Search

In this paper, we focus on next-generation cellular networks and discuss physical resources sharing among the operators. This implies cooperative usage of the available radio frequencies and also infrastructure sharing. In particular, we analyze the spectrum sharing gain achievable at different time scales and the main factors impacting on it. Then, we move towards a wider idea of resource sharing and consider a joint spectrum and infrastructure sharing (full sharing). We describe a two-layer resource management architecture that enables operators to reduce costs while still guaranteeing a good service level. The main findings of our investigations are to quantify the effectiveness of resource sharing and open up new perspectives for the operators of next-generation networks.

This paper presents some results from of the FP7 ICT-LOLA (achieving LOw LAtency in wireless communications) project on the design of clusterized wireless mesh network based on 3GPP LTE. First, we focus on the general MAC/PHY structure of the clusterized mesh network based on 3GPP LTE. Then, the concept of virtual link is presented for inter-cluster communications combining MAC layer forwarding, hybrid automatic repeat request (HARQ) and cooperative communications with Decode and Forward (DF). The goal of a virtual link is to enable low latency data transfer in inter-cluster communications. The virtual link solution is studied by simulations thanks to OpenAirInterface which integrates LTE MAC and PHY layer procedures, as well as adaptations needed for the LOLA wireless mesh network. Simulation results show that the proposed distributed solution smoothly adapts to the link conditions. A loss in throughput efficiency is the price to be paid in certain configurations for the distributed operation of the virtual link. Nevertheless, the technique helps in reducing the average number of transmissions thus contributing to improve the latency of the system., FP7 LOLA

The distributed Alamouti space-time code in two-way fixed gain amplify-and-forward (AF) relay is proposed in this paper. In particular, closed-form expressions for approximated ergodic sum-rate and exact pairwise error probability (PWEP) are derived for Nakagami-m fading channels. To reveal further insights into array and diversity gains, an asymptotic PWEPis also obtained. Finally, numerical results are provided to corroborate the proposed theoretical analysis.

This paper considers multicell multiuser MIMO systems with verylarge antenna arrays at the base station. We propose an eigenvalue-decomposition-based approach to channel estimation, that estimates the channel blindly from the received data. The approach exploits the asymptotic orthogonality of the channel vectors in very large MIMO systems. We show that the channel to each user can be estimated from the covariance matrix of the received signals, up to a remaining scalar multiplicative ambiguity. A short training sequence is required to resolve this ambiguity. Furthermore, to improve the performance of our approach, we combine it with the iterative least-square with projection (ILSP) algorithm. Numerical results verify the effectiveness of our channel estimation approach.

The delay constraints imposed by future wirelessapplications require a suitable metric for assessing their impacton the overall system performance. Since the classical Shannon’s ergodic capacity fails to do so, the so-called effective rate was recently established as a rigorous alternative. Yet, most priorrelevant works have considered only the typical case of Rayleighfading which allows for tractable manipulations. In this paper,we relax this assumption by considering the more general Rician fading model for multiple-input single-output (MISO) systems. Anew, analytical expression for the exact effective rate is derived, along with tractable expressions for the key parameters dictating the effective rate performance in the high and low signal-to-noise(SNR) regimes.

The delay constraints imposed by future wirelessapplications require a suitable metric for assessing their impacton the overall system performance. Since the classical Shannon’s ergodic capacity fails to do so, the so-called effective rate was recently established as a rigorous alternative. Yet, most priorrelevant works have considered only the typical case of Rayleighfading which allows for tractable manipulations. In this paper,we relax this assumption by considering the more general Rician fading model for multiple-input single-output (MISO) systems. Anew, analytical expression for the exact effective rate is derived, along with tractable expressions for the key parameters dictating the effective rate performance in the high and low signal-to-noise(SNR) regimes.

Large antenna arrays at the base station can facilitate power efficient single user downlink communication due to the inherent array power gain, i.e., under an average only total transmit power constraint, for a fixed desired information rate, the required total transmit power can be reduced by increasing the number of base station antennas (e. g. with i.i.d. fading, the required total transmit power can be reduced by roughly 3 dB with every doubling in the number of base station antennas, i.e., an O(N) array power gain can be achieved with N antennas). However, in practice, building power efficient large antenna arrays would require power efficient amplifiers/analog RF components. With current technology, highly linear power amplifiers generally have low power efficiency, and therefore linearity constraints on power amplifiers must be relaxed. Under such relaxed linearity constraints, the transmit signal that suffers the least distortion is a signal with constant envelope (CE). In this paper, we consider a single user Gaussian multiple-input single-output (MISO) downlink channel where the signal transmitted from each antenna is constrained to have a constant envelope (i.e., for every channel-use the amplitude of the signal transmitted from each antenna is constant, irrespective of the channel realization). We show that under such a per-antenna CE constraint, the complex noise-free received signal lies in the interior of a "doughnut" shaped region in the complex plane. The per-antenna CE constrained MISO channel is therefore equivalent to a doughnut channel, i.e., a single-input single-output (SISO) AWGN channel where the channel input is constrained to lie inside a "doughnut" shaped region. Using this equivalence, we analytically compute a closed-form expression for an achievable information rate under the per-antenna CE constraint. We then show that, for a broad class of fading channels (i.i.d. and direct-line-of-sight (DLOS)), even under the more stringent per-an

Large antenna arrays at the base station can facilitate power efficient single user downlink communication due to the inherent array power gain, i.e., under an average only total transmit power constraint, for a fixed desired information rate, the required total transmit power can be reduced by increasing the number of base station antennas (e. g. with i.i.d. fading, the required total transmit power can be reduced by roughly 3 dB with every doubling in the number of base station antennas, i.e., an O(N) array power gain can be achieved with N antennas). However, in practice, building power efficient large antenna arrays would require power efficient amplifiers/analog RF components. With current technology, highly linear power amplifiers generally have low power efficiency, and therefore linearity constraints on power amplifiers must be relaxed. Under such relaxed linearity constraints, the transmit signal that suffers the least distortion is a signal with constant envelope (CE). In this paper, we consider a single user Gaussian multiple-input single-output (MISO) downlink channel where the signal transmitted from each antenna is constrained to have a constant envelope (i.e., for every channel-use the amplitude of the signal transmitted from each antenna is constant, irrespective of the channel realization). We show that under such a per-antenna CE constraint, the complex noise-free received signal lies in the interior of a "doughnut" shaped region in the complex plane. The per-antenna CE constrained MISO channel is therefore equivalent to a doughnut channel, i.e., a single-input single-output (SISO) AWGN channel where the channel input is constrained to lie inside a "doughnut" shaped region. Using this equivalence, we analytically compute a closed-form expression for an achievable information rate under the per-antenna CE constraint. We then show that, for a broad class of fading channels (i.i.d. and direct-line-of-sight (DLOS)), even under the more stringent per-an

Large antenna arrays at the base station can facilitate power efficient single user downlink communication due to the inherent array power gain, i.e., under an average only total transmit power constraint, for a fixed desired information rate, the required total transmit power can be reduced by increasing the number of base station antennas (e. g. with i.i.d. fading, the required total transmit power can be reduced by roughly 3 dB with every doubling in the number of base station antennas, i.e., an O(N) array power gain can be achieved with N antennas). However, in practice, building power efficient large antenna arrays would require power efficient amplifiers/analog RF components. With current technology, highly linear power amplifiers generally have low power efficiency, and therefore linearity constraints on power amplifiers must be relaxed. Under such relaxed linearity constraints, the transmit signal that suffers the least distortion is a signal with constant envelope (CE). In this paper, we consider a single user Gaussian multiple-input single-output (MISO) downlink channel where the signal transmitted from each antenna is constrained to have a constant envelope (i.e., for every channel-use the amplitude of the signal transmitted from each antenna is constant, irrespective of the channel realization). We show that under such a per-antenna CE constraint, the complex noise-free received signal lies in the interior of a "doughnut" shaped region in the complex plane. The per-antenna CE constrained MISO channel is therefore equivalent to a doughnut channel, i.e., a single-input single-output (SISO) AWGN channel where the channel input is constrained to lie inside a "doughnut" shaped region. Using this equivalence, we analytically compute a closed-form expression for an achievable information rate under the per-antenna CE constraint. We then show that, for a broad class of fading channels (i.i.d. and direct-line-of-sight (DLOS)), even under the more stringent per-an

Blind decoding, used on control channels of some multi-user wireless access systems, is a technique for achieving adaptive modulation and coding. The idea is to adapt the modulation and coding scheme to the channel quality but instead of signaling the parameters used explicitly, the receiver blindly tries a number of fixed parameter combinations until a successful decoding attempt is detected, with the help of a cyclic redundancy check. In this paper we suggest a new method for reducing the complexity and energy consumption associated with such blind decoding schemes. Our idea is to use a mini-CRC injected early in the data stream to determine if the current decoding attempt is using the correct modulation and coding parameters. We analyze and exemplify the complexity gain of this approach and also investigate the impact of the rearrangement of the CRC scheme in terms of the probability of undetected error. The presented results for the complexity gain are promising and the impact on the error detection capability turns out to be small if any.

In this paper, we present an improved detector for ACK/NACK message detection in the LTE uplink control channel with imperfect channel state information at the receiver. The detector is based on the generalized likelihood-ratio test (GLRT) paradigm. We derive detection metrics for the cases when the noise variances at the receiver are known and unknown. Noise here may comprise both thermal noise and interference. Simulation results show remarkable performance gains of the GLRT-based detector with unknown noise variances compared to the training-based maximum-likelihood detector with unknown noise variances when the noise variances in two slots are different. Furthermore, the performance of the GLRT-based detector with unknown noise variances is nearly the same as that of the training-based maximum-likelihood detector with known noise variances.

The delay constraints imposed by future wirelessapplications require a suitable metric for assessing their impacton the overall system performance. Since the classical Shannon’s ergodic capacity fails to do so, the so-called effective rate was recently established as a rigorous alternative. Yet, most priorrelevant works have considered only the typical case of Rayleighfading which allows for tractable manipulations. In this paper,we relax this assumption by considering the more general Rician fading model for multiple-input single-output (MISO) systems. Anew, analytical expression for the exact effective rate is derived, along with tractable expressions for the key parameters dictating the effective rate performance in the high and low signal-to-noise(SNR) regimes.

The delay constraints imposed by future wirelessapplications require a suitable metric for assessing their impacton the overall system performance. Since the classical Shannon’s ergodic capacity fails to do so, the so-called effective rate was recently established as a rigorous alternative. Yet, most priorrelevant works have considered only the typical case of Rayleighfading which allows for tractable manipulations. In this paper,we relax this assumption by considering the more general Rician fading model for multiple-input single-output (MISO) systems. Anew, analytical expression for the exact effective rate is derived, along with tractable expressions for the key parameters dictating the effective rate performance in the high and low signal-to-noise(SNR) regimes.

Large antenna arrays at the base station can facilitate power efficient single user downlink communication due to the inherent array power gain, i.e., under an average only total transmit power constraint, for a fixed desired information rate, the required total transmit power can be reduced by increasing the number of base station antennas (e. g. with i.i.d. fading, the required total transmit power can be reduced by roughly 3 dB with every doubling in the number of base station antennas, i.e., an O(N) array power gain can be achieved with N antennas). However, in practice, building power efficient large antenna arrays would require power efficient amplifiers/analog RF components. With current technology, highly linear power amplifiers generally have low power efficiency, and therefore linearity constraints on power amplifiers must be relaxed. Under such relaxed linearity constraints, the transmit signal that suffers the least distortion is a signal with constant envelope (CE). In this paper, we consider a single user Gaussian multiple-input single-output (MISO) downlink channel where the signal transmitted from each antenna is constrained to have a constant envelope (i.e., for every channel-use the amplitude of the signal transmitted from each antenna is constant, irrespective of the channel realization). We show that under such a per-antenna CE constraint, the complex noise-free received signal lies in the interior of a "doughnut" shaped region in the complex plane. The per-antenna CE constrained MISO channel is therefore equivalent to a doughnut channel, i.e., a single-input single-output (SISO) AWGN channel where the channel input is constrained to lie inside a "doughnut" shaped region. Using this equivalence, we analytically compute a closed-form expression for an achievable information rate under the per-antenna CE constraint. We then show that, for a broad class of fading channels (i.i.d. and direct-line-of-sight (DLOS)), even under the more stringent per-an

In this article, we consider practical approaches to Costa precoding (also known as dirty paper coding). Specifically, we propose a symbol-by-symbol scheme for cancellation of interference known at the transmitter in a relay-aided downlink channel. For finite-alphabet signaling and interference, we derive the optimal (in terms of maximum mutual information) modulator under a given power constraint. A sub-optimal modulator is also proposed by formulating an optimization problem that maximizes the minimum distance of the signal constellation, and this non-convex optimization problem is approximately solved by semi-definite relaxation. For the case of binary signaling with binary interference, we obtain a closed-form solution for the sub-optimal modulator, which only suffers little performance degradation compared to the optimal modulator in the region of interest. For more general signal constellations and more general interference distributions, we propose an optimized Tomlinson-Harashima precoder (THP), which uniformly outperforms conventional THP with heuristic parameters. Bit-level simulation shows that the optimal and sub-optimal modulators can achieve significant gains over the THP benchmark as well as over non-Costa reference schemes, especially when the power of the interference is larger than the power of the noise., ©2011 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. Jinfeng Du, Erik G. Larsson, Ming Xiao and Mikael Skoglund, Optimal Symbol-by-Symbol Costa Precoding for a Relay-aided Downlink Channel, 2011, accepted IEEE Transactions on Communications.

We consider low complexity precoding for the Multiple Input Single Output (MISO)Gaussian Broadcast channel with $N_t$ antennas at the base station and $N_u$ singleantenna users in the downlink. Theoretical studies have suggested high throughputcommunication with increasing spatial dimensions i.e., $\min(N_t,N_u)$.Nevertheless, most modern communication standards are unable to exploitthe spatial dimension fully, since they are restricted to orthogonal communicationtechniques like TDMA/FDMA (Time/Frequency Division Multiplexed Access) which areknown to be sub-optimal.This restriction is mostly due to the prohibitive complexity of optimal/near-optimalprecoding schemes.On the other hand low complexity techniques like Zero Forcing (ZF) and MMSE have poor sum rate performance.In this paper, we propose a novel low-complexity user grouping based precoding scheme whichschedules all users on the same time-frequency resource (i.e., optimal utilization of resources).The proposed precoder is analytically shown to achieve a sum rate performance significantly better than the ZF precoderat similar complexity.Through simulations, it is also observed to achieve a significant fractionof the sum rate achieved by the optimal schemes., ©2011 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. Saif Khan Mohammed and Erik G. Larsson, A low complexity user grouping based multiuser MISO downlink precoder, 2011, accepted for IEEE GLOBECOM 2011

We consider low complexity precoding for the Multiple Input Single Output (MISO)Gaussian Broadcast channel with $N_t$ antennas at the base station and $N_u$ singleantenna users in the downlink. Theoretical studies have suggested high throughputcommunication with increasing spatial dimensions i.e., $\min(N_t,N_u)$.Nevertheless, most modern communication standards are unable to exploitthe spatial dimension fully, since they are restricted to orthogonal communicationtechniques like TDMA/FDMA (Time/Frequency Division Multiplexed Access) which areknown to be sub-optimal.This restriction is mostly due to the prohibitive complexity of optimal/near-optimalprecoding schemes.On the other hand low complexity techniques like Zero Forcing (ZF) and MMSE have poor sum rate performance.In this paper, we propose a novel low-complexity user grouping based precoding scheme whichschedules all users on the same time-frequency resource (i.e., optimal utilization of resources).The proposed precoder is analytically shown to achieve a sum rate performance significantly better than the ZF precoderat similar complexity.Through simulations, it is also observed to achieve a significant fractionof the sum rate achieved by the optimal schemes., ©2011 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. Saif Khan Mohammed and Erik G. Larsson, A low complexity user grouping based multiuser MISO downlink precoder, 2011, accepted for IEEE GLOBECOM 2011

We consider low complexity precoding for the Multiple Input Single Output (MISO)Gaussian Broadcast channel with $N_t$ antennas at the base station and $N_u$ singleantenna users in the downlink. Theoretical studies have suggested high throughputcommunication with increasing spatial dimensions i.e., $\min(N_t,N_u)$.Nevertheless, most modern communication standards are unable to exploitthe spatial dimension fully, since they are restricted to orthogonal communicationtechniques like TDMA/FDMA (Time/Frequency Division Multiplexed Access) which areknown to be sub-optimal.This restriction is mostly due to the prohibitive complexity of optimal/near-optimalprecoding schemes.On the other hand low complexity techniques like Zero Forcing (ZF) and MMSE have poor sum rate performance.In this paper, we propose a novel low-complexity user grouping based precoding scheme whichschedules all users on the same time-frequency resource (i.e., optimal utilization of resources).The proposed precoder is analytically shown to achieve a sum rate performance significantly better than the ZF precoderat similar complexity.Through simulations, it is also observed to achieve a significant fractionof the sum rate achieved by the optimal schemes., ©2011 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. Saif Khan Mohammed and Erik G. Larsson, A low complexity user grouping based multiuser MISO downlink precoder, 2011, accepted for IEEE GLOBECOM 2011

Dynamic OFDMA has been recognized as a promising technique forimproving the performance of future wireless cellularsystems. However, this potential performance improvement comes at thecost of additional signaling overhead, which can have a non-negligibleeffect on the system efficiency. In this paper, we propose a newmethod for optimizing the frame length for the downlink in OFDMAsystems. The method maximizes the system efficiency by taking intoaccount both the channel conditions and the amount of signalingoverhead needed to deliver scheduling maps to the users. We formulatethe frame length optimization problem mathematically. By exploitingthe structure of this problem, we develop an algorithm that solves asequence of dynamic programming problems. Simulation results revealsome insight into fundamental limitations as well as provide guidelinesfor the design of dynamic OFDMA systems.

We consider low complexity precoding for the Multiple Input Single Output (MISO)Gaussian Broadcast channel with $N_t$ antennas at the base station and $N_u$ singleantenna users in the downlink. Theoretical studies have suggested high throughputcommunication with increasing spatial dimensions i.e., $\min(N_t,N_u)$.Nevertheless, most modern communication standards are unable to exploitthe spatial dimension fully, since they are restricted to orthogonal communicationtechniques like TDMA/FDMA (Time/Frequency Division Multiplexed Access) which areknown to be sub-optimal.This restriction is mostly due to the prohibitive complexity of optimal/near-optimalprecoding schemes.On the other hand low complexity techniques like Zero Forcing (ZF) and MMSE have poor sum rate performance.In this paper, we propose a novel low-complexity user grouping based precoding scheme whichschedules all users on the same time-frequency resource (i.e., optimal utilization of resources).The proposed precoder is analytically shown to achieve a sum rate performance significantly better than the ZF precoderat similar complexity.Through simulations, it is also observed to achieve a significant fractionof the sum rate achieved by the optimal schemes., ©2011 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. Saif Khan Mohammed and Erik G. Larsson, A low complexity user grouping based multiuser MISO downlink precoder, 2011, accepted for IEEE GLOBECOM 2011

In this paper, we propose two spectrally efficient adaptive partial decode-and-forward (DF)cooperative communication schemes, which are adaptive partialrepetition DF with quantized feedback (APR-DF-QF) and adaptivepartial coded cooperation DF with quantized feedback (APCC-DF-QF).We assume the relay node only has partial channel-state information, which is obtainedvia an quantized feedback link. We use the so-called mutual information (MI)model to adaptively optimize the amount of data that need to beforwarded by the relay node under a given block-error-rateconstraint. Simulation results show that with the optimized feedback, the MI model can predict well theoptimal amount of information that needs to be forwarded by therelay node, and that the two proposed schemes can substantiallyincrease the spectral efficiency.

We consider low complexity precoding for the Multiple Input Single Output (MISO)Gaussian Broadcast channel with $N_t$ antennas at the base station and $N_u$ singleantenna users in the downlink. Theoretical studies have suggested high throughputcommunication with increasing spatial dimensions i.e., $\min(N_t,N_u)$.Nevertheless, most modern communication standards are unable to exploitthe spatial dimension fully, since they are restricted to orthogonal communicationtechniques like TDMA/FDMA (Time/Frequency Division Multiplexed Access) which areknown to be sub-optimal.This restriction is mostly due to the prohibitive complexity of optimal/near-optimalprecoding schemes.On the other hand low complexity techniques like Zero Forcing (ZF) and MMSE have poor sum rate performance.In this paper, we propose a novel low-complexity user grouping based precoding scheme whichschedules all users on the same time-frequency resource (i.e., optimal utilization of resources).The proposed precoder is analytically shown to achieve a sum rate performance significantly better than the ZF precoderat similar complexity.Through simulations, it is also observed to achieve a significant fractionof the sum rate achieved by the optimal schemes., ©2011 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. Saif Khan Mohammed and Erik G. Larsson, A low complexity user grouping based multiuser MISO downlink precoder, 2011, accepted for IEEE GLOBECOM 2011

This paper considers transmission of scheduling information in OFDMA-based cellular communication systems such as 3GPP long-term evolution (LTE). These systems provide efficient usage of radio resources by allowing users to be scheduled dynamically in both frequency and time. This requires considerable amounts of scheduling information to be sent to the users. The paper compares two basic transmission strategies: transmitting a separate scheduling message to each user versus broadcasting a joint scheduling message to all users. Different scheduling granularities are considered, as well as different scheduling algorithms. The schemes are evaluated in the context of the LTE downlink using multiuser system simulations, assuming a full-buffer situation. The results show that separate transmission of the scheduling information requires a slightly lower overhead than joint broadcasting, when proportional fair scheduling is employed and the users are spread out over the cell area. The results also indicate that the scheduling granularity standardized for LTE provides a good trade-off between scheduling granularity and overhead., ©2010 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. Reza Moosavi, Jonas Eriksson, Erik G. Larsson, Niclas Wiberg, Pål Frenger and Fredrik Gunnarsson, Comparison of Strategies for Signaling of Scheduling Assignments in Wireless OFDMA, 2010, IEEE Transactions on Vehicular Technology.http://dx.doi.org/10.1109/TVT.2010.2066589

This paper considers transmission of scheduling information in OFDMA-based cellular communication systems such as 3GPP long-term evolution (LTE). These systems provide efficient usage of radio resources by allowing users to be scheduled dynamically in both frequency and time. This requires considerable amounts of scheduling information to be sent to the users. The paper compares two basic transmission strategies: transmitting a separate scheduling message to each user versus broadcasting a joint scheduling message to all users. Different scheduling granularities are considered, as well as different scheduling algorithms. The schemes are evaluated in the context of the LTE downlink using multiuser system simulations, assuming a full-buffer situation. The results show that separate transmission of the scheduling information requires a slightly lower overhead than joint broadcasting, when proportional fair scheduling is employed and the users are spread out over the cell area. The results also indicate that the scheduling granularity standardized for LTE provides a good trade-off between scheduling granularity and overhead., ©2010 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. Reza Moosavi, Jonas Eriksson, Erik G. Larsson, Niclas Wiberg, Pål Frenger and Fredrik Gunnarsson, Comparison of Strategies for Signaling of Scheduling Assignments in Wireless OFDMA, 2010, IEEE Transactions on Vehicular Technology.http://dx.doi.org/10.1109/TVT.2010.2066589

This paper considers approximations of marginalization sums thatarise in Bayesian inference problems. Optimal approximations ofsuch marginalization sums, using a fixed number of terms, are analyzedfor a simple model. The model under study is motivated byrecent studies of linear regression problems with sparse parametervectors, and of the problem of discriminating signal-plus-noise samplesfrom noise-only samples. It is shown that for the model understudy, if only one term is retained in the marginalization sum, thenthis term should be the one with the largest a posteriori probability.By contrast, if more than one (but not all) terms are to be retained,then these should generally not be the ones corresponding tothe components with largest a posteriori probabilities., ©2009 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.Erik Axell, Erik G. Larsson and Jan-Åke Larsson, On the Optimal K-term Approximation of a Sparse Parameter Vector MMSE Estimate, 2009, Proceedings of the 2009 IEEE Workshop on Statistical Signal Processing (SSP'09), 245-248.http://dx.doi.org/10.1109/SSP.2009.5278594

Resource allocation and transmit optimization for the multiple-antenna Gaussian interference channel are important but difficult problems. Recently, there has been a large interest in algorithms that find operating points which are optimal in the sum-rate, proportional-fair, or minimax sense. Finding these points entails solving a nonlinear, non-convex optimization problem. In this paper, we develop an algorithm that solves these problems exactly, to within a prescribed level of accuracy and in a finite number of steps. The main idea is to rewrite the objective functions so that methods for monotonic optimization can be used. More precisely, we write each objective function as a difference between two functions which are strictly increasing over a normal constraint set. The so-obtained reformulated, equivalent problem can then be solved efficiently by using so-called polyblock optimization. Numerical examples illustrate the advantages of the proposed framework compared to an exhaustive grid search., ©2009 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.Eduard A. Jorswieck and Erik G. Larsson, Monotonic Optimization Framework for the MISO IFC, 2009, Proceedings of the 34th IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP'09), 3633-3636.http://dx.doi.org/10.1109/ICASSP.2009.4960413

This paper discusses implementation aspects of arecently proposed fixed-complexity soft-output (FCSO) symboldetector for MIMO systems [4]. A further approximation tothe FCSO detector is proposed which substantially reduces thecomplexity at the cost of a minor performance loss. With theresulting method, it is possible to carry out close-to ML detectionfor MIMO systems with a large number antennas (e.g. 4×4) usinghigher-order modulation schemes (e.g. 64-QAM) at low siliconcost in real-time. Furthermore, the parallelism inherited by theFCSO algorithm allows massive parallel processing which makesthe method suitable for implementation in multi-core basebandsignal processing hardware architectures., ©2009 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.Di Wu, Erik G. Larsson and Dake Liu, Implementation Aspects of Fixed-Complexity Soft-Output MIMO Detection, 2009, Proceedings of the 69th IEEE Vehicular Technology Conference (VTC'09), 1-5.http://dx.doi.org/10.1109/VETECS.2009.5073587

In this work, we consider a Federated Edge Learning (FEEL) system where training data are randomly generated over time at a set of distributed edge devices with long-term energy constraints. Due to limited communication resources and latency requirements, only a subset of devices is scheduled for participating in the local training process in every iteration. We formulate a stochastic network optimization problem for designing a dynamic scheduling policy that maximizes the time-average data importance from scheduled user sets subject to energy consumption and latency constraints. Our proposed algorithm based on the Lyapunov optimization framework outperforms alternative methods without considering time-varying data importance, especially when the generation of training data shows strong temporal correlation., Funding Agencies|ELLIIT; Knut and Alice Wallenberg (KAW) Foundation; Zenith

It is well known that GNSS receivers are vulnerable to jamming and spoofing attacks, and numerous such incidents have been reported in the last decade all over the world. The notion of participatory sensing, or crowdsensing, is that a large ensemble of voluntary contributors provides measurements, rather than relying on a dedicated sensing infrastructure. The participatory sensing network under consideration in this work is based on GNSS receivers embedded in, for example, mobile phones. The provided measurements refer to the receiver-reported carrier-to-noise-density ratio (C/N-0) estimates or automatic gain control (AGC) values. In this work, we exploit C/N-0 measurements to locate a GNSS jammer, using multiple receivers in a crowdsourcing manner. We extend a previous jammer position estimator by only including data that is received during parts of the sensing period where jamming is detected by the sensor. In addition, we perform hardware testing for verification and evaluation of the proposed and compared state-of-the-art algorithms. Evaluations are performed using a Samsung S20+ mobile phone as participatory sensor and a Spirent GSS9000 GNSS simulator to generate GNSS and jamming signals. The proposed algorithm is shown to work well when using C/N-0 measurements and outperform the alternative algorithms in the evaluated scenarios, producing a median error of 50 meters when the pathloss exponent is 2. With higher pathloss exponents the error gets higher. The AGC output from the phone was too noisy and needs further processing to be useful for position estimation., Funding Agencies|Security Link; SSF-SURPRISE

Positioning with high precision and reliability can be provided by 5G cellular networks in environments where satellite positioning is not available or reliable. The accuracy that can be achieved by classical methods like triangulation and trilateration however degrades significantly under non line of sight (NLOS) conditions. The problem can be mitigated with increasingly dense deployments of network transmission and reception points (TRPs), but that is both impractical and costly. As an alternative, this study investigates if multipath propagation of radio signals can be exploited to improve positioning accuracy and reduce the necessary deployment density. With 3GPP Rel. 17 new signaling support has been introduced to report the propagation delay, corresponding to the length, of multiple paths between the user equipment (UE) and a network TRP. The length of a multipath can, in combination with a partially known map of the environment, give additional information about the UE position. In this study we develop multipath-assisted tracking algorithms and evaluate their performances in realistic simulations using 3GPP standardized positioning reference signals and measurements in an indoor factory environment. Our evaluations show that multipath-assisted algorithms can achieve an accuracy below 0.9 m in 90% of the cases, which is more than tenfold better than a conventional LOS based algorithm. Moreover, one algorithm variant also shows an ability to track a UE using very few TRPs.

The number of wireless devices is drastically increasing, resulting in many devices contending for radio resources. In this work, we present an algorithm to detect active devices for unsourced random access, i.e., the devices are uncoordinated. The devices use a unique, but non-orthogonal preamble, known to the network, prior to sending the payload data. They do not employ any carrier sensing technique and blindly transmit the preamble and data. To detect the active users, we exploit partial channel state information (CSI), which could have been obtained through a previous channel estimate. For static devices, e.g., Internet of Things nodes, it is shown that CSI is less time-variant than assumed in many theoretical works. The presented iterative algorithm uses a maximum likelihood approach to estimate both the activity and a potential phase offset of each known device. The convergence of the proposed algorithm is evaluated. The performance in terms of probability of miss detection and false alarm is assessed for different qualities of partial CSI and different signal-to-noise ratio., Funding Agencies|European Union [101013425]

In massive multiple-input multiple-output (MIMO), most precoders result in downlink signals that suffer from high peak-to-average ratio (PAR), independently of modulation order and whether single-carrier or orthogonal frequency-division multiplexing (OFDM) transmission is used. The high PAR lowers the power efficiency of the base-station amplifiers. To increase the power efficiency, low-PAR precoders have been proposed. In this paper, we compare different transmission methods for massive MIMO in terms of the power consumed by the amplifiers. It is found that: 1) OFDM and single-carrier transmission have the same performance over a hardened massive MIMO channel and 2) when the higher amplifier power efficiency of low-PAR precoding is taken into account, conventional and low-PAR precoders lead to approximately the same power consumption. Since downlink signals with low PAR allow for simpler and cheaper hardware, than signals with high PAR, therefore, the results suggest that low-PAR precoding with either single-carrier or OFDM transmission should be used in a massive MIMO base station., Funding agencies: European Union [ICT-619086]; Swedish Research Council (Vetenskapsradet); ELLIIT

In massive multiple-input multiple-output (MIMO), most precoders result in downlink signals that suffer from high peak-to-average ratio (PAR), independently of modulation order and whether single-carrier or orthogonal frequency-division multiplexing (OFDM) transmission is used. The high PAR lowers the power efficiency of the base-station amplifiers. To increase the power efficiency, low-PAR precoders have been proposed. In this paper, we compare different transmission methods for massive MIMO in terms of the power consumed by the amplifiers. It is found that: 1) OFDM and single-carrier transmission have the same performance over a hardened massive MIMO channel and 2) when the higher amplifier power efficiency of low-PAR precoding is taken into account, conventional and low-PAR precoders lead to approximately the same power consumption. Since downlink signals with low PAR allow for simpler and cheaper hardware, than signals with high PAR, therefore, the results suggest that low-PAR precoding with either single-carrier or OFDM transmission should be used in a massive MIMO base station., Funding agencies: European Union [ICT-619086]; Swedish Research Council (Vetenskapsradet); ELLIIT

In massive multiple-input multiple-output (MIMO), most precoders result in downlink signals that suffer from high peak-to-average ratio (PAR), independently of modulation order and whether single-carrier or orthogonal frequency-division multiplexing (OFDM) transmission is used. The high PAR lowers the power efficiency of the base-station amplifiers. To increase the power efficiency, low-PAR precoders have been proposed. In this paper, we compare different transmission methods for massive MIMO in terms of the power consumed by the amplifiers. It is found that: 1) OFDM and single-carrier transmission have the same performance over a hardened massive MIMO channel and 2) when the higher amplifier power efficiency of low-PAR precoding is taken into account, conventional and low-PAR precoders lead to approximately the same power consumption. Since downlink signals with low PAR allow for simpler and cheaper hardware, than signals with high PAR, therefore, the results suggest that low-PAR precoding with either single-carrier or OFDM transmission should be used in a massive MIMO base station., Funding agencies: European Union [ICT-619086]; Swedish Research Council (Vetenskapsradet); ELLIIT

In massive multiple-input multiple-output (MIMO), most precoders result in downlink signals that suffer from high peak-to-average ratio (PAR), independently of modulation order and whether single-carrier or orthogonal frequency-division multiplexing (OFDM) transmission is used. The high PAR lowers the power efficiency of the base-station amplifiers. To increase the power efficiency, low-PAR precoders have been proposed. In this paper, we compare different transmission methods for massive MIMO in terms of the power consumed by the amplifiers. It is found that: 1) OFDM and single-carrier transmission have the same performance over a hardened massive MIMO channel and 2) when the higher amplifier power efficiency of low-PAR precoding is taken into account, conventional and low-PAR precoders lead to approximately the same power consumption. Since downlink signals with low PAR allow for simpler and cheaper hardware, than signals with high PAR, therefore, the results suggest that low-PAR precoding with either single-carrier or OFDM transmission should be used in a massive MIMO base station., Funding agencies: European Union [ICT-619086]; Swedish Research Council (Vetenskapsradet); ELLIIT

In massive multiple-input multiple-output (MIMO), most precoders result in downlink signals that suffer from high peak-to-average ratio (PAR), independently of modulation order and whether single-carrier or orthogonal frequency-division multiplexing (OFDM) transmission is used. The high PAR lowers the power efficiency of the base-station amplifiers. To increase the power efficiency, low-PAR precoders have been proposed. In this paper, we compare different transmission methods for massive MIMO in terms of the power consumed by the amplifiers. It is found that: 1) OFDM and single-carrier transmission have the same performance over a hardened massive MIMO channel and 2) when the higher amplifier power efficiency of low-PAR precoding is taken into account, conventional and low-PAR precoders lead to approximately the same power consumption. Since downlink signals with low PAR allow for simpler and cheaper hardware, than signals with high PAR, therefore, the results suggest that low-PAR precoding with either single-carrier or OFDM transmission should be used in a massive MIMO base station., Funding agencies: European Union [ICT-619086]; Swedish Research Council (Vetenskapsradet); ELLIIT

Sub-Nyquist cyclic nonuniform sampling (CNUS) of a sparse multi-band signal generates a nonuniformly sampled signal. Assuming that the corresponding uniformly sampled signal satisfies the Nyquist sampling criterion, the sequence obtained via CNUS can be passed through a reconstructor to recover the missing uniform-grid samples. In order to recover the missing uniform-grid samples, the sequence obtained via CNUS is passed through a reconstructor. At present, these reconstructors have very high design and implementation complexity that offsets the gains obtained due to sub-Nyquist sampling. In this paper, we propose a scheme that reduces the design and implementation complexity of the reconstructor. In contrast to the existing reconstructors which use only a multi-channel synthesis filter bank (FB), the proposed reconstructor utilizes both analysis and synthesis FBs which makes it feasible to achieve an order-of-magnitude reduction of the complexity. The analysis filters are implemented using polyphase networks whose branches are allpass filters with distinct fractional delays and phase shifts. In order to reduce both the design and the implementation complexity of the synthesis FB, the synthesis filters are implemented using a cosine-modulated FB. In addition to the reduced complexity of the reconstructor, the proposed multi-channel recovery scheme also supports online reconfigurability which is required in flexible (multi-mode) systems where the user subband locations vary with time.

Sub-Nyquist cyclic nonuniform sampling (CNUS) of a sparse multi-band signal generates a nonuniformly sampled signal. Assuming that the corresponding uniformly sampled signal satisfies the Nyquist sampling criterion, the sequence obtained via CNUS can be passed through a reconstructor to recover the missing uniform-grid samples. In order to recover the missing uniform-grid samples, the sequence obtained via CNUS is passed through a reconstructor. At present, these reconstructors have very high design and implementation complexity that offsets the gains obtained due to sub-Nyquist sampling. In this paper, we propose a scheme that reduces the design and implementation complexity of the reconstructor. In contrast to the existing reconstructors which use only a multi-channel synthesis filter bank (FB), the proposed reconstructor utilizes both analysis and synthesis FBs which makes it feasible to achieve an order-of-magnitude reduction of the complexity. The analysis filters are implemented using polyphase networks whose branches are allpass filters with distinct fractional delays and phase shifts. In order to reduce both the design and the implementation complexity of the synthesis FB, the synthesis filters are implemented using a cosine-modulated FB. In addition to the reduced complexity of the reconstructor, the proposed multi-channel recovery scheme also supports online reconfigurability which is required in flexible (multi-mode) systems where the user subband locations vary with time.

Sub-Nyquist cyclic nonuniform sampling (CNUS) of a sparse multi-band signal generates a nonuniformly sampled signal. Assuming that the corresponding uniformly sampled signal satisfies the Nyquist sampling criterion, the sequence obtained via CNUS can be passed through a reconstructor to recover the missing uniform-grid samples. In order to recover the missing uniform-grid samples, the sequence obtained via CNUS is passed through a reconstructor. At present, these reconstructors have very high design and implementation complexity that offsets the gains obtained due to sub-Nyquist sampling. In this paper, we propose a scheme that reduces the design and implementation complexity of the reconstructor. In contrast to the existing reconstructors which use only a multi-channel synthesis filter bank (FB), the proposed reconstructor utilizes both analysis and synthesis FBs which makes it feasible to achieve an order-of-magnitude reduction of the complexity. The analysis filters are implemented using polyphase networks whose branches are allpass filters with distinct fractional delays and phase shifts. In order to reduce both the design and the implementation complexity of the synthesis FB, the synthesis filters are implemented using a cosine-modulated FB. In addition to the reduced complexity of the reconstructor, the proposed multi-channel recovery scheme also supports online reconfigurability which is required in flexible (multi-mode) systems where the user subband locations vary with time.

Sub-Nyquist cyclic nonuniform sampling (CNUS) of a sparse multi-band signal generates a nonuniformly sampled signal. Assuming that the corresponding uniformly sampled signal satisfies the Nyquist sampling criterion, the sequence obtained via CNUS can be passed through a reconstructor to recover the missing uniform-grid samples. In order to recover the missing uniform-grid samples, the sequence obtained via CNUS is passed through a reconstructor. At present, these reconstructors have very high design and implementation complexity that offsets the gains obtained due to sub-Nyquist sampling. In this paper, we propose a scheme that reduces the design and implementation complexity of the reconstructor. In contrast to the existing reconstructors which use only a multi-channel synthesis filter bank (FB), the proposed reconstructor utilizes both analysis and synthesis FBs which makes it feasible to achieve an order-of-magnitude reduction of the complexity. The analysis filters are implemented using polyphase networks whose branches are allpass filters with distinct fractional delays and phase shifts. In order to reduce both the design and the implementation complexity of the synthesis FB, the synthesis filters are implemented using a cosine-modulated FB. In addition to the reduced complexity of the reconstructor, the proposed multi-channel recovery scheme also supports online reconfigurability which is required in flexible (multi-mode) systems where the user subband locations vary with time.

Sub-Nyquist cyclic nonuniform sampling (CNUS) of a sparse multi-band signal generates a nonuniformly sampled signal. Assuming that the corresponding uniformly sampled signal satisfies the Nyquist sampling criterion, the sequence obtained via CNUS can be passed through a reconstructor to recover the missing uniform-grid samples. In order to recover the missing uniform-grid samples, the sequence obtained via CNUS is passed through a reconstructor. At present, these reconstructors have very high design and implementation complexity that offsets the gains obtained due to sub-Nyquist sampling. In this paper, we propose a scheme that reduces the design and implementation complexity of the reconstructor. In contrast to the existing reconstructors which use only a multi-channel synthesis filter bank (FB), the proposed reconstructor utilizes both analysis and synthesis FBs which makes it feasible to achieve an order-of-magnitude reduction of the complexity. The analysis filters are implemented using polyphase networks whose branches are allpass filters with distinct fractional delays and phase shifts. In order to reduce both the design and the implementation complexity of the synthesis FB, the synthesis filters are implemented using a cosine-modulated FB. In addition to the reduced complexity of the reconstructor, the proposed multi-channel recovery scheme also supports online reconfigurability which is required in flexible (multi-mode) systems where the user subband locations vary with time.

We discuss possible definitions of structural balance conditions in a network with preference orderings as node attributes. The main result is that for the case with three alternatives (A, B, C) we reduce the (3!)(3) = 216 possible configurations of triangles to 10 equivalence classes, and use these as measures of balance of a triangle towards possible extensions of structural balance theory. Moreover, we derive a general formula for the number of equivalent classes for preferences on n alternatives. Finally, we analyze a real-world data set and compare its empirical distribution of triangle equivalence classes to a null hypothesis in which preferences are randomly assigned to the nodes., Funding Agencies|ELLIIT; KAW foundation

Deep learning (DL) is a powerful technique for many real-time applications, but it is vulnerable to adversarial attacks. Herein, we consider DL-based modulation classification, with the objective to create DL models that are robust against attacks. Specifically, we introduce three defense techniques: i) randomized smoothing, ii) hybrid projected gradient descent adversarial training, and iii) fast adversarial training, and evaluate them under both white-box (WB) and black-box (BB) attacks. We show that the proposed fast adversarial training is more robust and computationally efficient than the other techniques, and can create models that are extremely robust to practical (BB) attacks., Funding Agencies|Security-Link; Start-Up Research Grant of IIT Guwahati

Radio frequency (RF) wireless power transfer (WPT) is a promising technology for 6G use cases. It enables a massive yet sustainable deployment of batteryless energy neutral (EN) devices at an unprecedented scale. Recent research on 6G is exploring high operating frequencies up to the THz spectrum, where antenna arrays with large apertures are capable of forming narrow, "laser-like" beams. At sub-10 GHz frequencies, physically large antenna arrays are considered that are operating in the array near field. Transmitting spherical wavefronts, power can be focused to a focal point rather than a beam, which allows for efficient and radiation-safe WPT. We formulate a multipath channel model comprising specular components and diffuse scattering to find the WPT power budget in a realistic indoor scenario. Specular components can be predicted by means of a geometric model. This is used to transmit power via multiple beams simultaneously, increasing the available power budget and expanding the initial access distance. We show that exploiting this "beam diversity" reduces the required fading margin for the initial access to EN devices., Funding Agencies|European Unions Horizon 2020 research and innovation programme [101013425]

GNSS receivers are vulnerable to jamming and spoofing attacks, and numerous such incidents have been reported worldwide in the last decade. It is important to detect attacks fast and localize attackers, which can be hard if not impossible without dedicated sensing infrastructure. The notion of participatory sensing, or crowdsensing, is that a large ensemble of voluntary contributors provides the measurements, rather than relying on dedicated sensing infrastructure. This work considers embedded GNSS receivers to provide measurements for participatory jamming detection and localization. Specifically, this work proposes a novel jamming localization algorithm, based on participatory sensing, that exploits AGC and C/N-0 estimates from commercial GNSS receivers. The proposed algorithm does not require knowledge of the jamming power nor of the channels, but automatically estimates all parameters. The algorithm is shown to outperform similar state-of-the-art localization algorithms in relevant scenarios., Funding Agencies|Security Link

Today, no simple methods are available for measurements of interference signals that give a proper indication of the impact in terms of the bit error probability (BEP) on a digital radio receiver. Such measure should quantify the corresponding impact and the measurements should be relatively easy to perform. By only using the root mean square (RMS) value of the interference average power the BEP can be underestimated with several magnitudes. To address this problem, an impulsiveness correction factor (ICF) has earlier been proposed to adjust for these errors. The ICF opens up for considerably more accurate BEP estimations whereas the simplicity in the calculations is maintained. However, how to determine the ICF for an arbitrary interference source through measurements has not earlier been known. In this paper, we show that the ICF can be obtained in two alternative ways. One way is to use the measured amplitude probability distribution (APD). The other way is to use the peak- and RMS values from standard measurement detectors. Both methods take the interference waveform properties into consideration and the BEP can thus be more accurately estimated.

Today, no simple methods are available for measurements of interference signals that give a proper indication of the impact in terms of the bit error probability (BEP) on a digital radio receiver. Such measure should quantify the corresponding impact and the measurements should be relatively easy to perform. By only using the root mean square (RMS) value of the interference average power the BEP can be underestimated with several magnitudes. To address this problem, an impulsiveness correction factor (ICF) has earlier been proposed to adjust for these errors. The ICF opens up for considerably more accurate BEP estimations whereas the simplicity in the calculations is maintained. However, how to determine the ICF for an arbitrary interference source through measurements has not earlier been known. In this paper, we show that the ICF can be obtained in two alternative ways. One way is to use the measured amplitude probability distribution (APD). The other way is to use the peak- and RMS values from standard measurement detectors. Both methods take the interference waveform properties into consideration and the BEP can thus be more accurately estimated.

A new method for multiple-input multiple-output (MIMO) detection with soft-output, the partial marginalization (PM) algorithm, was recently proposed. Advantages of the method are that it is straightforward to parallelize, and that it offers a fully predictable runtime. PM trades performance for computational complexity via a user-defined parameter. In the limit of high computational complexity, the algorithm becomes the MAP demodulator. The PM algorithm also works with soft-input, but until now it has been unclear how to apply it for other modulation formats than binary phase-shift keying (BPSK) per real dimension. In this paper, we explain how to extend PM with soft-input to general signaling constellations, while maintaining the low complexity advantage of the original algorithm., ©2010 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. Daniel Persson and Erik G. Larsson, Partial Marginalization Soft MIMO Detection with Higher Order Constellations, 2010, IEEE Transactions on Signal Processing.http://dx.doi.org/10.1109/TSP.2010.2068293

We point out an error in a derivation in the recent paper [1], and provide a correct and much shorter calculation of the result in question. In passing, we also connect the results in [1] to the literature on array signal processing and on principal component analysis, and show that the main findings of [1] follow as special cases of standard results in these fields., ©2011 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. Erik Axell and Erik G. Larsson, Comments on "Multiple Antenna Spectrum Sensing in Cognitive Radios", 2011, IEEE Transactions on Wireless Communications, (10), 5, 1678-1680. http://dx.doi.org/10.1109/TWC.2011.030911.101111

We point out an error in a derivation in the recent paper [1], and provide a correct and much shorter calculation of the result in question. In passing, we also connect the results in [1] to the literature on array signal processing and on principal component analysis, and show that the main findings of [1] follow as special cases of standard results in these fields., ©2011 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. Erik Axell and Erik G. Larsson, Comments on "Multiple Antenna Spectrum Sensing in Cognitive Radios", 2011, IEEE Transactions on Wireless Communications, (10), 5, 1678-1680. http://dx.doi.org/10.1109/TWC.2011.030911.101111