Citation Context

...y methods such as orthogonal matching pursuit (OMP) [29]. When norm is used, this problem can be3236 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 61, NO. 12, JUNE 15, 2013 solved via convex programs =-=[30]-=-. Generally speaking, as discussed in [2] and [30], the required number of samples for sparse recovery in the noiseless case scales logarithmically with the length- link vector ,whichincreases if disc...

Citation Context

...and MF (right); tested at dB. , , .TheCSAsimulation recovers the link parameters by solving (41) with the OMP algorithm [29], which is a popular choice to approximate the solution of a sparse problem =-=[36]-=-. To motivate our selection of OMP, we refer to Section VIII for an empirical evaluation of the OMP against two well-known -Homotopy [38], [39]. minimizers, SpaRSA [37] and A. Signal Detection Perform...

Citation Context

...zation parameter and or are the sparsity regularization constraint. If the constraint is imposed, then the problem is approximately solved via greedy methods such as orthogonal matching pursuit (OMP) =-=[29]-=-. When norm is used, this problem can be3236 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 61, NO. 12, JUNE 15, 2013 solved via convex programs [30]. Generally speaking, as discussed in [2] and [30], ...

Citation Context

...ency is obtained as (16) over all possible , , to compute the generalized likelihood ratio (12) with estimates obtained at every shift . The expression of the generalized likelihood ratio is given in =-=[26]-=- for cases with known or unknown noise variance . Without loss of generality, we consider the most general case where is unknown. In this case, the ratio is obtained as (13) Using this ratio as the te...

Citation Context

...he solution of a sparse problem [36]. To motivate our selection of OMP, we refer to Section VIII for an empirical evaluation of the OMP against two well-known -Homotopy [38], [39]. minimizers, SpaRSA =-=[37]-=- and A. Signal Detection Performance We first test the case of completely unknown active user sets, as discussed in Section V-B-1. In Fig. 2, all receivers are unaware of the random set of active user...

Citation Context

...sults pertaining to sparsity-aware estimation/detection [1], [2], [4], [12]–[16] the literature on analog compressed sensing and sub-Nyquist sampling [4], [8], [10], [17], [18], [23] and FRI sampling =-=[19]-=-, [20], [22] such that sampling and acquisition operations are considered jointly. To measure the benefits of the proposed CSA scheme, we analyze the practical trade-off between the implementation cos...

Citation Context

...r choice to approximate the solution of a sparse problem [36]. To motivate our selection of OMP, we refer to Section VIII for an empirical evaluation of the OMP against two well-known -Homotopy [38], =-=[39]-=-. minimizers, SpaRSA [37] and A. Signal Detection Performance We first test the case of completely unknown active user sets, as discussed in Section V-B-1. In Fig. 2, all receivers are unaware of the ...

Citation Context

...pertaining to sparsity-aware estimation/detection [1], [2], [4], [12]–[16] the literature on analog compressed sensing and sub-Nyquist sampling [4], [8], [10], [17], [18], [23] and FRI sampling [19], =-=[20]-=-, [22] such that sampling and acquisition operations are considered jointly. To measure the benefits of the proposed CSA scheme, we analyze the practical trade-off between the implementation costs in ...

Citation Context

...ur work bridges the results pertaining to sparsity-aware estimation/detection [1], [2], [4], [12]–[16] the literature on analog compressed sensing and sub-Nyquist sampling [4], [8], [10], [17], [18], =-=[23]-=- and FRI sampling [19], [20], [22] such that sampling and acquisition operations are considered jointly. To measure the benefits of the proposed CSA scheme, we analyze the practical trade-off between ...

Citation Context

...ers by creating a dictionary from the known templates and viewing the signal as a sparse linear combination of these templates. Without knowledge of signal presence, the proposed detection schemes in =-=[12]-=-–[16] use generic compressed measurements to detect the presence of certain signals within a specific observation window, starting from an abstract discrete model. We refer 1053-587X/$31.00 © 2013 IEE...

Citation Context

...ent statistic is then exploited to detect the presence of signals and determine the link parameters. We refer to such techniques as Direct Sampling (DS) methods (e.g. [5]–[8]). A second approach [4], =-=[9]-=-, [10] facilitates the search of both the active set and link parameters by Matched Filtering (MF). This approach compares the filtered outputs of from a bank of filters constructed by shifting and mo...

Citation Context

...isition of a single receiver plugged in a network populated by users, out of which are randomly chosen to be actively transmitting. The user signature codes, ’s in (1), belong to a set of M-sequences =-=[35]-=-, which are quasi-orthogonal BPSK sequences of length with unit power .Duetotheuser dislocation, mobility and possible scattering, each path of this asynchronous multi-user channel is characterized by...

Citation Context

...he appropriate energy gain to rise above noise. Reducing the sampling rate and the associated overhead incurred at the analog-to-digital (A/D) front-end is the concern of another line of studies [17]–=-=[21]-=- on signals with Finite Rate of Innovations (FRI) [22]. In general, an FRI signal has a sparse parametric representation. Given the preamble for each user traveling through channels, the class of sign...

Citation Context

...ersion of the exhaustive MF output. The difference is that the samples here are obtained directly from the A/D architecture, instead of linearly compressing the exhaustive MF filterbank outputs as in =-=[14]-=-, [15], where the latter would be much more complex. On the other hand, the difference in post-processing between the MF and CMS architectures is that MF allows to simply pick the hypothesis correspon...

Citation Context

...tatistic is then exploited to detect the presence of signals and determine the link parameters. We refer to such techniques as Direct Sampling (DS) methods (e.g. [5]–[8]). A second approach [4], [9], =-=[10]-=- facilitates the search of both the active set and link parameters by Matched Filtering (MF). This approach compares the filtered outputs of from a bank of filters constructed by shifting and modulati...

Citation Context

...sition, is that of detecting the presence of signals, and identifying the link parameters (e.g., delays, carrier offsets) of an unknown subset of active components out of possible sources. Similar to =-=[1]-=-, [2], we consider the case where the active users transmit known and distinct training preambles to the destination. Usually these Manuscript received December 09, 2011; revised September 15, 2012 an...

Citation Context

...distance of the hypotheses in the SR-LRT. IV. COMPRESSIVE SEQUENTIAL LINK ACQUISITION A. Compressive Multichannel Sampling (CMS) We propose to use the A/D front-end in Fig. 1, typical in FRI sampling =-=[17]-=-, [19], [20], [22], [23]. The signal is sampled every by a -channel filterbank (21) We call this architecture the Compressive Multichannel Sampling (CMS) module, which forms the A/D conversion front-e...

Citation Context

...formance. One class of papers suggests using sparse signal recovery for the purpose of either detection or estimation. For instance, assuming that the signal is present, the results in [1], [2], [4], =-=[11]-=- deal with identification of the active users and/or estimation of signal parameters by creating a dictionary from the known templates and viewing the signal as a sparse linear combination of these te...

Citation Context

...sts. Our work bridges the results pertaining to sparsity-aware estimation/detection [1], [2], [4], [12]–[16] the literature on analog compressed sensing and sub-Nyquist sampling [4], [8], [10], [17], =-=[18]-=-, [23] and FRI sampling [19], [20], [22] such that sampling and acquisition operations are considered jointly. To measure the benefits of the proposed CSA scheme, we analyze the practical trade-off be...

Citation Context

... pattern for is independent of ,hereweomitthe subscript for convenience. A. Motivation of Maximizing the Average KL Distance In choosing the KL distance we are motivated by the Chernoff-Stein’s lemma =-=[31]-=-, whose statement indicates that the probability of confusing and decreases exponentially with the pair-wise KL distance between them. By defining ,thepair-wise KL distance between any and depends on ...

Citation Context

...e number of measurements to handle less data by spending a higher premium for sparse recovery. Therefore, we discuss this trade-off in detail in Section VIII. B. CMS Observation Model Similar to [1], =-=[2]-=-, we follow the analog description of (5) but discretize the parameters as in the MF approach. For notational convenience, we introduce the triple-index coefficient (22) Fig. 1. The compressive sample...

Citation Context

...r. Gold sequences used in GPS and M-sequences used in spread spectrum communications, for example, are known to have good properties in this regard. The design of these sequences is well investigated =-=[33]-=- and we do not aim to cover here. B. Optimization of Compressive Samplers Given and , we propose an optimal that maximizes the average KL distance if there is a unique solution to the optimization; wh...

Citation Context

... of the exhaustive MF output. The difference is that the samples here are obtained directly from the A/D architecture, instead of linearly compressing the exhaustive MF filterbank outputs as in [14], =-=[15]-=-, where the latter would be much more complex. On the other hand, the difference in post-processing between the MF and CMS architectures is that MF allows to simply pick the hypothesis corresponding t...

Citation Context

...ng the sampling rate and the associated overhead incurred at the analog-to-digital (A/D) front-end is the concern of another line of studies [17]–[21] on signals with Finite Rate of Innovations (FRI) =-=[22]-=-. In general, an FRI signal has a sparse parametric representation. Given the preamble for each user traveling through channels, the class of signals lies in a subspace with no more than dimensions, w...

Citation Context

... that yield identical average KL distance ,wechoosethematrixthat gives the least occurrence of events .Weusethe results in the following lemma for our optimization. Lemma 1: (Ratio Trace Maximization =-=[34]-=-) Given a pair of positive semi-definite matrices and an full column rank matrix , the ratio trace problem is (50) The optimal is given by the generalized eigenvectors corresponding to largest general...

Citation Context

... requires accumulating observations and repeating the test sequentially. The signal features extracted from the link information are essential for the receiver to determine if it can decode data [3], =-=[4]-=- and refine the link parameters using mid-ambles and decoded data after the initial training phase. A. Related Works on Link Acquisition of Multiuser Signals We can categorize link acquisition algorit...

Citation Context

...y creating a dictionary from the known templates and viewing the signal as a sparse linear combination of these templates. Without knowledge of signal presence, the proposed detection schemes in [12]–=-=[16]-=- use generic compressed measurements to detect the presence of certain signals within a specific observation window, starting from an abstract discrete model. We refer 1053-587X/$31.00 © 2013 IEEE323...

Citation Context

...bles or spreading codes that modulate data. For a typical wireless application such as GPS or IS-95/IMT-2000, transmitters continuously send out preamble sequences with length on the order of [24] or =-=[25]-=-, respectively. This means that in order to detect the presence of such preambles and acquire the synchronization parameters, architectures using DS, MF or SA approaches would have to store a large am...

Citation Context

...popular choice to approximate the solution of a sparse problem [36]. To motivate our selection of OMP, we refer to Section VIII for an empirical evaluation of the OMP against two well-known -Homotopy =-=[38]-=-, [39]. minimizers, SpaRSA [37] and A. Signal Detection Performance We first test the case of completely unknown active user sets, as discussed in Section V-B-1. In Fig. 2, all receivers are unaware o...

Citation Context

...t mid-ambles or spreading codes that modulate data. For a typical wireless application such as GPS or IS-95/IMT-2000, transmitters continuously send out preamble sequences with length on the order of =-=[24]-=- or [25], respectively. This means that in order to detect the presence of such preambles and acquire the synchronization parameters, architectures using DS, MF or SA approaches would have to store a ...

Citation Context

... weighting functions is equivalent to assuming a uniform distribution on the users, delays and Dopplers together with i.i.d. Gaussian priors on the amplitudes in in a Bayesian framework. According to =-=[32]-=-, the pair-wise KL distance has the same expression as the Chernoff information, which determines the Bayesian detection error exponent. However, if any of the pair-wise KL distance is zero, then the ...

Citation Context

...n associated with the sufficient statistic is then exploited to detect the presence of signals and determine the link parameters. We refer to such techniques as Direct Sampling (DS) methods (e.g. [5]–=-=[8]-=-). A second approach [4], [9], [10] facilitates the search of both the active set and link parameters by Matched Filtering (MF). This approach compares the filtered outputs of from a bank of filters c...

Citation Context

...tification and parameter estimation, one approach is to approximate (8) by a sparse model with a dictionary constructed from the ensemble of possible templates [1], [4] and/or discretized delays [2], =-=[28]-=- (similar to the MF templates), where the joint recovery of active users and unknown parameters is relaxed as a sparse estimation problem. These sparse methods, which we call the Direct Sparsity Aware...