Low-Complexity Near-MAP Decoding of Large Non-Orthogonal STBCs Using PDA

Non-orthogonal space-time block codes (STBC) from cyclic division algebras (CDA) are attractive because they can simultaneously achieve both high spectral efficiencies (same spectral efficiency as in V-BLAST for a given number of transmit antennas) as well as full transmit diversity. Decoding of non-orthogonal STBCs with hundreds of dimensions has been a challenge. In this paper, we present a probabilistic data association (PDA) based algorithm for decoding non-orthogonal STBCs with large dimensions. Our simulation results show that the proposed PDA-based algorithm achieves near SISO AWGN uncoded BER as well as near-capacity coded BER (within 5 dB of the theoretical capacity) for large non-orthogonal STBCs from CDA. We study the effect of spatial correlation on the BER, and show that the performance loss due to spatial correlation can be alleviated by providing more receive spatial dimensions. We report good BER performance when a training-based iterative decoding/channel estimation is used (instead of assuming perfect channel knowledge) in channels with large coherence times. A comparison of the performances of the PDA algorithm and the likelihood ascent search (LAS) algorithm (reported in our recent work) is also presented.

Modified linear prediction method for directions of arrival estimation of narrow-band plane waves

A modified linear prediction (MLP) method is proposed in which the reference sensor is optimally located on the extended line of the array. The criterion of optimality is the minimization of the prediction error power, where the prediction error is defined as the difference between the reference sensor and the weighted array outputs. It is shown that the L2-norm of the least-squares array weights attains a minimum value for the optimum spacing of the reference sensor, subject to some soft constraint on signal-to-noise ratio (SNR). How this minimum norm property can be used for finding the optimum spacing of the reference sensor is described. The performance of the MLP method is studied and compared with that of the linear prediction (LP) method using resolution, detection bias, and variance as the performance measures. The study reveals that the MLP method performs much better than the LP technique.

STBCs with Reduced Sphere Decoding Complexity for Two-User MIMO-MAC

In this paper, Space-Time Block Codes (STBCs) with reduced Sphere Decoding Complexity (SDC) are constructed for two-user Multiple-Input Multiple-Output (MIMO) fading multiple access channels. In this set-up, both the users employ identical STBCs and the destination performs sphere decoding for the symbols of the two users. First, we identify the positions of the zeros in the R matrix arising out of the Q-R decomposition of the lattice generator such that (i) the worst case SDC (WSDC) and (ii) the average SDC (ASDC) are reduced. Then, a set of necessary and sufficient conditions on the lattice generator is provided such that the R matrix has zeros at the identified positions. Subsequently, explicit constructions of STBCs which results in the reduced ASDC are presented. The rate (in complex symbols per channel use) of the proposed designs is at most 2/N-t where N-t denotes the number of transmit antennas for each user. We also show that the class of STBCs from complex orthogonal designs (other than the Alamouti design) reduce the WSDC but not the ASDC.

Optimal Weighted Antenna Selection For Imperfect Channel Knowledge From Training

Receive antenna selection (AS) reduces the hardware complexity of multi-antenna receivers by dynamically connecting an instantaneously best antenna element to the available radio frequency (RF) chain. Due to the hardware constraints, the channels at various antenna elements have to be sounded sequentially to obtain estimates that are required for selecting the ``best'' antenna and for coherently demodulating data. Consequently, the channel state information at different antennas is outdated by different amounts. We show that, for this reason, simply selecting the antenna with the highest estimated channel gain is not optimum. Rather, the channel estimates of different antennas should be weighted differently, depending on the training scheme. We derive closed-form expressions for the symbol error probability (SEP) of AS for MPSK and MQAM in time-varying Rayleigh fading channels for arbitrary selection weights, and validate them with simulations. We then derive an explicit formula for the optimal selection weights that minimize the SEP. We find that when selection weights are not used, the SEP need not improve as the number of antenna elements increases, which is in contrast to the ideal channel estimation case. However, the optimal selection weights remedy this situation and significantly improve performance.

A Training-Based Iterative Detection/Channel Estimation Scheme for Large Non-Orthogonal STBC MIMO Systems

In this paper, we propose a training-based channel estimation scheme for large non-orthogonal space-time block coded (STBC) MIMO systems.The proposed scheme employs a block transmission strategy where an N-t x N-t pilot matrix is sent (for training purposes) followed by several N-t x N-t square data STBC matrices, where Nt is the number of transmit antennas. At the receiver, we iterate between channel estimation (using an MMSE estimator) and detection (using a low-complexity likelihood ascent search (LAS) detector) till convergence or for a fixed number of iterations. Our simulation results show that excellent bit error rate and nearness-to-capacity performance are achieved by the proposed scheme at low complexities. The fact that we could show such good results for large STBCs (e.g., 16 x 16 STBC from cyclic division algebras) operating at spectral efficiencies in excess of 20 bps/Hz (even after accounting for the overheads meant for pilot-based channel estimation and turbo coding) establishes the effectiveness of the proposed scheme.

Optimal Receive Antenna Selection in Time-Varying Fading Channels with Practical Training Constraints

Hardware constraints, which motivate receive antenna selection, also require that various antenna elements at the receiver be sounded sequentially to obtain estimates required for selecting the `best' antenna and for coherently demodulating data thereafter. Consequently, the channel state information at different antennas is outdated by different amounts and corrupted by noise. We show that, for this reason, simply selecting the antenna with the highest estimated channel gain is not optimum. Rather, a preferable strategy is to linearly weight the channel estimates of different antennas differently, depending on the training scheme. We derive closed-form expressions for the symbol error probability (SEP) of AS for MPSK and MQAM in time-varying Rayleigh fading channels for arbitrary selection weights, and validate them with simulations. We then characterize explicitly the optimal selection weights that minimize the SEP. We also consider packet reception, in which multiple symbols of a packet are received by the same antenna. New suboptimal, but computationally efficient weighted selection schemes are proposed for reducing the packet error rate. The benefits of weighted selection are also demonstrated using a practical channel code used in third generation cellular systems. Our results show that optimal weighted selection yields a significant performance gain over conventional unweighted selection.

Optimum aperture distributions in the presence of blockage

A method is presented for optimising the performance indices of aperture antennas in the presence of blockage. An N-dimensional objective function is formed for maximising the directivity factor of a circular aperture with blockage under sidelobe-level constraints, and is minimised using the simplex search method. Optimum aperture distributions are computed for a circular aperture with blockage of circular geometry that gives the maximum directivity factor under sidelobe-level constraints.

Application of novel method for surface-ray tracing over hyperboloidal scatterers

A novel geodesic constant method has been developed for the hitherto unsolved problem of surface-ray tracing over a class of surface, namely the general hyperboloid of revolution (GHOR). All the ray-geometric parameters are obtained analytically in a one-parameter form. The ray parameters derived here for the first time can be readily used in the UTD formulation for computing the mutual coupling between the antennas located on the GHOR.

A Novel, Balanced, and Energy-Efficient Training Method for Receive Antenna Selection

In receive antenna selection (AS), only signals from a subset of the antennas are processed at any time by the limited number of radio frequency (RF) chains available at the receiver. Hence, the transmitter needs to send pilots multiple times to enable the receiver to estimate the channel state of all the antennas and select the best subset. Conventionally, the sensitivity of coherent reception to channel estimation errors has been tackled by boosting the energy allocated to all pilots to ensure accurate channel estimates for all antennas. Energy for pilots received by unselected antennas is mostly wasted, especially since the selection process is robust to estimation errors. In this paper, we propose a novel training method uniquely tailored for AS that transmits one extra pilot symbol that generates accurate channel estimates for the antenna subset that actually receives data. Consequently, the transmitter can selectively boost the energy allocated to the extra pilot. We derive closed-form expressions for the proposed scheme's symbol error probability for MPSK and MQAM, and optimize the energy allocated to pilot and data symbols. Through an insightful asymptotic analysis, we show that the optimal solution achieves full diversity and is better than the conventional method.

Recent advances in radar technology

The technical developments and advances that have taken place thus far are reviewed in those areas impacting future phased array active aperture radar systems. The areas covered are printed circuit antennas and antenna arrays, GaAs MMIC design and fabrication leading to affordable transmitter-receiver (T-R) modules, and novel hardware and software developments. The use of fiber-optic distribution networks to interconnect the monolithically integrated optical components with the T-R modules is discussed. Beamforming and sidelobe control techniques for active phased array systems are also examined.

Current State of Domestic Concealed Wiring Practices in Bangalore, India

In a modernising world, building and construction trends in recent urban centres such as Bangalore, set precedence for developments in other urban centres of the country. Under such conditions, evaluating the current state of building practices could prove useful for identifying the likely nature of nationwide building trends. This paper comprises a study to evaluate the current state of domestic concealed wiring practices in the context of a modern urban centre area in India. Presently, concealed wiring is the predominant wiring method adopted for residences, both bungalows and apartments. A modern residential block in the city of Bangalore (India) was chosen as the study area. The study included extensive interaction and surveys amongst residents, professionals (architects and engineers) and site personnel (contractors and electricians). In addition, the study also included site verification on the state of wiring practices in the residential block. The study indicates that while aesthetics was the prime reason that dictated the choice of concealed wiring, its effectiveness as an appropriate and safe wiring method is severely compromised. Details of the study, results and recommendations are presented in this paper.

Reduced ML-Decoding Complexity, Full-Rate STBCs for 4 Transmit Antenna Systems

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

Training-Symbol Embedded, High-Rate Complex Orthogonal Designs for Relay Networks

Distributed Space-Time Block Codes (DSTBCs) from Complex Orthogonal Designs (CODs) (both square and non-square CODs other than the Alamouti design) are known to lose their single-symbol ML decodable (SSD) property when used in two-hop wireless relay networks using the amplify and forward protocol. For such a network, a new class of high rate, training-symbol embedded (TSE) SSD DSTBCs are proposed from TSE-CODs. The constructed codes include the training symbols within the structure of the code which is shown to be the key point to obtain high rate along with the SSD property. TSE-CODs are shown to offer full-diversity for arbitrary complex constellations. Non-square TSE-CODs are shown to provide better rates (in symbols per channel use) compared to the known SSD DSTBCs for relay networks when the number of relays is less than 10. Importantly, the proposed DSTBCs do not contain zeros in their codewords and as a result, antennas of the relay nodes do not undergo a sequence of switch on and off transitions within every codeword use. Hence, the proposed DSTBCs eliminate the antenna switching problem.

Robust Transceiver Design for Multiuser MIMO Downlink

In this paper, we consider robust joint linear precoder/receive filter design for multiuser multi-input multi-output (MIMO) downlink that minimizes the sum mean square error (SMSE) in the presence of imperfect channel state information (CSI). The base station is equipped with multiple transmit antennas, and each user terminal is equipped with multiple receive antennas. The CSI is assumed to be perturbed by estimation error. The proposed transceiver design is based on jointly minimizing a modified function of the MSE, taking into account the statistics of the estimation error under a total transmit power constraint. An alternating optimization algorithm, wherein the optimization is performed with respect to the transmit precoder and the receive filter in an alternating fashion, is proposed. The robustness of the proposed algorithm to imperfections in CSI is illustrated through simulations.

High-Rate Space-Time Coded Large MIMO Systems: Low-Complexity Detection and Performance

Large MIMO systems with tens of antennas in each communication terminal using full-rate non-orthogonal space-time block codes (STBC) from Cyclic Division Algebras (CDA) can achieve the benefits of both transmit diversity as well as high spectral efficiencies. Maximum-likelihood (ML) or near-ML decoding of these large-sized STBCs at low complexities, however, has been a challenge. In this paper, we establish that near-ML decoding of these large STBCs is possible at practically affordable low complexities. We show that the likelihood ascent search (LAS) detector, reported earlier by us for V-BLAST, is able to achieve near-ML uncoded BER performance in decoding a 32x32 STBC from CDA, which employs 32 transmit antennas and sends 32(2) = 1024 complex data symbols in 32 time slots in one STBC matrix (i.e., 32 data symbols sent per channel use). In terms of coded BER, with a 16x16 STBC, rate-3/4 turbo code and 4-QAM (i.e., 24 bps/Hz), the LAS detector performs close to within just about 4 dB from the theoretical MIMO capacity. Our results further show that, with LAS detection, information lossless (ILL) STBCs perform almost as good as full-diversity ILL (FD-ILL) STBCs. Such low-complexity detectors can potentially enable implementation of high spectral efficiency large MIMO systems that could be considered in wireless standards.