorithm, and show that it encompasses all existing sphere decoders as special cases. The proposed generic algorithm further allows for an interesting classification of tree search decoders, sheds more light on the structural properties of all known sphere decoders, and inspires the design of more efficient decoders. In particular, an efficient decoding algorithm that resembles the well known Fano sequential decoder is identified. The excellent performance-complexity tradeoff achieved by the proposed MMSE-Fano decoder is established via simulation results and analytical arguments in several MIMO and ISI scenarios.

The design of space-time signals for noncoherent block-fading channels where the channel state information is not known a priori at the transmitter and the receiver is considered. In particular, a new algebraic formulation for the diversity advantage design criterion is developed. The new criterion encompasses, as a special case, the well-known diversity advantage for unitary space-time signals and, more importantly, applies to arbitrary signaling schemes and arbitrary channel distributions. This criterion is used to establish the optimal diversity-versus-rate tradeoff for training based schemes in block-fading channels. Our results are then specialized to the class of affine space-time signals which allows for a low complexity decoder. Within this class, space-time constellations based on the threaded algebraic space-time (TAST) architecture are considered. These constellations achieve the optimal diversity-versus-rate tradeoff over noncoherent block-fading channels and outperform previously proposed codes in the considered scenarios as demonstrated by the numerical results. Using the analytical and numerical results developed in this paper, nonunitary space-time codes are argued to offer certain advantages in block-fading channels where the appropriate use of coherent space-time codes is shown to offer a very efficient solution to the noncoherent space-time communication paradigm.

Minimum mean square error generalized decision-feedback equalizer (MMSE-GDFE) lattice decoding is shown to be an efficient decoding strategy for under-determined linear channels. The proposed algorithm consists of an MMSE-GDFE front-end followed by a lattice reduction algorithm with a greedy ordering technique and, finally, a lattice search stage. By introducing flexibility in the termination strategy of the lattice search stage, we allow for trading performance for a reduction in the complexity. The proposed algorithm is shown, through experimental results in MIMO quasistatic channels, to offer significant gains over the state of the art decoding algorithms in terms of performance enhancement and complexity reduction. On the one hand, when the search is pursued until the best lattice point is found, the performance of the proposed algorithm is shown to be within a small fraction of a dB from the maximum likelihood (ML) decoder while offering a large reduction in complexity compared to the most efficient implementation of ML decoding proposed by Dayal and Varanasi (e.g., an order of magnitude in certain representative scenarios). On the other hand, when the search is terminated after the first point is found, the algorithm only requires linear complexity while offering significant performance gains (in the order of several dBs) over the linear complexity algorithm proposed recently by Yao and Wornell.

In this paper, we introduce the class of lattice space-time (LAST) codes. We show that these codes achieve the optimal diversity-vs-multiplexing tradeoff defined by Zheng and Tse under generalized minimum Euclidean distance lattice decoding. Our scheme is based on a generalization of Erez and Zamir mod-/spl Lambda/ scheme to the MIMO case. This result settles the open problem posed by Zheng and Tse on the construction of explicit coding and decoding schemes that achieve the optimal diversity-vs-multiplexing tradeoff. Moreover, our results shed more light on the structure of optimal coding/decoding techniques in delay limited MIMO channels. In particular: 1) we show that MMSE-GDFE plays a fundamental role in approaching the limits of delay limited MIMO channels in the high SNR regime, unlike the AWGN channel case and 2) our random coding arguments represent a major departure from traditional space-time code designs based on the rank and/or mutual information design criteria.

A novel parametric approach for constructing families of intersymbol-interference (ISI)-free pulses is presented and examined. Some new pulses so constructed have smaller maximum distortion, a more open receiver eye, and a smaller probability of error in the presence of symbol-timing error than the Nyquist raised-cosine pulse for the same excess bandwidth. The parametric approach gives more degrees of freedom in the design of ISI-free pulses, and subsumes previous ISI-free pulses as special cases. A number of theorems that relate time-domain behaviors of a pulse to the pulse's frequency spectrum are proved. A previously known result relating pulse tail-time decay to discontinuity of the pulse-frequency spectrum is corrected and clarified.

This paper considers communication over coherent multiple-input multiple-output (MIMO) flat-fading channels where the channel is only known at the receiver. For this setting, we introduce the class of LAttice Space-Time (LAST) codes. We show that these codes achieve the optimal diversity-multiplexing tradeoff defined by Zheng and Tse under generalized minimum Euclidean distance lattice decoding. Our scheme is based on a generalization of Erez and Zamir mod-Lambda scheme to the MIMO case. In our construction the scalar "scaling" of Erez-Zamir and Costa Gaussian "dirty-paper" schemes is replaced by the minimum mean-square error generalized decision-feedback equalizer (MMSE-GDFE). This result settles the open problem posed by Zheng and Tse on the construction of explicit coding and decoding schemes that achieve the optimal diversity-multiplexing tradeoff. Moreover, our results shed more light on the structure of optimal coding/decoding techniques in delay-limited MIMO channels, and hence, open the door for novel approaches for space-time code constructions. In particular, 1) we show that MMSE-GDFE plays a fundamental role in approaching the limits of delay-limited MIMO channels in the high signal-to-noise ratio (SNR) regime, unlike the additive white Gaussian noise (AWGN) channel case and 2) our random coding arguments represent a major departure from traditional space-time code designs based on the rank and/or mutual information design criteria.

The diversity-vs-rate tradeoffs of linear space-time constellations are derived and analyzed under different constraints on the receiver complexity, and the rate scaling with the signal-to-noise ratio (multiplexing gain). New constellations from the threaded algebraic space-time (TAST) signaling framework are matched to the receiver in the sense of achieving the optimal diversity-vs-rate tradeoffs for a given complexity of the sphere decoder or the nulling and cancellation receiver.

A new algebraic formulation for the diversity advantage design criterion for arbitrary space-time signals in noncoherent block fading channels is developed. It is shown that the new criterion encompasses, as a special case, the well-known diversity advantage criterion for unitary space-time signaling. Using the proposed criterion, the optimal diversity-vs-rate tradeoff is derived for training based noncoherent signaling schemes. Our results are then specialized to the class of affine space-time signals which allow for an efficient polynomial complexity decoder. Within this class, new space-time constellations based on the threaded algebraic space-time (TAST) framework are proposed. These codes achieve the optimal diversity-vs-rate tradeoff and outperform previously proposed codes in the considered scenarios as demonstrated by numerical results. Using these analytical and numerical results, we argue that non-unitary space-time codes offer certain advantages in block fading channels and the appropriate use of coherent space-time codes is shown to offer a very efficient solution to the noncoherent space-time communication paradigm.

Space-time constellations that are linear over the field of complex numbers are considered. Relevant design criteria for these constellations are summarized and some fundamental limits to their achievable performances are established. A new family of constellations that achieve optimal or near optimal performance with respect to the different criteria is presented. The proposed constellations belong to the threaded algebraic space-time signaling framework and achieve the optimal minimum squared Euclidean distance and the optimal delay in addition to the full rate, full diversity properties. For systems with one receive antenna, these constellations also achieve the optimal peak-to-average power ratio for QAM and PSK input constellations, as well as optimal coding gains in certain scenarios. The framework is general for any number of transmits and receives antennas and allow for realizing the optimal tradeoff between multiplexing rate and diversity.

Diversity-vs-rate tradeoffs of linear space-time constellations are investigated under different constraints on the peak power, receiver complexity, and rate scaling with the signal-to-noise ratio (multiplexing gain). New constellations from the threaded algebraic space-time (TAST) signaling framework are shown to achieve the optimal tradeoffs.

Theoretical and practical aspects of diagonal algebraic space-time block codes over n transmit and m receive antennae are examined. These codes are obtained by sending a rotated version of the information symbols over the principal diagonal of the n /spl times/ n space-time matrix over n transmit antennae and n symbol periods. The output signal-to-noise ratios of two predecoding filters and two decoding algorithms are derived. Analysis of the information loss incurred by using the codes considered is used to clarify their structures, and the expected performances. Different algebraic real and complex rotations presented in the literature are analyzed and compared as regards the achieved coding gains, the complexities, performances, and peak-to-mean envelope power ratios.

We examine some algebraic properties of two high-rate linear space-time block codes over M=2,3 transmit antennas. Although these high-rate codes have positive coding gain, the gain decreases when increasing the constellation size. We give tight upper and lower bounds on the achieved coding gains as functions of the size of the constellations used. We show that when using the irrational numbers /spl radic/3 and /spl radic/2, the coding gains express the approximation of these numbers by continued fractions depending on the constellations used. The poor approximation of these numbers by rational numbers is then shown to make the coding gains decrease slowly when increasing the constellation size.

Some M/spl times/T modulation matrices for M transmit antennas and T symbol periods, with M=2,3,4 and T=2, and M=T=4 are studied. A transmission rate of M symbols per channel use and a transmit diversity order of min(M,T) are achieved over a quasi-static fading channel when using rotated versions of a multidimensional quadratic amplitude modulation with spectral efficiency 2 bits/symbol. Extension to input constellations with higher spectral efficiencies is then considered. The modulations are then generalized to any number of transmit antennas M and any number of symbol periods T, such that a transmission rate of M symbols per channel use, and a transmit diversity of T are achieved under fast fading (ergodic scenario). By means of signal space diversity, the proposed modulations exploit the degrees of freedom of multiantenna channels and have moderate detection complexity at moderate and large signal-to-noise ratios (SNRs).

Space-time (ST) constellations that are linear over the field of complex numbers are considered. Relevant design criteria for these constellations are summarized and some fundamental limits to their achievable performances are established. The fundamental tradeoff between rate and diversity is investigated under different constraints on the peak power, receiver complexity, and rate scaling with the signal-to-noise ratio (SNR). A new family of constellations that achieve optimal or near-optimal performance with respect to the different criteria is presented. The proposed constellations belong to the threaded algebraic ST (TAST) signaling framework, and achieve the optimal minimum squared Euclidean distance and the optimal delay. For systems with one receive antenna, these constellations also achieve the optimal peak-to-average power ratio for quadrature amplitude modulation (QAM) and phase-shift keying (PSK) input constellations, as well as optimal coding gains in certain scenarios. The framework is general for any number of transmit and receive antennas and allows for realizing the optimal tradeoff between rate and diversity under different constraints. Simulation results demonstrate the performance gains offered by the proposed designs in average power and peak power limited systems.

A simple and systematic approach for constructing full diversity m-dimensional constellations, carved from lattices over a number ring R, is proposed for an arbitrary dimension m. When R=Z[w/sub n/], the nth cyclotomic number ring, all the possible dimensions that allow for achieving the optimal minimum product distances using the proposed approach are determined. It turns out that one can construct optimal unitary transformations using our construction if and only if m factors into a power of 2 and powers of the primes dividing n. For m not satisfying these conditions, a method based on Diophantine approximation theory is proposed to "optimize" the minimum product distance. A lower bound on the product distance is given in this case, thus ensuring full diversity with "good" minimum product distances. Furthermore, the proposed approach subsumes the optimal unitary transformations proposed by Giraud et al. over R=Z[w/sub 4/] and R=Z[w/sub 3/], while giving optimal unitary transformations for infinitely many new values of n and m.

Maximum-likelihood (ML) decoding algorithms for Gaussian multiple-input multiple-output (MIMO) linear channels are considered. Linearity over the field of real numbers facilitates the design of ML decoders using number-theoretic tools for searching the closest lattice point. These decoders are collectively referred to as sphere decoders in the literature. In this paper, a fresh look at this class of decoding algorithms is taken. In particular, two novel algorithms are developed. The first algorithm is inspired by the Pohst enumeration strategy and is shown to offer a significant reduction in complexity compared to the Viterbo-Boutros sphere decoder. The connection between the proposed algorithm and the stack sequential decoding algorithm is then established. This connection is utilized to construct the second algorithm which can also be viewed as an application of the Schnorr-Euchner strategy to ML decoding. Aided with a detailed study of preprocessing algorithms, a variant of the second algorithm is developed and shown to offer significant reductions in the computational complexity compared to all previously proposed sphere decoders with a near-ML detection performance. This claim is supported by intuitive arguments and simulation results in many relevant scenarios.

A universal framework is developed for constructing full-rate and full-diversity coherent space-time codes for systems with arbitrary numbers of transmit and receive antennas. The proposed framework combines space-time layering concepts with algebraic component codes optimized for single-input-single-output (SISO) channels. Each component code is assigned to a "thread" in the space-time matrix, allowing it thus full access to the channel spatial diversity in the absence of the other threads. Diophantine approximation theory is then used in order to make the different threads "transparent" to each other. Within this framework, a special class of signals which uses algebraic number-theoretic constellations as component codes is thoroughly investigated. The lattice structure of the proposed number-theoretic codes along with their minimal delay allow for polynomial complexity maximum-likelihood (ML) decoding using algorithms from lattice theory. Combining the design framework with the Cayley transform allows to construct full diversity differential and noncoherent space-time codes. The proposed framework subsumes many of the existing codes in the literature, extends naturally to time-selective and frequency-selective channels, and allows for more flexibility in the tradeoff between power efficiency, bandwidth efficiency, and receiver complexity. Simulation results that demonstrate the significant gains offered by the proposed codes are presented in certain representative scenarios.

We explore code-division multiple-access systems with multiple transmitter and receiver antennas combined with algebraic constellations over a quasi-static multipath fading channel. We first propose a technique to obtain transmit diversity for a single user over quasi-static fading channels by combining algebraic constellations with full spatial diversity and spreading sequences with good cross-correlation properties. The proposed scheme is then generalized to a multiuser system using the same algebraic constellation and different spreading sequences. We also propose a linear multiuser detector based on the combination of linear decorrelation with respect to all users, and the application of the sphere decoder to decode each user separately. Finally, we consider the generalization to multipath fading channels where the additional diversity advantage due to multipath is exploited by the sphere decoder, and a method of blind channel estimation based on subspace decomposition is examined.

A novel framework is described here for constructing full rate, full diversity, and polynomial complexity space-time signals for systems with arbitrary numbers of transmit and receive antennas. By combining the space-time threading concepts with algebraic number theoretic constellations, we construct universal codes for scenarios where the channel state information (CSI) is known a-priori at the transmitter and receiver (TR-CSI), receiver only (R-CSI), and neither one of them (N-CSI).

We construct a new family of linear space-time (ST) block codes by the combination of rotated constellations and the Hadamard transform, and we prove them to achieve the full transmit diversity over a quasi-static or fast fading channels. The proposed codes transmit at a normalized rate of 1 symbol/s. When the number of transmit antennas n=1, 2, or n is a multiple of four, we spread a rotated version of the information symbol vector by the Hadamard transform and send it over n transmit antennas and n time periods; for other values of n, we construct the codes by sending the components of a rotated version of the information symbol vector over the diagonal of an n /spl times/ n ST code matrix. The codes maintain their rate, diversity, and coding gains for all real and complex constellations carved from the complex integers ring Z [i], and they outperform the codes from orthogonal design when using complex constellations for n > 2. The maximum-likelihood (ML) decoding of the proposed codes can be implemented by the sphere decoder at a moderate complexity. It is shown that using the proposed codes in a multiantenna system yields good performances with high spectral efficiency and moderate decoding complexity.

We construct a full data rate space-time (ST) block code over M=2 transmit antennas and T=2 symbol periods, and we prove that it achieves a transmit diversity of 2 over all constellations carved from Z[i]/sup 4/. Further, we optimize the coding gain of the proposed code and then compare it to the Alamouti code. It is shown that the new code outperforms the Alamouti (see IEEE J Select. Areas Commun., vol.16, p.1451-58, 1998) code at low and high signal-to-noise ratio (SNR) when the number of receive antennas N>1. The performance improvement is further enhanced when N or the size of the constellation increases. We relate the problem of ST diversity gain to algebraic number theory, and the coding gain optimization to the theory of simultaneous Diophantine approximation in the geometry of numbers. We find that the coding gain optimization is equivalent to finding irrational numbers "the furthest," from any simultaneous rational approximations.

Space-time coding is an established technique for combating the impairments of wireless channels by means of the transmit diversity which is obtained by coding the information symbols over M transmit antennas and T symbol periods. Many existing space-time codes have good performance over the wireless channel, however, they offer small data rates compared to the actual capacity of the multi-antenna system. We study some M/spl times/T space-time block codes, for M=2,3,4 and T=2,4, with a rate of M symbols per channel use and a transmit diversity of T over a quasi-static or fast fading channel when using rotated versions of a multidimensional quadratic amplitude modulation with spectral efficiency of 2 bits per symbol. An extension to constellations with a higher spectral efficiency is also considered. We generalize the proposed codes to any number of transmit antennae M and any number of symbol periods T, such that we transmit at a rate of M symbols per channel use, and achieve a transmit diversity of T in fast fading.

The algebraic properties of two new space-time block codes over M transmitter antennas and T symbol periods are examined. The first code transmits at a rate of 2 symbols per channel use and has a transmit diversity of 2 over all 4-dimensional constellations carved from Z[i]/sup 4/ for M=T=2. From this code, we construct a space-time block code for M=T=3 which transmits at a rate of 4/3 symbols per channel use and has a transmit diversity of 3. We give upper and lower bounds to the achieved coding gains and prove that irrational numbers that are poorly approximated by rational numbers are particularly useful to enhance the coding gains of our schemes.

We construct a full data rate space-time block code over M=2 transmit-antennas and T=2 symbol periods, and we prove it achieves a transmit diversity of 2 over all 4-dimensional constellations carved from the 4-dimensional ring of complex integers Z[i]/sup 4/. Further, we optimize the coding gain of our ST code and then compare it to the Alamouti scheme (see Alamouti, S.M., IEEE Journal Selec. Areas on Communications, vol.16, p.1451-8, 1998). For N>1, we prove that our code has a better performance than the Alamouti code. The performance improvement is further enhanced when N or the size of the constellation increases. We relate the problem of ST diversity gain to algebraic number theory, and the ST coding gain optimization to the theory of simultaneous Diophantine approximation in the geometry of numbers.

Antenna spacings, the angle spread and the Rice factor significantly affect the correlation of fading coefficients in a multi-antenna system. We study the effect of these parameters on the performance of different types of detection schemes in a BLAST architecture. We show that the detection method based on lattice decoding is more resistant to the correlated fading than other types of detection which are based on successive interference cancellation. We notice that highly correlated fades significantly degrade the performance of detection techniques based on successive interference cancellation whereas they slightly affect the lattice decoding algorithm. We also study the effects of correlated fades on some space-time block codes. We show that space-time block codes from orthogonal design are more resistant to correlation than other high rate linear space-time block codes.

We present a generalized sphere decoding (GSD) algorithm and its application for detecting information symbols in the case where one has a system with more inputs (symbols) than outputs or the opposite situation. We study the special case of a multi-antenna scenario in a cellular system with N antennas at the mobile and M/spl ges/N antennas at the base station. GSD reaches the maximum likelihood (ML) performance for both up and down link with a moderate complexity.