Ebrahim Karami

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 Eb/No. Also, it is concluded that in low Eb/No values, the number of transmitter antennas has negligible effect on the optimal value of the forgetting factor.

Blind Multi-Input–Multi-Output Channel Tracking Using Decision-Directed Maximum-Likelihood Estimation

In this paper, a new channel-estimation algorithm based on maximum-likelihood (ML) algorithm for estimation and tracking of the multiple-input-multiple-output (MIMO) channels is presented. The ML algorithm presents the optimum estimation when the exact channel model is known. The derived channel-estimation algorithm is very efficient, with a computational complexity comparable to the least mean square and much lower than the recursive least squares and the Kalman algorithms. The proposed algorithm is analyzed, and the effect of the channel-tracking error is applied as a modifying component for the derived algorithm. The proposed algorithm is simulated for half- and full-rank flat-fading time-varying MIMO channels for the different values of fDT, Eb/N0, and training lengths via Monte Carlo simulation technique. The minimum mean-square-error (mmse) joint detector is considered as the detection algorithm. The output of the mmse receiver is considered as the virtual training data in the blind mode of operation: the same as in the decision-directed algorithm. By various simulations, the bit error rate and the mse of tracking the proposed algorithm for different values of f DT, presenting the speed of channel variations, are evaluated and compared with the Kalman filtering approach. By simulating the proposed algorithm for different values of the training length, the minimum training length required for different channel conditions is extracted

Frequency domain block filtering GNSS receivers

Partial matched filtering is a candidate receiver type to handle large Doppler frequency uncertainty in joint timing and frequency acquisition as has been demonstrated during the last ten years. In addition, frequency domain matched filtering has been attained more interest recently since it allows fast acquisition and efficient implementation of generic filters in addition to a fact that it can serve several modulations. This paper joins partial matched and frequency domain filtering presenting a frequency domain partial matched filtering approach. Complexity analysis shows that this is an efficient scheme to implement joint time-frequency acquisition systems. Simulation results verify the performance showing that the receiver performs like the theory predicts, i.e., as well as time domain counterparts.

Performance of MIMO Schemes with Channel Estimation Errors

In this paper, we investigate the optimum detection of MIMO signals in the presence of channel estimation errors. A maximum likelihood (ML)-based detection algorithm is proposed for optimal MIMO signal detection based on the modified ML criterion which takes into account channel estimation errors. Moreover, we evaluate for both the uncoded and coded case, the bit-error-rate (BER) performance of the hard decoded MIMO systems. The new algorithm, taking into account channel estimation errors, achieves improvement in terms of BER gain over the conventional MIMO detector algorithm ignoring channel estimation errors. Moreover, the optimal designed constellations taking channel estimation errors into account, show an increase in the capacity over conventional schemes.

Optimization of routing, network coding and scheduling in wireless multicast ad-hoc networks with topology compression

In this paper, we present new methodology and results for joint routing and link scheduling optimization in multicast wireless ad-hoc networks. The impact of multicast diversity on scheduling is controlled by using topology compression concept quantified through compressed multicast topology matrix. To define topology matrix, first a set of all possible multicast paths, including network coded paths, is identified. A subset of these paths with appropriate rates is chosen to maximize achievable throughput or throughput per sum of transmitting powers on the route, in a conflict free environment created by proper scheduling. Therefore this optimization provides two improvement gains, throughput gain from scheduling on a compressed network topology and the gain from mixed path selection optimizations with a careful compromise between the multicast diversity and network coding. Numerical results, as illustration, are presented for a simple wireless butterfly network. If just throughput regardless of power consumption is maximized, then depending on the system parameters both a network coded structure or a plain routing can be optimum. On the other hand if throughput per power is maximized, a mixed set of plain routing paths is the optimum solution.

Optimization of Wireless Multi-Source Multicast Ad-Hoc Networks Using Asymmetric Matrix Games

In this paper, we use matrix games framework for joint optimization of routing and network coding under conflict free scheduling for multi-source wireless ad-hoc networks. The impact of multicast diversity on scheduling is controlled by using topology compression concept quantified through compressed multicast topology matrix. To define topology matrix, first a set of all possible paths, including network coded paths, is identified and compressed. Depending on the nature of data selected path can be unicast or multicast. Then by switching between these paths with appropriate rates (frequencies), achievable scaled throughput is maximized. A link conflict free environment is designed by appropriate conflict free network partitioning using network graph coloring algorithm. For each possible coloring scheme and considering priority assigned to each source, link scheduling partitions topology matrix into multiple sub-matrices, one for each partial topologies. Each sub-matrix is used as a payoff matrix for an asymmetrical matrix game where against any single move of the second player, first player has multiple (K) moves, corresponding to different partial topologies or their equivalent colors. The strategy sets for the players are links and paths respectively. Such a game will be formally referred to as Asymmetrical Matrix Game with notation AMG(2,K,1) and the value of this game is inverse of the scaled throughput. In this notation 2 indicates two dimensional games. At the equilibrium, mixed strategy vector of the first player indicates optimum percentage of time or optimum number of time slots dedicated to the selected partial topologies for a given partitioning of the network graph while, mixed strategy vectors of the second player is proportional to optimum usage rates of the paths. Numerical results are presented for a simple butterfly network including 6 nodes and 2 sources. One source transmits multicast and second one unicast data with different priority.

Equalization of MIMO-OFDM Channels Using Bussgang Algorithm

In this paper, Bussgang algorithm is developed as a blind equalizer for multi-carrier multi-input multi-output (MIMO) channels to combat both spatial multiplexing interference and channel variations. Also, the Bussgang technique is extended with adapting the one or two parameters in its nonlinear function. The Bussgang algorithm and its two extended version are simulated and compared to the full known channel (ideal) and decision directed cases. Frame error rate (FER) and bit error rate (BER) of both coded and uncoded cases, are considered as comparison criteria and it is shown that the much performance improvement is achieved compared to decision directed algorithm and each of the three proposed schemes presents the best performance in the different criteria and Eb/NO.

A Near Optimum Low Complexity Detection Algorithm for MIMO OFDM Channels

In this paper, a joint detection algorithm is proposed for multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) channels. In MIMO OFDM channels, if enough cyclic prefix (CP) is used, intersymbol interference is completely cancelled and consequently spatial multiplexing interference (SMI) is the main limiting factor in performance. The proposed algorithm is based on a new soft parallel interference cancellation (SPIC) technique where, in each iteration, a part of SMI proportional to the probability of correctness of estimation in last iteration is cancelled. This probability is calculated approximately assuming the correct estimation for other sub-streams in last iteration. The proposed algorithm approaches the optimum performance in only a few iterations. The proposed algorithm is simulated for 4 states 1/2 turbo code and 8times12, 12times12 and 4times4 MIMO OFDM channels for different values of the Eb/N0. Bit error rate (BER) and frame error rate (FER) are considered as comparison criteria and it is shown that its performance is good and very close to interference free (lower bound) case.

Stochastic Models of Coalition Games for Spectrum Sharing in Large Scale Interference Channels

In this paper, we present a framework for analysis of self organized distributed coalition formation process for spectrum sharing in interference channel for large scale ad hoc networks. In this approach we define coalition clusters within the network where mutual interdependency between different clusters is characterized by the concept of spatial network correlation. Then by using stochastic models of the process we give up some details which are characteristic for coalition game theory in order to be able to include some additional parameters for network scaling. Applications of this model are: a) Estimation of average time to reach grand coalition and its variance through closed form equations. These parameters are important in designing the process in dynamic environment. b) Dimensioning the coalition cluster within the network c) Modelling the network spatial correlation characterizing mutual visibility of the interfering links. d) Modelling of the effect of the new link activation/inactivation on the coalition forming process. e) Modelling the effect of link mobility on the coalition forming process.

A near optimum joint detection and decoding algorithm for MIMO-OFDM channels

In this paper, a joint detection and decoding algorithm is proposed for the spatial multiplex multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) channels. In the spatial multiplexed MIMO-OFDM channels, if enough cyclic prefix (CP) at least equal to the channel length is used, inter symbol interference is completely canceled and consequently spatial multiplexing interference (SMI) is the main limiting factor on the performance [4]. Optimum SMI cancellation is more complex for practically usage. In this paper, a novel technique is proposed to approach to the performance of the optimum algorithm in much lower complexity. The proposed algorithm is based on a modified soft partially parallel interference cancellation (SPPIC) technique where, in each iteration, a part of the SMI proportional to the probability of the correct estimation in the last iteration, is cancelled. The output of this soft joint detector is fed to a turbo decoder. In the first iteration of the decoding, the probability of the correctness is calculated approximately assuming the correct estimation for other sub-streams in the last iteration and in the next iterations, it is updated using the output LLR of the turbo decoder. The proposed modified SPPIC algorithm is simulated and compared to the minimum mean square of error (MMSE), interference free case (lower bound), and SPPIC algorithms for 4 states frac12 turbo code in 4times4 MIMO OFDM channel assuming Micro cell Winner channel model considering 64 and 512 sub-carriers. Bit error rate (BER) and frame error rate (FER) are considered as comparison criteria and it is shown that the performance of the new algorithm is much better than MMSE algorithm and is very close to the interference-free lower bound.