On Bayesian Fisher Information Maximization for Distributed Vector Estimation

Widely distributed multiple-input multiple-output (MIMO) radar systems offer parameter estimation improvement for target localization, proportional to the product of the number of transmitting and receiving radars and the total transmitted power. Thus far, power allocation has been uniformly distributed between the system transmitters. For a large number of radars, the achievable localization mean-square error (MSE), with full resource allocation, may extend beyond the system predetermined performance goals, such as target localization accuracy (i.e., minimum estimation MSE) and total power radiation. In this study, power allocation schemes are developed, taking into account system constraints. The first is concerned with minimizing the total transmitted power such that a predefined estimation MSE objective is met, while keeping the transmitted power at each station within an acceptable range. The second, optimally distributes a given power budget among all transmitting radars to maximize performance, i.e., minimize the attainable localization MSE. As the Cramer-Rao bound (CRB) is known to be asymptotically tight to the maximum likelihood estimator (MLE) MSE at high SNR, it is used as a metric for the estimation MSE. The CRB is derived for a signal model that incorporates the propagation path loss, the target radar cross section (RCS), and the transmitters' powers. It is shown that uniform or equal power allocation is not in general optimal and that the proposed allocation algorithms result in a local optimum that provided either better localization MSE for the same power budget or requires less power to establish the same performance in terms of estimation MSE. A physical interpretation of these conclusions is offered.

In this paper, we consider the subject of diagonal precoder matrix design for a three-input multiple-output system using spatial multiplexing with binary symbols from the constellation {0,1} and noncoherent reception in flat Rayleigh fading having a uniform transmit covariance matrix. For this system, the symbol vector error probability (SEP) tends to saturate at high values of average signal-to-noise ratio per symbol vector per diversity branch. The saturation value of the SEP is minimized with respect to the precoder parameters to obtain the best error performance. It is found that when the number of receive antennas is large, the optimal values of the precoder parameters are almost independent of the number of receive antennas. Numerical results show the advantage of using noncoherent reception over coherent reception with imperfect channel state information.

The scaling of coherent and non-coherent channel capacity is studied in a single-input multiple-output (SIMO) block Rayleigh fading channel as both the bandwidth and the number of receiver antennas go to infinity jointly with the transmit power fixed. The transmitter has no channel state information (CSI), while the receiver may have genie-provided CSI (coherent receiver), or the channel statistics only (non-coherent receiver). Our results show that if the available bandwidth is smaller than a threshold bandwidth which is proportional (up to leading order terms) to the square root of the number of antennas, there is no gap between the coherent capacity and the non-coherent capacity in terms of capacity scaling behavior. On the other hand, when the bandwidth is larger than this threshold, there is a capacity scaling gap. Since achievable rates using pilot symbols for channel estimation are subject to the non-coherent capacity bound, this work reveals that pilot-assisted coherent receivers in systems with a large number of receive antennas are unable to exploit excess spectrum above a given threshold for capacity gain.

The IEEE 802.15.4a standard for wireless sensor networks is designed for highly accurate ranging with impulse radio Ultra Wideband (UWB) signals. The standard is designed for coherent and non-coherent (energy detector) receivers, thus the choice of complexity is left to the implementer. In this paper, the maximal operating distance is analyzed for ranging, using a coherent receiver and an energy detector under FCC/EC regulations. The analysis is based on the working points of the receivers and a link budget calculation. The preamble of the standard is defined by several parameters, which influence the allowed FCC transmit power, the free space losses and thus the maximal operating distance. It is shown which code and channel combinations achieve the largest operating distance. The best performance is achieved by using long spreaded codes, where coherent receivers can achieve a maximal operating distance up to several thousand meters and energy detectors up to several hundred meters.

This paper investigates the problem of adaptive power allocation for distributed best linear unbiased estimation (BLUE) of a random parameter at the fusion center (FC) of a wireless sensor network (WSN). An optimal power-allocation scheme is proposed that minimizes the $L^2$-norm of the vector of local transmit powers, given a maximum variance for the BLUE estimator. This scheme results in the increased lifetime of the WSN compared to similar approaches that are based on the minimization of the sum of the local transmit powers. The limitation of the proposed optimal power-allocation scheme is that it requires the feedback of the instantaneous channel state information (CSI) from the FC to local sensors, which is not practical in most applications of large-scale WSNs. In this paper, a limited-feedback strategy is proposed that eliminates this requirement by designing an optimal codebook for the FC using the generalized Lloyd algorithm with modified distortion metrics. Each sensor amplifies its analog noisy observation using a quantized version of its optimal amplification gain, which is received by the FC and used to estimate the unknown parameter.

The complexity of the multiple-symbol detection structures for partial response continuous phase modulation (CPM) signals goes exponentially with the length of the pulse shaping filter and the observation length as well. Simple no coherent trellis receivers for partial response CPM signals are proposed in this paper. Parallel to the simple coherent detectors, where CPM signals are approximately represented by a sum of Phase Amplitude Modulation waveforms, Laurent decomposition is applied to reduce the complexity. The proposed no coherent receiver is structured with only fixed K matched filters in the front-end and a processor which uses Viterbi algorithm with a 2N-1 states trellis to perform the sequence estimation. It is attractive because the structure does not involve any matrix calculations. The good error performance is confirmed by simulation results.

In this paper, we consider the problem of sensor management for target tracking in a wireless sensor network (WSN). To determine the set of sensors with the most informative data, we develop a probabilistic sensor management scheme based on the concepts developed in compressive sensing. In the proposed scheme where each sensor transmits its observation with a certain probability via a coherent multiple access channel (MAC), the observation vector received at the fusion center becomes a compressed version of the original observations. In this framework, the sensor management problem can be cast as the problem of finding the probability of transmission at each node so that a given performance metric is optimized. Our goal is to determine the optimal values of the probabilities of transmission so that the trace of the Fisher information matrix (FIM) is maximized at any given time instant with a constraint on the available energy. We consider two cases, where the fusion center has i) complete information and ii) only partial information, regarding the sensor transmissions. The expression for FIM is derived for both cases and the optimal values of the probabilities of transmission are found accordingly. With nonidentical probabilities, we obtain the results numerically while under the assumption that each sensor transmits with equal probability, we obtain the optimal values analytically. We provide numerical results to illustrate the performance of the proposed probabilistic sensor management scheme.

Optimal linear minimum mean square error (MMSE) transceiver design techniques are proposed for Bayesian learning (BL)-based sparse parameter vector estimation in a multiple-input multiple-output (MIMO) wireless sensor network (WSN). Our proposed transceiver designs rely on majorization theory and hyperparameter estimates obtained from the BL module for minimizing the mean square error (MSE) of parameter estimation at the fusion center (FC). The linear transceiver design framework is initially proposed for the general scenario with arbitrary SNR sensor observations, followed by a special case with high-SNR sensor observations scenario. Our analysis also incorporates the channel correlation. The MMSE channel estimates are determined for the sensors (SNs), followed by a robust transceiver design procedure that is resilient to the channel state information (CSI) uncertainty arising due to the channel estimation error, an aberration that is unavoidable in practical implementations. Our simulation results demonstrate the improved performance of the proposed BL framework and optimal MMSE transceiver design in sparse parameter estimation relyingon realistic imperfect channel estimates over the benchmarks.

Coherent reception of signals with digital modulation requires information about the channel state, in particular, about the magnitude decay and phase offset introduced by the channel. Actually, receiving side usually estimates channel state using special pilot elements incorporated into the signal structure. Transmission of these redundant pilot signals requires extra power and time-frequency resource, that reduces spectral and energy efficiency of the communication system, so the number of pilots should be minimized. The paper describes two views on the reception of short data packets transmitted using quadrature amplitude modulation. On the one hand, coherent reception with semi-blind channel estimation is considered, namely, signal level and phase offset estimation is performed by blind algorithms using all symbols of the packet, and pilot symbols are only used to resolve ambiguity inherent for blind estimates of phase offset. On the other hand, the whole packet can be treated as a signal from a signal set suitable for noncoherent reception. High-correlation approximation for bit error probability is evaluated and compared with results obtained for coherent reception with channel estimation. Computer simulation showed that even for moderately short QAM packets bit error probability for semi-blind channel estimation is close to achievable limits for noncoherent reception of the packet as a whole with a loss about 0.4 dB.

In this work we study the achievable rates of memoryless signaling strategies adapted to ultra-wideband (UWB) multipath fading channels. We focus on strategies that do not have explicit knowledge of the instentaneous channel realization, but may have knowledge of the channel statistics. We evaluate the average mutual information of the general binary flash-signaling rates as a function of channel statistics and derive random coding bounds for m-ary PPM using different noncoherent receivers as well as an imperfect coherent receiver. Then we extend the results to multiband m-PPM signaling and show that for data rates on the order of 400 Mbits/s, at 4 m distance between the transmitter and the receiver, can be achieved using simple noncoherent receivers.

We consider the joint power-distortion optimization in one-help-one problem, also called the 1-helper problem where one source provides partial side information to the fusion center (FC) to help reconstruction of the other correlated source. Both correlated sources communicate information about their observations to the FC through an orthogonal multiple access channel (MAC) without cooperating with each other. We investigate the joint optimization of source coding and power allocation from an information theory perspective, where the power allocation is verified using Shannon capacity formula and the source coding problem is analyzed using rate-distortion theory. We show that the joint optimization in the Gaussian 1-helper problem can be solved analytically. We provide closed-form expressions for the optimal distortion and the optimal power allocation in terms of the cost weights.

UWB signal reception can be accomplished by coherent or non-coherent receivers. Correlation receiver is a type of coherent receiver while energy detection (ED) receiver belongs to non-coherent type. In this paper, we evaluate their ranging performance using the channel profiles measured in a typical indoor office environment. The effects of ranging parameters such as search window length are also investigated. The results show that correlation receiver outperforms ED receiver in the line-of-sight (LOS) scenario and smaller integration interval gives better performance for ED. For the non-line-of-sight (NLOS) scenario, surprisingly, ED receiver outperforms correlation receiver and larger integration interval brings better performance for ED when the detection threshold exceeds certain level. The study also shows that regardless of the receiver types used, the resultant ranging errors for the LOS or NLOS environments can be described by unified models with the parameters being distance dependent.

As there are many use cases considered for robotics communications, the data rate variation may be very large. Some sensor applications may require very low data rate, telemetry data may require low-to-medium data rates and e.g. video application will require high data rates. On the other hand, robots may have to operate in very difficult radio propagation environments such as nuclear power plants or industrial facilities. To combat difficult propagation characteristics, an often used and well known mechanism is to use spread spectrum signal structures. Thus in this paper a novel modulation method is considered which offers the inherent signal structure and processing opportunities of spread spectrum signal and at the same time offers an easy mechanism to adapt the data rate from low to high depending on the requirement at hand thus addressing two important communication requirements for robotics. The introduction of $$m$$ MFSK generated the idea of applying the given approach to other modulation methods. To further enlarge the modulation alphabet sizes (with the price of larger spectrum usage) it was realized that combining the $$m$$ MFSK and $$m$$ MCSK would be an interesting choice. The $$m$$ MCSK--- $$m$$ MFSK modulation is hence considered. A method to analyze this two-component modulation is developed and the performance analyses give results for $$m$$ MCSK--- $$m$$ MFSK modulation in AWGN and flat Rayleigh fading channels for both coherent and non-coherent receivers. The performance was also assessed with orthogonal and non-orthogonal code constructs for coherent receiver.

In recent years, cooperative spectrum sensing (CSS) for cognitive radio networks (CRN) have been widely investigated in various research aspects. With an aim to develop easy-to-implement CSS schemes, this paper proposes two optimal strategies to manipulate the transmit powers of the cooperative secondary users (SU) in the CSS intervals. When the joint channel statistics (CS) of the sensing and reporting channels are perfectly known at the fusion center (FC), we first derive a CS aided optimal user power manipulation (CSA-OUPM) scheme in closed-form; when the CS are entirely unknown, a blind user power control method is developed, namely the principal eigenvector aided OUPM (PEV-OUPM). Theoretical analysis and computer simulations verify that the proposed OUPM schemes are capable of potentially allocating more power to the cooperative SUs with better channel condition and hence achieve significantly ameliorated performance.

This dissertation presents new approaches for cognitive radio networks that combat fading effects and improve detection accuracy. We propose an advance framework for performance analysis of cooperative spectrum sensing over non-identical Nakagami- A detect-amplify-and-forward strategy is proposed to mitigate bandwidth requirements of relaying local observations to a fusion center. The end-to-end performance of a relay-based cooperative spectrum sensing over independent identically distributed Rayleigh fading channels is also investigated in this dissertation. Specifically, we aim to incorporate sensing time, end-to-end SNR, and end-to-end channel statistic into the performance analysis of cooperative CR networks. We also propose a cluster-based cooperative spectrum sensing approach to overcome the bandwidth limitations of the reporting links. The approach reduces the number of reporting terminals to a minimal reporting set and replaces the global fusion center by a local fusion center to mitigate the destructive channel conditions of global relaying channels. A new approach is proposed to select the location of the local fusion center using the general center scheme in graph theory. We aim to show that multipath fading on relaying channels yields similar performance degradations as multipath fading on sensing channels. With the detect-amplify-and forward strategy, refraining the heavily faded relays improves the detection accuracy. A gain of 3 dB is achieved by switching from amplify-and-forward strategy to detect-amplify-and-forward strategy with 3 cooperative users. Compared to the non-cooperative spectrum sensing, a gain of up to 8 dB is achieved with 4 cooperative users and equal gain combining receiver. Similar experimental set up but with selection combining receiver, a gain of 5 dB is achieved.