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Recently, lattice-reduction (LR) aided detection has been proposed in combination with linear and non-linear spatial multiplexing (SM) schemes, like zero-forcing (ZF) and VBLAST, in order to improve the performance of wireless communications systems. The performance of the LR-ZF detector is parallel to the maximum-likelihood-detector with some pena...
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... SM performs only better than QOSTBC for low SNR of about 2dB. However, the gap in power efficiency between ML and LR-ZF is increased to 1.7dB for the code rate n T 2 QOSTBC in comparison to the rate one QOSTBC and also to SM with BSPK. By increasing the transmission rate to 8bit/sec/Hz, i.e. QAM for SM and 16QAM for the QOSTBC, we observe in Fig. 5 that the gap between ML and LR-ZF is dramatically increased in case of SM to about 6dB. On the other hand, the gap between ML and LR-ZF for the QOSTBC and 16QAM is reduced in comparison to the gap achieved with QAM (cf. Fig. 4) to about 1.3dB. Although the performance of SM with ML detection is better than that of the QOSTBC for low ...
Citations
... In [6,7], lattice reduction aided (LRA) method is combined with suboptimal detectors in order to improve performance of the suboptimal decoders in multiple-input multiple-output (MIMO) communications systems. In [8], the QOSTBC is employed to reduce gap between error ratio of ML and LRA methods. This work also compares the performances of spatial multiplexing and QOSTBC with those of LRA zero-forcing and ML decoders. ...
Motivated by the decompositions of sphere and QR-basedmethods, in this paper we present an extremely fast maximum-likelihood (ML) detection approach for quasi-orthogonal space-time block code (QOSTBC). The proposed algorithm with a relatively simple design exploits structure of quadrature amplitude modulation (QAM) constellations to achieve its goal and can be extended to any arbitrary constellation. Our decoder utilizes a new decomposition technique for ML metric which divides the metric into independent positive parts and a positive interference part. Search spaces of symbols are substantially reduced by employing the independent parts and statistics of noise. Symbols within the search spaces are successively evaluated until the metric is minimized. Simulation results confirm that the proposed decoder's performance is superior to many of the recently published state-of-theart solutions in terms of complexity level. More specifically, it was possible to verify that application of the new algorithms with 1024-QAM would decrease the computational complexity compared to state-of-the-art solution with 16-QAM.
... One of those schemes, a double space time transmit diversity (DSTTD) scheme, which is also called " stacked STBC " [6] , allows two STBC signals to be sent simultaneously . The theoretical performances of STBC and DSTTD were analyzed in789. There is also a lot of research to make STBC system work in the multi-user environment1011121314. ...
... where h i, k (j) is the channel coefficient from the jth transmit antenna of user k to the ith BS receive antenna, and (·)*, (·) T , and (·) H denote complex conjugate, transpose , and Hermitian transpose, respectively. In this case, the equivalent channel model is the same as the DSTTD scheme, and analytic studies of their performances with the optimal MLD and suboptimal LRA ZF detector were analyzed in [8,9] . (Note that the system model with uplink multi-user MIMO detection appears as a generalization of known single-user MIMO concepts to the multi-user case.) ...
Recently, a lattice reduction-aided (LRA) multiple-input multiple-output detection scheme has been proposed in junction with linear (as well as nonlinear) detectors. It is well known that these schemes provide a full diversity, and its complexity is comparable to that of linear detectors for the block fading channels. For the fast varying channels, however, the decoding complexity of LRA detection scheme is unreasonably high. This article proposes an efficient iterative lattice reduction (LR) scheme for an uplink system with two receive antennas at the base station and two users, each employing the Alamouti space-time block code (STBC). By taking advantage of the certain inherent STBC structure of transmitted symbols from users, the proposed scheme provides the same performance as a conventional LR while saving about 80% computational complexity. We also show that it can be successfully extended to handle the scenario where another interfering user, who is also employing the Alamouti STBC, is present.
... At the receiver side, an appropriate multi-user or multistream detection has to be applied in order to decouple the received superposition of the transmitted signals. Hereby, the receiver structures range from linear detection schemes such as matched filtering [9], zero-forcing, MMSE detector to successive interference cancelation [5], sphere decoding, lattice reduction aided detection [10], [11] and the optimal, however highly complex, ML detector. The reduction of receiver complexity is of particular interest for the research community as well as for the industry and ways to do that were explored in e.g. ...
The tradeoff between diversity, interference alignment and rate for a K user multiple-antenna interference network is analyzed. It is assumed that the sources employ a space-time code in combination with linear preceding, while the receiving nodes use linear detectors. We show that interference alignment is needed if the system is operating at or close to the maximum achievable rate. For low rates the preferred strategy is to utilize all antennas in order to achieve high diversity gains, rather than using some of the antennas to align the interference. For the case of K = 3 users, an exact characterization of the tradeoff is provided. We also investigate the impact of channel estimation errors on the diversity of the system. It turns out that small channel estimation errors can be tolerated, while larger errors reduce the diversity gain significantly.
... These algorithms are built around solving the unconstrained least-squares problem and slicing to the nearest constellation point (see Section 1.5.1). For example, in [33] the error performance of the n T = L = 4 QOSTBC is analyzed for a receiver that performs lattice-reduction-aided zero-forcing; ...
... Unlike in the spatial multiplexing case, there is no loss in diversity gain. These curves are consistent with similar studies, such as that in [33] 1 . The fact that the diversity gain is preserved by the zero-forcing algorithm antenna QOSTBCs proposed in [11]. ...
... Although the receiver in[33] performs lattice-reduction-aided zero-forcing, the study goes on to argue that performing lattice reduction has little effect when decoding QOSTBCs. ...
The metric expression for a generic linear space-time block code (STBC) is studied using a different approach to vectorization and a new representation of the metric. The new representation lends itself to a simple measure of reliability based on the sum of inner products, and provides a quantifiable definition for minimum distance of a STBC. This provides the framework for a new family of near-maximum-likelihood (ML) and ML decoding algorithms. It also has applications in the development of optimality test criteria for STBCs, as well as in the design of STBCs with low decoding complexity.
... Optimizing the MSE is also relevant for detectors employing a linear front end like the VBLAST algorithm or sphere detectors. The loss associated with suboptimal schemes, such as the MMSE receiver, and the optimal ML decoder was analyzed in [21] and [22] for QSTBC and in [23] for SM and references therein. ...
... . Applying this to (21), it follows that the pdf of the harmonic mean of two independent chi-square distributed random variables is given as where is the Whittaker W function given in [48,p.XXVI]. Using this in (20), we arrive at (22) where is the generalized hypergeometric function [47]. ...
In this paper, we study a MIMO system with a transmitter using a linear dispersion code (LDC) and a linear minimum mean square-error (MMSE) detector at the receiver in a Ricean flat-fading environment. We assume that the receiver has perfect channel state information and the transmitter knows only the mean channel matrix either by feedback or channel estimation. The focus of our work is the analysis of the optimal transmit strategy using different types of LDC. On the one hand, we consider spatial multiplexing schemes that achieve high data rates, but sacrifice diversity. On the other hand, we have schemes that achieve full diversity like quasi-orthogonal space-time block codes or orthogonal space-time block code. Depending on the LDC in use, the optimization problem is either convex or nonconvex. For both of these classes of LDC, we first derive the properties of the average normalized MSE and then analyze the impact of the mean component on the MSE, the optimal transmit strategy and the optimal power allocation. Finally, we derive some bounds on the error rate performance for different scenarios with the MMSE receiver.
... Lattice reduction (LR) techniques have been introduced to improve the performance of low-complexity equalizers without increasing the complexity significantly [111,67,19,89,87,117,121,122]. ...
Receiver design, especially equalizer design, in communications is a major concern in both academia and industry. It is a problem with both theoretical challenges and severe implementation hurdles. While much research has been focused on reducing complexity for optimal or near-optimal schemes, it is still common practice in industry to use simple techniques (such as linear equalization) that are generally significantly inferior. Although digital signal processing (DSP) technologies have been applied to wireless communications to enhance the throughput, the users' demands for more data and higher rate have revealed new challenges. For example, to collect the diversity and combat fading channels, in addition to the transmitter designs that enable the diversity, we also require the receiver to be able to collect the prepared diversity. Most wireless transmissions can be modeled as a linear block transmission system. Given a linear block transmission model assumption, maximum likelihood equalizers (MLEs) or near-ML decoders have been adopted at the receiver to collect diversity which is an important metric for performance, but these decoders exhibit high complexity. To reduce the decoding complexity, low-complexity equalizers, such as linear equalizers (LEs) and decision feedback equalizers (DFEs) are often adopted. These methods, however, may not utilize the diversity enabled by the transmitter and as a result have degraded performance compared to MLEs. In this dissertation, we will present efficient receiver designs that achieve low bit-error-rate (BER), high mutual information, and low decoding complexity. Our approach is to first investigate the error performance and mutual information of existing low-complexity equalizers to reveal the fundamental condition to achieve full diversity with LEs. We show that the fundamental condition for LEs to collect the same (outage) diversity as MLE is that the channels need to be constrained within a certain distance from orthogonality. The orthogonality deficiency (od) is adopted to quantify the distance of channels to orthogonality while other existing metrics are also introduced and compared. To meet the fundamental condition and achieve full diversity, a hybrid equalizer framework is proposed. The performance-complexity trade-off of hybrid equalizers is quantified by deriving the distribution of od. Another approach is to apply lattice reduction (LR) techniques to improve the ``quality' of channel matrices. We present two widely adopted LR methods in wireless communications, the Lenstra-Lenstra-Lovasz (LLL) algorithm [51] and Seysen's algorithm (SA), by providing detailed descriptions and pseudo codes. The properties of output matrices of the LLL algorithm and SA are also quantified. Furthermore, other LR algorithms are also briefly introduced. After introducing LR algorithms, we show how to adopt them into the wireless communication decoding process by presenting LR-aided hard-output detectors and LR-aided soft-output detectors for coded systems, respectively. We also analyze the performance of proposed efficient receivers from the perspective of diversity, mutual information, and complexity. We prove that LR techniques help to restore the diversity of low-complexity equalizers without increasing the complexity significantly. When it comes to practical systems and simulation tool, e.g., MATLAB, only finite bits are adopted to represent numbers. Therefore, we revisit the diversity analysis for finite-bit represented systems. We illustrate that the diversity of MLE for systems with finite-bit representation is determined by the number of non-vanishing eigenvalues. It is also shown that although theoretically LR-aided detectors collect the same diversity as MLE in the real/complex field, it may show different diversity orders when finite-bit representation exists. Finally, the VLSI implementation of the complex LLL algorithms is provided to verify the practicality of our proposed designs.
Multiple-input-multiple-output (MIMO) linear receivers are often of more practical interest than maximum-likelihood (ML) receivers due to their low decoding complexity but at the cost of worse diversity gain performance. Such a statement on performance loss is due to the assumption of using an independent identically distributed complex Gaussian vector as channel input. By removing this assumption, we find that the diversity performance of MIMO linear receivers can be significantly improved. In an extreme case, it can be the same as that of ML receivers. Specifically, in this paper, we investigate the diversity-multiplexing tradeoff (DMT) performance of MIMO linear receivers with colored and possibly degenerate Gaussian channel inputs. By varying the rank of the covariance matrix of the channel input vector and by allowing temporal coding across multiple channel uses, we show that the MIMO linear receiver can achieve a much better DMT performance than the currently known one. Explicit optimal code constructions are provided, along with simulation results, to justify the above findings. For the case of (2 × 2) and (3 × 3) MIMO linear receivers, simulation results show that the newly proposed codes provide significant gains of 10 and 12.08 dB in Eb/N0 at bit error rate 10-4 compared to the conventional schemes, respectively.
