Blind estimation of MIMO relay channels

In this paper, we integrate two blind source separation (BSS) methods to estimate the individual channel state information (CSI) for the source-relay and relay-destination links of three-node two-hop multiple-input multiple-output (MIMO) relay systems. In particular, we propose a first-order Z-domain precoding technique for the blind estimation of the relay-destination channel matrix, while an algorithm based on the constant modulus and mutual information properties is developed to estimate the source-relay channel matrix. Compared with training-based MIMO relay channel estimation approaches, our algorithm has a better bandwidth efficiency as no bandwidth is wasted for sending the training sequences. Numerical examples are shown to demonstrate the performance of the proposed algorithm. © 2014 IEEE.

Estimation of Symmetric Channels for Discrete Cosine Transform Type-I Multicarrier Systems: A Compressed Sensing Approach

The problem of channel estimation for multicarrier communications is addressed. We focus on systems employing the Discrete Cosine Transform Type-I (DCT1) even at both the transmitter and the receiver, presenting an algorithm which achieves an accurate estimation of symmetric channel filters using only a small number of training symbols. The solution is obtained by using either matrix inversion or compressed sensing algorithms. We provide the theoretical results which guarantee the validity of the proposed technique for the DCT1. Numerical simulations illustrate the good behaviour of the proposed algorithm.

Enhanced detection-guided NLMS estimation of sparse FIR-modeled signal channels

In various signal-channel-estimation problems, the channel being estimated may be well approximated by a discrete finite impulse response (FIR) model with sparsely separated active or nonzero taps. A common approach to estimating such channels involves a discrete normalized least-mean-square (NLMS) adaptive FIR filter, every tap of which is adapted at each sample interval. Such an approach suffers from slow convergence rates and poor tracking when the required FIR filter is "long." Recently, NLMS-based algorithms have been proposed that employ least-squares-based structural detection techniques to exploit possible sparse channel structure and subsequently provide improved estimation performance. However, these algorithms perform poorly when there is a large dynamic range amongst the active taps. In this paper, we propose two modifications to the previous algorithms, which essentially remove this limitation. The modifications also significantly improve the applicability of the detection technique to structurally time varying channels. Importantly, for sparse channels, the computational cost of the newly proposed detection-guided NLMS estimator is only marginally greater than that of the standard NLMS estimator. Simulations demonstrate the favourable performance of the newly proposed algorithm. © 2006 IEEE.

Superimposed channel training algorithm for time-varying MIMO relay systems

Two-way relaying systems are known to be capable of providing higher spectral efficiency compared with one-way relaying systems. However, the channel estimation problem for two-way relaying systems becomes more complicated. In this paper, we propose a superimposed channel training scheme for two-way MIMO relay communication systems, where the individ-ual channel information for users-relay and relay-users links are estimated. The optimal structure of the source and relay training sequences are derived when the mean-squared error (MSE) of channel estimation is minimized. We also optimize the power allocation between the source and relay training sequences to improve the performance of the algorithm. Numerical examples are shown to demonstrate the performance of the proposed channel training algorithm.

Are SC-FDE systems robust to CFO?

This paper investigates the impact of carrier frequency offset (CFO) on Single Carrier wireless communication systems with Frequency Domain Equalization (SC-FDE). We show that CFO in SC-FDE systems causes irrecoverable channel estimation error, which leads to inter-symbol-interference (ISI). The impact of CFO on SC-FDE and OFDM is compared in the presence of CFO and channel estimation errors. Closed form expressions of signal to interference and noise ratio (SINR) are derived for both systems, and verified by simulation results. We find that when channel estimation errors are considered, SC-FDE is similarly or even more sensitive to CFO, compared to OFDM. In particular, in SC-FDE systems, CFO mainly deteriorates the system performance via degrading the channel estimation. Both analytical and simulation results highlight the importance of accurate CFO estimation in SC-FDE systems.

A simple orientation robust transmit polarization signalling scheme

A special transmit polarization signalling scheme is presented to alleviate the power reduction as a result of polarization mismatch from random antenna orientations. This is particularly useful for hand held mobile terminals typically equipped with only a single linearly polarized antenna, since the average signal power is desensitized against receiver orientations. Numerical simulations also show adequate robustness against incorrect channel estimations.

Experimental evaluation of the performance of 2×2 MIMO-OFDM for vehicle-to-infrastructure communications

In this paper, a novel 2×2 multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) testbed based on an Analog Devices AD9361 highly integrated radio frequency (RF) agile transceiver was specifically implemented for the purpose of estimating and analyzing MIMO-OFDM channel capacity in vehicle-to-infrastructure (V2I) environments using the 920 MHz industrial, scientific, and medical (ISM) band. We implemented two-dimensional discrete cosine transform-based filtering to reduce the channel estimation errors and show its effectiveness on our measurement results. We have also analyzed the effects of channel estimation error on the MIMO channel capacity by simulation. Three different scenarios of subcarrier spacing were investigated which correspond to IEEE 802.11p, Long-Term Evolution (LTE), and Digital Video Broadcasting Terrestrial (DVB-T)(2k) standards. An extensive MIMO-OFDM V2I channel measurement campaign was performed in a suburban environment. Analysis of the measured MIMO channel capacity results as a function of the transmitter-to-receiver (TX-RX) separation distance up to 250 m shows that the variance of the MIMO channel capacity is larger for the near-range line-of-sight (LOS) scenarios than for the long-range non-LOS cases, using a fixed receiver signal-to-noise ratio (SNR) criterion. We observed that the largest capacity values were achieved at LOS propagation despite the common assumption of a degenerated MIMO channel in LOS. We consider that this is due to the large angular spacing between MIMO subchannels which occurs when the receiver vehicle rooftop antennas pass by the fixed transmitter antennas at close range, causing MIMO subchannels to be orthogonal. In addition, analysis on the effects of different subcarrier spacings on MIMO-OFDM channel capacity showed negligible differences in mean channel capacity for the subcarrier spacing range investigated. Measured channels described in this paper are available on request.

Leveraging coherent distributed space-time codes for noncoherent communication in relay networks via training

For point to point multiple input multiple output systems, Dayal-Brehler-Varanasi have proved that training codes achieve the same diversity order as that of the underlying coherent space time block code (STBC) if a simple minimum mean squared error estimate of the channel formed using the training part is employed for coherent detection of the underlying STBC. In this letter, a similar strategy involving a combination of training, channel estimation and detection in conjunction with existing coherent distributed STBCs is proposed for noncoherent communication in Amplify-and-Forward (AF) relay networks. Simulation results show that the proposed simple strategy outperforms distributed differential space-time coding for AF relay networks. Finally, the proposed strategy is extended to asynchronous relay networks using orthogonal frequency division multiplexing.

Robust THP Transceiver Designs for Multiuser MIMO Downlink with Imperfect CSIT

We present robust joint nonlinear transceiver designs for multiuser multiple-input multiple-output (MIMO) downlink in the presence of imperfections in the channel state information at the transmitter (CSIT). The base station (BS) is equipped with multiple transmit antennas, and each user terminal is equipped with one or more receive antennas. The BS employs Tomlinson-Harashima precoding (THP) for interuser interference precancellation at the transmitter. We consider robust transceiver designs that jointly optimize the transmit THP filters and receive filter for two models of CSIT errors. The first model is a stochastic error (SE) model, where the CSIT error is Gaussian-distributed. This model is applicable when the CSIT error is dominated by channel estimation error. In this case, the proposed robust transceiver design seeks to minimize a stochastic function of the sum mean square error (SMSE) under a constraint on the total BS transmit power. We propose an iterative algorithm to solve this problem. The other model we consider is a norm-bounded error (NBE) model, where the CSIT error can be specified by an uncertainty set. This model is applicable when the CSIT error is dominated by quantization errors. In this case, we consider a worst-case design. For this model, we consider robust (i) minimum SMSE, (ii) MSE-constrained, and (iii) MSE-balancing transceiver designs. We propose iterative algorithms to solve these problems, wherein each iteration involves a pair of semidefinite programs (SDPs). Further, we consider an extension of the proposed algorithm to the case with per-antenna power constraints. We evaluate the robustness of the proposed algorithms to imperfections in CSIT through simulation, and show that the proposed robust designs outperform nonrobust designs as well as robust linear transceiver designs reported in the recent literature.

Low-Complexity Near-ML Decoding of Large Non-Orthogonal STBCs using Reactive Tabu Search

Non-orthogonal space-time block codes (STBC) with large dimensions 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 large dimensions has been a challenge. In this paper, we present a reactive tabu search (RTS) based algorithm for decoding non-orthogonal STBCs from cyclic division algebras (CDA) having largedimensions. Under i.i.d fading and perfect channel state information at the receiver (CSIR), our simulation results show that RTS based decoding of 12 X 12 STBC from CDA and 4-QAM with 288 real dimensions achieves i) 10(-3) uncoded BER at an SNR of just 0.5 dB away from SISO AWGN performance, and ii) a coded BER performance close to within about 5 dB of the theoretical MIMO capacity, using rate-3/4 turbo code at a spectral efficiency of 18 bps/Hz. RTS is shown to achieve near SISO AWGN performance with less number of dimensions than with LAS algorithm (which we reported recently) at some extra complexity than LAS. We also report good BER performance of RTS when i.i.d fading and perfect CSIR assumptions are relaxed by considering a spatially correlated MIMO channel model, and by using a training based iterative RTS decoding/channel estimation scheme.

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.

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.

On a Ratio of Functions of Exponential Random Variables and Some Applications

Consider L independent and identically distributed exponential random variables (r.vs) X-1, X-2 ,..., X-L and positive scalars b(1), b(2) ,..., b(L). In this letter, we present the probability density function (pdf), cumulative distribution function and the Laplace transform of the pdf of the composite r.v Z = (Sigma(L)(j=1) X-j)(2) / (Sigma(L)(j=1) b(j)X(j)). We show that the r.v Z appears in various communication systems such as i) maximal ratio combining of signals received over multiple channels with mismatched noise variances, ii)M-ary phase-shift keying with spatial diversity and imperfect channel estimation, and iii) coded multi-carrier code-division multiple access reception affected by an unknown narrow-band interference, and the statistics of the r.v Z derived here enable us to carry out the performance analysis of such systems in closed-form.

Training-Symbol Embedded, High-Rate, Single-Symbol ML-Decodable, Distributed STBCs for Relay Networks

Distributed space-time block codes (DSTBCs) from complex orthogonal designs (CODs) (both square and nonsquare), coordinate interleaved orthogonal designs (CIODs), and Clifford unitary weight designs (CUWDs) are known to lose their single-symbol ML decodable (SSD) property when used in two-hop wireless relay networks using amplify and forward protocol. For such networks, in this paper, three new classes of high rate, training-symbol embedded (TSE) SSD DSTBCs are constructed: TSE-CODs, TSE-CIODs, and TSE-CUWDs. The proposed codes include the training symbols inside the structure of the code which is shown to be the key point to obtain the SSD property along with the channel estimation capability. TSE-CODs are shown to offer full-diversity for arbitrary complex constellations and the constellations for which TSE-CIODs and TSE-CUWDs offer full-diversity are characterized. It is shown that DSTBCs from nonsquare TSE-CODs provide better rates (in symbols per channel use) when compared to the known SSD DSTBCs for relay networks. Important from the practical point of view, the proposed DSTBCs do not contain any zeros in their codewords and as a result, antennas of the relay nodes do not undergo a sequence of switch on/off transitions within every codeword, and, thus, avoid the antenna switching problem.