Full Diversity Unitary Precoded Integer-Forcing

We consider a point-to-point flat-fading MIMO channel with channel state information known both at transmitter and receiver. At the transmitter side, a lattice coding scheme is employed at each antenna to map information symbols to independent lattice codewords drawn from the same codebook. Each lattice codeword is then multiplied by a unitary precoding matrix ${\bf P}$ and sent through the channel. At the receiver side, an integer-forcing (IF) linear receiver is employed. We denote this scheme as unitary precoded integer-forcing (UPIF). We show that UPIF can achieve full-diversity under a constraint based on the shortest vector of a lattice generated by the precoding matrix ${\bf P}$. This constraint and a simpler version of that provide design criteria for two types of full-diversity UPIF. Type I uses a unitary precoder that adapts at each channel realization. Type II uses a unitary precoder, which remains fixed for all channel realizations. We then verify our results by computer simulations in $2\times2$, and $4\times 4$ MIMO using different QAM constellations. We finally show that the proposed Type II UPIF outperform the MIMO precoding X-codes at high data rates.Comment: 12 pages, 8 figures, to appear in IEEE-TW

Achieving Low-Complexity Maximum-Likelihood Detection for the 3D MIMO Code

The 3D MIMO code is a robust and efficient space-time block code (STBC) for the distributed MIMO broadcasting but suffers from high maximum-likelihood (ML) decoding complexity. In this paper, we first analyze some properties of the 3D MIMO code to show that the 3D MIMO code is fast-decodable. It is proved that the ML decoding performance can be achieved with a complexity of O(M^{4.5}) instead of O(M^8) in quasi static channel with M-ary square QAM modulations. Consequently, we propose a simplified ML decoder exploiting the unique properties of 3D MIMO code. Simulation results show that the proposed simplified ML decoder can achieve much lower processing time latency compared to the classical sphere decoder with Schnorr-Euchner enumeration

Transmission and detection for space-time block coding and v-blast systems

This dissertation focuses on topics of data transmission and detection of space -time block codes (STBC). The STBCs can be divided into two main categories, namely, the orthogonal space-time block codes (OSTBC) and the quasi-orthogonal space-time codes (Q-OSTBC). The space-time block coded systems from transceiver design perspective for both narrow-band and frequency selective wireless environment are studied. The dissertation also processes and studies a fast iterative detection scheme for a high-rate space-time transmission system, the V-BLAST system. In Chapter 2, a new OSTBC scheme with full-rate and full-diversity, which can be used on QPSK transceiver systems with four transmit antennas and any number of receivers is studied. The newly proposed coding scheme is a non-linear coding. Compared with full-diversity QOSTBC, an obvious advantage of our proposed new OSTBC is that the coded signals transmitted through all four transmit antennas do not experience any constellation expansion. In Chapter 3, a new fast coherent detection algorithm is proposed to provide maximum likelihood (ML) detection for Q-OSTBC. The new detection scheme is also very useful to analysis the diversity property of Q-OSTBC and design full diversity Q-OSTBC codes. The complexity of the new proposed detection algorithm can be independent to the modulation order and is especially suitable for high data rate transmission. In Chapter 4, the space-time coding schemes in frequency selective channels are studied. Q-OSTC transmission and detection schemes are firstly extended for frequency selective wireless environment. A new block based quasi-orthogonal space-time block encoding and decoding (Q-OSTBC) scheme for a wireless system with four transmit antennas is proposed in frequency selective fading channels. The proposed MLSE detection scheme effectively combats channel dispersion and frequency selectivity due to multipath, yet still provides full diversity gain. However, since the computational complexity of MLSE detection increases exponentially with the maximum delay of the frequency selective channel, a fast sub-optimal detection scheme using MMSE equalizer is also proposed, especially for channels with large delays. The Chapter 5 focuses on the V-BLAST system, an important high-rate space-time data transmission scheme. A reduced complexity ML detection scheme for VBLAST systems, which uses a pre-decoder guided local exhaustive search is proposed and studied. A polygon searching algorithm and an ordered successive interference cancellation (O-SIC) sphere searching algorithm are major components of the proposed multi-step ML detectors. At reasonable high SNRs, our algorithms have low complexity comparable to that of O-SIC algorithm, while they provide significant performance improvement. Another new low complexity algorithm termed ordered group-wise interference cancellation (O-GIC) is also proposed for the detection of high dimensional V-BLAST systems. The O-GIC based detection scheme is a sub-optimal detection scheme, however, it outperforms the O-SIC

Quantum search algorithms, quantum wireless, and a low-complexity maximum likelihood iterative quantum multi-user detector design

The high complexity of numerous optimal classic communication schemes, such as the maximum likelihood (ML) multiuser detector (MUD), often prevents their practical implementation. In this paper, we present an extensive review and tutorial on quantum search algorithms (QSA) and their potential applications, and we employ a QSA that finds the minimum of a function in order to perform optimal hard MUD with a quadratic reduction in the computational complexity when compared to that of the ML MUD. Furthermore, we follow a quantum approach to achieve the same performance as the optimal soft-input soft-output classic detectors by replacing them with a quantum algorithm, which estimates the weighted sum of a function’s evaluations. We propose a soft-input soft-output quantum-assisted MUD (QMUD) scheme, which is the quantum-domain equivalent of the ML MUD. We then demonstrate its application using the design example of a direct-sequence code division multiple access system employing bit-interleaved coded modulation relying on iterative decoding, and compare it with the optimal ML MUD in terms of its performance and complexity. Both our extrinsic information transfer charts and bit error ratio curves show that the performance of the proposed QMUD and that of the optimal classic MUD are equivalent, but the QMUD’s computational complexity is significantly lower

Turbo space-time coding for mimo systems : designs and analyses

Multiple input multiple output (MIMO) systems can provide high diversity, high data rate or a mix of both, for wireless communications. This dissertation combines both modes and suggests analyses and techniques that advance the state of the art of MIMO systems. Specifically, this dissertation studies turbo space-time coding schemes for MIMO systems. Before the designs of turbo space-time codes are presented, a fundamental tool to analyze and design turbo coding schemes, the extrinsic information transfer (EXIT) chart method, is extended from the binary/nonbinary code case to coded modulation case. This extension prepares the convergence analysis for turbo space-time code. Turbo space-time codes with symbols precoded by randomly chosen unitary time variant linear transformations (TVLT) are investigated in this dissertation. It is shown that turbo codes with TVLT achieve full diversity gain and good coding gain with high probability. The probability that these design goals are not met is shown to vanish exponentially with the Hamming distance between codewords (number of different columns). Hence, exhaustive tests of the rank and the determinant criterion are not required. As an additional benefit of the application of TVLT, with the removal of the constant modulation condition, it is proved that throughput rates achieved by these codes are significantly higher than the rates achievable by conventional space-time codes. Finally, an EXIT chart analysis for turbo space-time codes with TVLT is developed, with application to predicting frame error rate (FER) performance without running full simulation. To increase the data rate of turbo-STC without exponentially increasing the decoding complexity, a multilevel turbo space-time coding scheme with TVLT is proposed. An iterative joint demapping and decoding receiver algorithm is also proposed. For MIMO systems with a large number of transmit antennas, two types of layered turbo space-time (LTST) coding schemes are studied. For systems with low order modulation, a type of LTST with a vertical encoding structure and a low complexity parallel interference cancellation (PlC) receiver is shown to achieve close to capacity performance. For high order modulation, another type of LTST with a horizontal encoding structure, TVLT, and an ordered successive interference cancellation (OSIC) receiver is shown to achieve better performance than conventional layered space-time coding schemes, where ordering is not available in the SIC detection

Cyclic division algebras: a tool for space-time coding

Multiple antennas at both the transmitter and receiver ends of a wireless digital transmission channel may increase both data rate and reliability. Reliable high rate transmission over such channels can only be achieved through Space–Time coding. Rank and determinant code design criteria have been proposed to enhance diversity and coding gain. The special case of full-diversity criterion requires that the difference of any two distinct codewords has full rank. Extensive work has been done on Space–Time coding, aiming at finding fully diverse codes with high rate. Division algebras have been proposed as a new tool for constructing Space–Time codes, since they are non-commutative algebras that naturally yield linear fully diverse codes. Their algebraic properties can thus be further exploited to improve the design of good codes. The aim of this work is to provide a tutorial introduction to the algebraic tools involved in the design of codes based on cyclic division algebras. The different design criteria involved will be illustrated, including the constellation shaping, the information lossless property, the non-vanishing determinant property, and the diversity multiplexing trade-off. The final target is to give the complete mathematical background underlying the construction of the Golden code and the other Perfect Space–Time block codes

Low-complexity dominance-based Sphere Decoder for MIMO Systems

The sphere decoder (SD) is an attractive low-complexity alternative to maximum likelihood (ML) detection in a variety of communication systems. It is also employed in multiple-input multiple-output (MIMO) systems where the computational complexity of the optimum detector grows exponentially with the number of transmit antennas. We propose an enhanced version of the SD based on an additional cost function derived from conditions on worst case interference, that we call dominance conditions. The proposed detector, the king sphere decoder (KSD), has a computational complexity that results to be not larger than the complexity of the sphere decoder and numerical simulations show that the complexity reduction is usually quite significant