In this paper, the distributed cooperative communication of unmanned aerial vehicles (UAVs) is studied, where the condition number (CN) and the inner product (InP) are used to measure the quality of communication links. By optimizing the relative position of UAVs, large channel capacity and stable communication links can be obtained. Using the spherical wave model under the line of sight (LOS) channel, CN expression of the channel matrix is derived when there are Nt transmitters and two receivers in the system. In order to maximize channel capacity, we derive the UAVs position constraint equation (UAVs-PCE), and the constraint between BS elements distance and carrier wavelength is analyzed. The result shows there is an area where no matter how the UAVs' positions are adjusted, the CN is still very large. Then a special scenario is considered where UAVs form a rectangular lattice array, and the optimal constraint between communication distance and UAVs distance is derived. After that, we derive the InP of channel matrix and the gradient expression of InP with respect to UAVs' position. The particle swarm optimization (PSO) algorithm is used to minimize the CN and the gradient descent (GD) algorithm is used to minimize the InP by optimizing UAVs' position iteratively. Both of the two algorithms present great potentials for optimizing the CN and InP respectively. Furthermore, a hybrid algorithm named PSO-GD combining the advantage of the two algorithms is proposed to maximize the communication capacity with lower complexity. Simulations show that PSO-GD is more efficient than PSO and GD. PSO helps GD to break away from local extremum and provides better positions for GD, and GD can converge to an optimal solution quickly by using the gradient information based on the better positions. Simulations also reveal that a better channel can be obtained when those parameters satisfy the UAVs position constraint equation (UAVs-PCE), meanwhile, theory analysis also explains the abnormal phenomena in simulations.

In this letter, a switching detection scheme based on a channel condition number for the MIMO-OFDM system is proposed. The switching algorithm operates by selecting one of three detection schemes of QRD-M, LR-aided MMSE-DFE, and LR-aided MMSE. The switching detection uses the threshold based on the switching algorithm according to the channel condition number. From the simulation results, the proposed detection scheme shows error detection performance and computational complexity in accordance with the threshold for switching detection.

The numerical error of a sample Mahalanobis distance (T2=y'S-1y) with sample covariance matrix S is investigated. It is found that in order to suppress the numerical error of T2, the following conditions need to be satisfied. First, the reciprocal square root of the condition number of S should be larger than the relative error of calculating floating-point real-number variables. The second proposed condition is based on the relative error of the observed sample vector y in T2. If the relative error of y is larger than the relative error of the real-number variables, the former governs the numerical error of T2. Numerical experiments are conducted to show that the numerical error of T2 can be suppressed if the two above-mentioned conditions are satisfied.

When Zero-Forcing (ZF) is adopted as a detector, decreasing the condition number of the channel matrix increases the BER performance. In this paper, we propose a new detection algorithm which reduces the condition number of channel matrix down to nearly 2 on average. Since the least singular value of the channel matrix is a major factor determining the condition number, we, first, project the received signal into a space spanned by singular vectors that are orthogonal to the one corresponding to the least singular value. Then, LR decomposition is performed to reduce further the condition number of the projected channel matrix. Computer simulations show that the performance of the proposed algorithm is comparable to that of the ML detector for both correlated and uncorrelated channels. And also the proposed algorithm provides an at least 2dB improvement compared to the conventional LR-based Ordered Successive Interference Cancellation (LR-OSIC) detector with a Bit Error Rate (BER) of 10-3 and a comparable computation load.

In this letter, an improved channel-adaptive detection scheme based on condition number combined with a QRD-M and CLLL algorithms is presented for MIMO-OFDM systems. The proposed scheme estimates the channel state by using the condition number and then the number of layers for the QRD-M is changed according to the condition number of channel. After the number of layers is determined, the proposed scheme performs the combined QRD-M and CLLL. Simulation results show that the BER curves of the proposed scheme and QRD-M using CLLL have similar performance. However, the complexity of the proposed scheme is about 27% less than QRD-M detection using CLLL.

Genetic algorithm (GA) is now an important tool in the field of wireless communications. For multiple-input/multiple-output (MIMO) wireless communications system employing spatial multiplexing transmission, we evaluate the effects of GA parameters value on channel parameters in fading channels. We assume transmit-correlated Rayleigh and Rician fading with realistic Laplacian power azimuth spectrum. Azimuth spread (AS) and Rician K-factor are selected according to the measurement-based WINNER II channel model for several scenarios. Herein we have shown the effects of GA parameters and channel parameters in different WINNER II scenarios (i.e., AS and K values) and rank of the deterministic components. We employ meta GA that suitably selects the population (P), generation (G) and mutation probability (pm) for the inner GA. Then we show the cumulative distribution function (CDF) obtain experimentally for the condition number C of the channel matrix H. It is found that, GA parameters depend on the channel parameters, i.e., GA parameters are the functions of the channel parameters. It is also found that for the poorer channel conditions smaller GA parameter values are required for MIMO detection. This approach will help to achieve maximum performance in practical condition for the lower numerical complexity.

Multiple-input multiple-output (MIMO) systems with antenna selection are practical in that they can alleviate the computational complexity at the receiver and achieve good reception performance. Channel correlation, not just carrier-to-noise ratio (CNR), has a great impact on reception performance in MIMO channels. We propose a practical receive antenna subset selection algorithm with reduced complexity that uses the condition number of the partial channel matrix and a predetermined CNR threshold. This paper describes the algorithm and its performance evaluation by both computer simulation and indoor experiments using a prototype receiver and received signals obtained in an actual mobile outdoor experiment. The results confirm that our proposed method provides good bit error rate performance by setting the CNR threshold properly.

This letter proposes the use of a new near-An-lattice sphere decoding (LSD) technique for optimum detection in block-data transmission systems instead of the traditional LSD technique. The proposed channel matrix mimics the generator matrix of an An lattice. The condition number (λ) of the proposed channel matrix is less than those of traditional LSD matrices and the initial radius (d) is deterministic, thus the proposed technique achieves significant improvement in performance and complexity reduction.

This paper discusses an efficient discrete model for nonlinear RF power amplifier (PA) with long-term memory effects and analyzes its error. The procedure of converting RF signals and systems into a discrete domain is explained for a discrete baseband memory polynomial model. Unlike a previous simple memory polynomial model, the proposed discrete model has two different sampling frequencies: one for nonlinear system with long-term memory effects and one for input signal. A method to choose an optimal sampling frequency for the system and a discrete memory depth is proposed to minimize the sensitivity of the system for perturbation of the measured data. A two-dimensional sensitivity function which is a product of relative residual and matrix condition number is defined for least square problem of the proposed model. Examples with a wideband WiBro 3FA signal and a WCDMA 4FA signal for nonlinear transmitters are presented to describe the overall procedure and effectiveness of the proposed scheme.

In this paper, we study low complexity transceiver for double space time transmit diversity (DSTTD) and orthogonal frequency division multiplexing (OFDM) system with antenna shuffling. Firstly, we propose a novel antenna shuffling method based on the criterion of minimizing the condition number of channel correlation matrix. The condition number is an indicator about the quality of the channel. By selecting the minimum of condition number which has better channel quality, consequently, a linear detector with respect to this new channel may achieve better performance results. A low complexity variant of the condition number calculation is also proposed, and it is shown that this criterion can be reduced to the minimum mean square error (MMSE) based criterion. Furthermore, the weighted soft decision Viterbi decoding is applied to mitigate noise enhancement inherent to zero forcing (ZF) and MMSE linear receivers and improve error rate performance. Next, we propose an algorithm to reduce the amount of feedback by exploiting the fact that the channel frequency responses across OFDM subcarriers are correlated. In the proposed algorithm, subcarriers are clustered in blocks, which are allocated the same shuffling pattern with the largest number of the shuffling patterns in the cluster. This way, the signaling overhead can be reduced in comparison with each subcarrier based feedback. Extensive simulations show that the proposed techniques for DSTTD-OFDM system outperform other existing techniques under both uncorrelated and highly spatial correlated frequency selective MIMO fading channels.

It is known that MIMO channel matrix condition number influences detectors performance. Several authors have proposed combined decoders, mainly suboptimal, to cope with this fact. These combined algorithms require an estimation of the MIMO channel matrix condition number and a selection of a suitable threshold condition number. This letter presents practical algorithms to carry out the referred tasks and shows their performance in practice.

Recently, a data-selective method has been proposed to achieve low misalignment in affine projection algorithm (APA) by keeping the condition number of an input data matrix small. We present an improved method, and a complexity reduction algorithm for the APA with the data-selective method. Experimental results show that the proposed algorithm has lower misalignment and a lower condition number for an input data matrix than both the conventional APA and the APA with the previous data-selective method.

This letter presents a new mathematical expression for the excess mean-square error (EMSE) of the affine projection (AP) algorithm. The proposed expression explicitly shows the proportional relationship between the EMSE and the condition number of the input signals.

We consider space division multiplexing in a MIMO-OFDM system for high data rate transmission. Channel estimation is very important for suppressing interference and demultiplexing signals. In a wireless LAN system such as IEEE 802.11a, only a few training symbols are inserted in each subcarrier. First, we propose a channel estimation method for a MIMO-OFDM system with two training symbols per subcarrier. The basic idea is to estimate the time-domain channel responses between the transmit and receive antennas. The array response vectors for each subcarrier are calculated by applying a fast Fourier transform to them. We then can obtain the adaptive weights to cancel the interference. We show that employing training symbols having a lower condition number of the matrix used for the channel estimation improves the estimation accuracy. Furthermore, we show the bit error rate for several signal detection schemes using the above estimated channel. It is shown that an ordered successive detection based on an MMSE criterion has excellent performance, that is, it can achieve higher-speed transmissions with a lower transmit power.

The suitability of a complex MIMO channel matrix for spatial multiplexing is verified experimentally in terms of the Demmel condition number. The instantaneous 2 2 MIMO-OFDM channel measurements in several indoor environments indicate the location dependency of the condition number. Wideband frequency characteristics are also analyzed to evaluate the applicability of spatial multiplexing.