Channel Rank Research Articles

Performance analysis of decision directed maximum likelihood MIMO channel tracking algorithm

SUMMARYIn this paper, the performance of decision directed (DD) maximum likelihood (ML) channel tracking algorithm is analyzed. The ML channel tracking algorithm presents efficient performance especially in the decision directed mode of the operation. In this paper, after introducing the method for analysis of DD algorithms, the performance of ML MIMO channel tracking algorithm in the DD mode of operation is analyzed. In this method channel tracking error is evaluated for a given decision error rate. Then, the decision error rate is approximated for a given channel tracking error. By solving these two derived equations jointly, both the decision error rate and the channel tracking error are computed. The presented analysis is compared with simulation results for different channel ranks, Doppler frequency shifts, and signal‐to‐noise ratios, and it is shown that the analysis is a good match for simulation results especially in high rank MIMO channels and high Doppler shifts. Copyright © 2012 John Wiley & Sons, Ltd.

Information-Theoretic Analysis of MIMO Channel Sounding

The large majority of commercially available multiple-input multiple-output (MIMO) radio channel measurement devices (sounders) is based on time-division multiplexed switching (TDMS) of a single transmit/receive radio frequency chain into the elements of a transmit/receive antenna array. While being cost-effective, such a solution can cause significant measurement errors due to phase noise and frequency offset in the local oscillators. In this paper, we systematically analyze the resulting errors and show that, in practice, overestimation of channel capacity by several hundred percent can occur. Overestimation is caused by phase noise (and to a lesser extent by frequency offset), leading to an increase of the MIMO channel rank. Our analysis furthermore reveals that the impact of phase errors is, in general, most pronounced if the physical channel has low rank (typical for line-of-sight or poor scattering scenarios). The extreme case of a rank-1 physical channel is analyzed in detail. The capacity bounds derived in this paper show excellent agreement with measurement results. In light of the findings of this paper, the results obtained through MIMO channel measurement campaigns using TDMS-based channel sounders should be interpreted with great care.

High inter-reviewer variability of spike detection on intracranial EEG addressed by an automated multi-channel algorithm

ObjectiveThe goal of this study was to determine the consistency of human reviewer spike detection and then develop a computer algorithm to make the intracranial spike detection process more objective and reliable. MethodsThree human reviewers marked interictal spikes on samples of intracranial EEGs from 10 patients. The sensitivity, precision and agreement in channel ranking by activity were calculated between reviewers. A computer algorithm was developed to parallel the way human reviewers detect spikes by first identifying all potential spikes on each channel using frequency filtering and then block scaling all channels at the same time in order to exclude potential spikes that fall below an amplitude and slope threshold. Its performance was compared to the human reviewers on the same set of patients. ResultsHuman reviewers showed surprisingly poor inter-reviewer agreement, but did broadly agree on the ranking of channels for spike activity. The computer algorithm performed as well as the human reviewers and did especially well at ranking channels from highest to lowest spike frequency. ConclusionsOur algorithm showed good agreement with the different human reviewers, even though they demonstrated different criteria for what constitutes a ‘spike’ and performed especially well at the clinically important task of ranking channels by spike activity. SignificanceAn automated, objective method to detect interictal spikes on intracranial recordings will improve both research and the surgical management of epilepsy patients.

A comparison between detectors of high frequency oscillations

Objective High frequency oscillations (HFOs) are a biomarker of epileptogenicity. Visual marking of HFOs is highly time-consuming and inevitably subjective, making automatic detection necessary. We compare four existing detectors on the same dataset. Methods HFOs and baselines were identified by experienced reviewers in intracerebral EEGs from 20 patients. A new feature of our detector to deal with channels where baseline cannot be found is presented. The original and an optimal configuration are implemented. Receiver operator curves, false discovery rate, and channel ranking are used to evaluate performance. Results All detectors improve performance with the optimal configuration. Our detector had higher sensitivity, lower false positives than the others, and similar false detections. The main difference in performance was in very active channels. Conclusions Each detector was developed for different recordings and with different aims. Our detector performed better in this dataset, but was developed on data similar to the test data. Moreover, optimizing on a particular data type improves performance in any detector. Significance Automatic HFO detection is crucial to propel their clinical use as biomarkers of epileptogenic tissue. Comparing detectors on a single dataset is important to analyze their performance and to emphasize the issues involved in validation.

A decision theoretic approach for channel ranking in crowded unlicensed bands

Interference is disruptive to the operation of wireless sensor networks (WSNs) in unlicensed bands as wireless systems proliferate on the spectrum. The design of a spectrum sharing scheme for WSNs to enable coexistence with geographically collocated heterogeneous wireless systems having multiple parallel interfering channels is a persistent challenge. In this context, interference identification and channel ranking in terms of spectrum access opportunities are addressed in this paper. The goal is to develop a low complexity channel ranking algorithm from channel energy measurements at sensors when a packet-reception-ratio to signal-to-interference-and-noise-ratio (PRR-SINR) interference model is unavailable at network initialization phase. The interference characterizing estimators, temporal occupancy and strength level of a channel, are proposed for interference identification. The effectiveness of the estimators is tested on a sensor platform at 2.4 GHz ISM band under interference from WLAN. Subsequently, the impact of the interference estimators on a channel quality from a receiver perspective is determined with a decision theoretic approach. The estimators are weighted according to their influence on the fitness of a channel and channel ranking is established. The proposed channel ranking achieves a significant gain over heuristic channel ranking (HCR) and gives an accurate interference profile of the channels.

A probabilistic model for sub-carrier allocation in OFDMA systems

Orthogonal frequency division multiple-access technique showed a successful utilization of channel features. It implements an orthogonal sub-carrier space to be shared among different users. The management of these sub-carriers in both power and frequency allocation is reflected on the systems performance as better utilization of bandwidth, and hence, better capacity is obtained. Sub-carrier allocation is used to avoid deep fading that might occur at some user’s locations but not at other user’s locations. In this paper, we devise an algorithm based on probabilistic model for sub-carrier allocation to avoid deep fading in some user’s signals. By controlling the sub-carrier allocation for each user, we can create a full rank channel for each user and hence, provide maximum capacity for the system. Simulation results showed that using the devised algorithm will avoid deep fading and utilize the bandwidth up to 40% more than localized allocation strategies.

HTRCI and Channel Ranking Based Joint Symbols Detection for MQRD-PCM/MIMO-OFDM

MIMO-OFDM is considered a key technology in emerging high-data rate systems. In MIMO-OFDM systems, channel estimation and signal detection are important to distinguish transmit signals from multiple transmit antennas. Previously, we have proposed a parallel detection algorithm using multiple QR decompositions (Q is an orthogonal square matrix, R is upper triangular matrix) with permuted channel matrix (MQRD-PCM) to reduce the system complexity of MIMO-OFDM. This method achieves a good BER performance with a low system complexity. However, since MQRD-PCM is a kind of parallel detection method, the wrong detection probability is increased due to the bad channel signal-to-interference plus noise power ratio (SINR) of the transmitted signals. As a result, the average BER performance is influenced by the wrong detection probability of the bad channel SINR. To overcome the above-mentioned problems, in this paper, we propose the high time resolution carrier interferometry and channel ranking based joint signal detection for MQRD-PCM/MIMO-OFDM.

Improving the identification of High Frequency Oscillations

High Frequency Oscillations (HFOs), including Ripples (80-250Hz) and Fast Ripples (250-500Hz), can be recorded from intracranial macroelectrodes in patients with intractable epilepsy. We implemented a procedure to establish the duration for which a stable measurement of rate of HFOs is achieved. To determine concordance, Kappa coefficient was computed. The information gained when increasing the duration was analyzed in terms of HFO rates and ranking of channels with respect to HFO and spike rates. In a group of 30 patients, Kappa was 0.7 for ripples, 0.7 for fast ripples and 0.67 for spikes. Five minutes provided the same information as 10min in terms of rates in 9/10 patients and with respect to ranking of channels in 8/10 patients; 5/30 patients did not achieve stable measurements of HFOs or spikes and needed marking for 10min. We propose that 5min provides in most cases the same information as a longer interval when identifying HFOs and spikes in slow wave sleep, and present methods to identify when this is not the case. This procedure is useful to control for consistency between readers and to evaluate if the selected interval provides stable information, for automatic and visual identification of events.

Retrieval of upper tropospheric relative humidity profiles over low clouds from the Atmospheric Infrared Sounder

In this paper we discuss a method to retrieve humidity profiles in the upper troposphere using cloud‐affected radiances measured by the Atmospheric Infrared Sounder (AIRS). The magnitude of retrieval error for temperature and water vapor profiles caused by ignoring cloud presence depends strongly on the height of clouds as well as on the cloud fraction in the sensor's field of view. Error analysis based on radiative transfer calculations performed for 155 channels using a set of diverse atmospheric profiles shows that the relative humidity in the upper troposphere at pressure levels between 200 and 400 hPa could be estimated if the cloud height was lower than the height of the 800 hPa pressure level. Applying the channel ranking technique to evaluate the cloud influence in the observed spectra, we examined a high‐resolution humidity map of the upper troposphere over land and sea.

Performance Enhancement of MQRD-PCM/MIMO-OFDM Using Channel Ranking Based Joint Symbols Detection

MIMO-OFDM is considered a key technology in emerging high-data rate systems. With MIMO techniques, the transmission quality deteriorates due to inter-antenna interference (IAI). Several signal detection schemes have been proposed to mitigate this problem. However, it is impractical to use the conventional methods without reducing theirs computational complexity. Previously, we have proposed a parallel detection algorithm using multiple QR decompositions with permuted channel matrix (MQRD-PCM) for MIMO-OFDM to reduce the system complexity. This method achieves a good BER performance with low system complexity. However, since MQRD-PCM is a kind of parallel detection method, the wrong detection probability is increased due to the bad channel SINR of the transmitted signal. As a result, the average BER performance is influenced by the wrong detection probability of the bad channel SINR. To overcome this problem, in this paper, we propose the channel ranking based joint symbols detection for MQRD-PCM/MIMO-OFDM.

Hierarchical Space-Time Block Code Recognition Using Correlation Matrices

The blind recognition of communication parameters is a key research issue for commercial and military communication systems. The results of numerous investigations about symbol timing estimation, modulation recognition as well as identification of the number of transmitters have been reported in the literature. But, to our knowledge, none of them have dealt with the recognition of the Space-Time Block Codes (STBC) used in multiple transmitter communications. In order to blindly recognize the STBC of a wireless communication, this paper proposes a method based on the space-time correlations of the received signals. Under perfect timing synchronization and under ideal conditions (full rank channel and a number of receivers greater or equal to the number of transmitters), it shows that the Frobenius norms of these statistics present non-null values whose positions only depend on the STBC at the transmitter side. A classifier for the space-time code recognition of 5 linear STBC (Spatial Multiplexing, Alamouti Coding, and 3 Orthogonal STBC using 3 antennas) is presented. Simulations show that the proposed method performs well even at low signal-to-noise ratios.

Tracking Performance of Least Squares MIMO Channel Estimation Algorithm

In this paper, the tracking performance analysis of the least squares (LS) multiple-input multiple-output (MIMO) channel estimation and tracking algorithm is presented. MIMO channel estimation is a novel application of the LS algorithm that presents near-optimum performance by Karami and Shiva in 2003 and 2006. In this paper, the mean square error (MSE) of tracking of the LS MIMO channel estimator algorithm is derived as a closed-form function of the Doppler shift, forgetting factor, channel rank, and the length of training sequences. In the analysis, all training symbols are considered as randomly generated equal-power vectors on the unit circle, or in other words, phase-shift keying (PSK) signaling. By evaluating this function, some insights into the tracking behavior of the LS MIMO channel estimator are achieved. Then, the calculated tracking error is compared with the tracking error derived from Monte Carlo simulation for quaternary-PSK-based training signals to verify the validation of the presented analysis. Finally, the optimum forgetting factor is derived to minimize the error function, and it is shown that the optimum forgetting factor is highly dependent on the training length, Doppler shift, and E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> /N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sub> . Also, it is concluded that in low E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> /N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sub> values, the number of transmitter antennas has negligible effect on the optimal value of the forgetting factor.

Degrees of Freedom for the MIMO Interference Channel

In this correspondence, we show that the exact number of spatial degrees of freedom (DOF) for a two user nondegenerate (full rank channel matrices) multiple-input-multiple-output (MIMO) Gaussian interference channel with M1, M2 antennas at transmitters 1, 2 and N1, N2 antennas at the corresponding receivers, and perfect channel knowledge at all transmitters and receivers, is min{M1 + M2, N1 + M2, max(M1, N2), max(M2, N1)}. A constructive achievability proof shows that zero forcing is sufficient to achieve all the available DOF on the two user MIMO interference channel. We also show through an example of a share-and-transmit scheme how the gains of transmitter cooperation may be entirely offset by the cost of enabling that cooperation so that the available DOF are not increased.

The influence of geological fabric and scale on drainage pattern analysis in a catchment of metamorphic terrain: Laceys Creek, southeast Queensland, Australia

The relationship between geological fabric and drainage patterns in the 81.8 km 2 Laceys Creek sub-catchment of the North Pine River catchment, southeast Queensland, Australia, is analysed using a new channel–ordination system. The Laceys Creek catchment is situated on the South D'Aguilar Block, which underwent metamorphism, faulting and uplift from the Late Carboniferous to Late Triassic. The catchment drains exposures of two main rock units, the Neranleigh–Fernvale Beds and the Bunya Phyllite. Both units are composed of metamorphosed deep-sea sediments that accumulated as an accretionary wedge during late Palaeozoic subduction of the palaeo-Pacific plate under the eastern margin of the Australian craton. The new channel ordination system used in this study allows improved classification of stream segments of equal prominence or rank in comparison to previous schemes. A 10 m contour digital elevation model (DEM) was produced within which drainage channels were digitised. Planar geological features, including bedding, faults, joints and cleavage, were mapped in the field and collated with data from previous geological mapping programs. Regional and local trends of geological fabric are reflected in the variable orientation of channels of different rank in the catchment. Cleavage and fractures are the dominant planar features of the Bunya Phyllite and these correlate most closely with the orientation of middle-order incised stream segments. In contrast, middle-order channels on the Neranleigh–Fernvale Beds most closely correlate with bedding, which dominates the fabric of this unit. Although anthropogenic factors exert local influence and climatic processes exert broad influence on the catchment, this study focuses on structural and lithological fabrics, which are the apparent dominant controls on middle-order channel orientations. Identification of congruent patterns between bedrock fabric and channel ranks is variable, depending on the scale and number of channels included in the analysis. Many low-rank channels correspond closely to the orientation of fine-scale bedding and foliation and these influences may not be detected by coarse-scale mapping. Understanding the extent of geological controls on the morphology of a catchment may assist geo-hazard identification, land-use planning and civil-engineering projects.

Design and performance assessment of maximum capacity MIMO architectures in line-of-sight

The authors investigate the capacity of multiple-input, multiple-output (MIMO) communication systems in line-of-sight (LoS). Under this scenario, the channel is normally rank deficient owing to the linear dependence of the LoS rays&apos; phases on the receive elements. To overcome this problem, specifically designed antenna arrays can be employed, where the antenna elements are positioned in such a way as to preserve orthogonality; hence maximising the channel rank. To help in the design of such systems we derive the criterion for achieving maximum MIMO capacity in a LoS environment as a function of the transmit–receive separation distance, the array orientation and the inter-element spacings. We investigate the performance and the capacity sensitivity for a number of MIMO architectures using a Monte-Carlo simulation and a stochastic channel model. We then present a number of MIMO measurements performed inside an anechoic chamber and in an indoor office environment. Finally, our theoretic predictions are compared against the LoS measurements.

Mutual Information of Multiple-Input Multiple-Output (MIMO) Transmission Schemes

We analyze the mutual information of some common multiple-input multiple-output (MIMO) transmission schemes. Whereas most capacity evaluations are done under the assumption of Gaussian transmit symbols, we take into account restrictions on the transmit symbol alphabet and analyze real world signal constellations. Moreover, we include suboptimum detectors which might be applied in practical systems in the capacity evaluation. Furthermore, we consider not only spatially uncorrelated full rank channels but also channel degradations such as spatial correlation and keyhole effects. The results show that in many practical relevant cases, simple space-time block codes are a robust solution which achieves similar, sometimes even better capacities than spatial multiplexing even though they do not exploit all available MIMO dimensions.

General Capacity Bounds for Spatially Correlated Rician MIMO Channels

This paper considers the capacity of spatially correlated Rician multiple-input multiple-output (MIMO) channels. We consider the general case with double-sided correlation and arbitrary rank channel means. We derive tight upper and lower bounds on the ergodic capacity. In the particular cases when the numbers of transmit and receive antennas are equal, or when the correlation is single sided, we derive more specific bounds which are computationally efficient. The bounds are shown to reduce to known results in cases of independent and identically distributed (i.i.d.) and correlated Rayleigh MIMO channels. We also analyze the outage characteristics of the correlated Rician MIMO channels at high signal-to-noise ratio (SNR). We derive the mean and variance of the mutual information and show that it is well approximated by a Gaussian distribution. Finally, we present numerical results which show the effect of the antenna configuration, correlation level (angle spreads), Rician K-factor, and the geometry of the dominant Rician paths.

Pilot-assisted channel estimation based on second-order statistics

A survey about linear channel estimation exploiting slowly varying channel properties is given for receivers with multiple antenna elements. The slowly varying channel properties are described by the channel's second-order statistics. First, a detailed comparison of classical linear pilot-based channel estimators, a novel matched filter, and reduced-rank (RR) approaches is made in a common framework with respect to the model they assume for the channel, their performance (MSE), and complexity. The matched filter channel estimator is introduced, which exploits second-order statistics with quadratic order of complexity. For flat correlated Rayleigh fading channels, an analytical performance comparison of all estimators in terms of the uncoded bit error probability is provided. It is a generalization of previous results and shows that the matched filter is a low complexity alternative with good performance at an interesting signal-to-noise ratio (SNR) range. The effects of these approaches on linear equalization are briefly discussed in the context of direct-sequence code division multiple access (DS-CDMA), where the focus is on a generalization of the rake receiver in space and time, which reduces the channel rank based on its second-order statistics, resulting in a complexity reduction of the equalizer. For this discussion, a new notation for the generalized rake is presented, which allows for its interpretation in the context of channel estimation and reveals alternatives for implementation. We conclude that exploiting second-order channel statistics results in significant performance gains, and RR channel estimation should only be used together with equalization in the reduced signal subspace.

Demodulation with a Multichannel Estimation Method Using a Reduced Rank Constraint

This paper deals with the Maximum Likelihood Estimation of the multichannel impulse response in a mobile communication system whose base stations are equipped with antennas arrays. The following problem is solved: using the training sequence, find the maximum likelihood multichannel impulse response from one mobile to the base station under a reduced rank constraint in the presence of gaussian noise and jammers with unknown covariance matrix. This method finds applications in demodulation (the reduced rank channel estimate can be used in a Viterbi Algorithm), and experimental results using real signals demonstrate its high performance compared with the standard Minimum Mean Square Error (MMSE) multichannel estimate.

Outdoor MIMO wireless channels: models and performance prediction

We present a new model for multiple-input-multiple-output (MIMO) outdoor wireless fading channels and their capacity performance. The proposed model is more general and realistic than the usual independent and identically distributed (i.i.d.) model, and allows us to investigate the behavior of channel capacity as a function of the scattering radii at transmitter and receiver, distance between the transmit and receive arrays, and antenna beamwidths and spacing. We show how the MIMO capacity is governed by spatial fading correlation and the condition number of the channel matrix through specific sets of propagation parameters. The proposed model explains the existence of channels which exhibit low spatial fading correlation at both ends of the link but still have poor rank properties, and hence, low ergodic capacity. In fact, the model suggests the existence of a more general family of channels spanning continuously from full rank i.i.d. to low-rank pinhole cases. We suggest guidelines for predicting high rank (and hence, high ergodic capacity) in MIMO channels, and show that even at long ranges, high channel rank can easily be sustained under mild scattering conditions. Finally, we validate our results by simulations using ray tracing techniques. Connections with basic antenna theory are made.