Null Space

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Andrea Goldsmith - One of the best experts on this subject based on the ideXlab platform.

  • Null Space learning in cooperative mimo cellular networks using interference feedback
    IEEE Transactions on Wireless Communications, 2015
    Co-Authors: Alexandros Manolakos, Yair Noam, Andrea Goldsmith
    Abstract:

    We present schemes for acquiring the Null Space of the interference channel between a User Equipment (UE) and an interfering Base Station Group (BSG) in Cooperative Multi-point cellular networks, whose only required network information is the interference levels at the UE. Specifically, the interfering BSG transmits a sequence of learning signals which inflicts interference on a UE served by a neighboring BSG. The UE treats interference as noise, measures its overall interference plus noise power, and feeds this value back to its serving BSG. Then, the latter distributes this information to the interfering BSG, from which it learns the Null Space of the interfering channel. We also present a Null Space tracking algorithm, whose performance includes an inherent tradeoff between the accuracy of the Null Space learning and the inflicted interference during learning, and characterize analytically and via simulations its performance under channel variations and noisy measurements. The proposed algorithms do not affect the transmission protocol between the UE and the serving BSG, do not add any signaling to the control channel between them, and do not require any protocol changes from the UE side.

  • Null Space learning with interference feedback for spatial division multiple access
    IEEE Transactions on Wireless Communications, 2014
    Co-Authors: Yair Noam, Alexandros Manolakos, Andrea Goldsmith
    Abstract:

    We propose a learning technique for MIMO communication systems to perform spatial division multiple access with minimal cooperation between users. In the proposed technique, each user (in a two-user receiver-transmitter pair) learns the Null Space of the interference channel to the other user by transmitting a learning signal and observing an affine function of the other user's interference plus noise power. The only requirement is that each system broadcasts, through a low-rate control channel, a periodic beacon that is a function of its noise plus interference power, which in practice is typically known by each system's receiver and transmitter. Thus, the learning can be made by the two users' transmitters without affecting the communication protocol between each user's receiver and transmitter. The proposed learning scheme is particularly attractive for underlay cognitive radio, where only the secondary user (SU), which must not interfere with the primary user (PU), has to learn the Null Space. In this case, the PU can broadcast the scheme's beacon without being aware of the SU. Furthermore, if the PU uses a power control mechanism which maintains a constant signal to interference plus noise ratio, the SU can learn the Null Space even without a beacon, i.e., without any cooperation with the PU.

  • ICC - Interference due to Null Space mismatch in cooperative multipoint MIMO cellular networks
    2014 IEEE International Conference on Communications (ICC), 2014
    Co-Authors: Manolakos Alexandros, Yair Noam, Andrea Goldsmith
    Abstract:

    Cooperative Multi-Point (CoMP) has emerged as a new paradigm to improve both average cell and cell edge throughput in cellular networks. However, the performance is significantly degraded due to Out-of-Group Interference (OGI). One way to mitigate OGI is to restrict the interfering signal to lie inside the Null Space of the unintended receiver. Yet, accurately tracking this Null Space is a challenge in time-varying channels. In this work, we address the effect of Null Space variations on the OGI mitigation. A measure for accuracy of Null Space estimates is proposed and bounds are derived on the residual average worst-case interference. We define the Null Space Update Rate as the inverse of the Null Space Coherence Time; i.e., the time it takes a Null Space estimate to become outdated relative to an interference threshold on the unintended receiver. In the case of Rayleigh fading channels, we derive a bound on the Null Space Coherence Time in closed form, and compare the performance of a given Null Space tracking algorithm against this bound. Both Monte Carlo simulations and the analytical bounds show that the worst-case interference levels are sensitive to Null Space variations, independent of the Null Space learning algorithm employed.

  • one bit Null Space learning for mimo underlay cognitive radio
    Information Theory and Applications, 2013
    Co-Authors: Yair Noam, Andrea Goldsmith
    Abstract:

    We present a new algorithm, called the One-Bit Null Space Learning Algorithm (OBNSLA), for MIMO cognitive radio Secondary Users (SU) to learn the Null Space of the interference channel to the Primary User (PU). The SU observes a binary function that indicates whether the interference it inflicts on the PU has increased or decreased in comparison to the SU's previous transmitted signal. This function is obtained by listening to the PU's transmitted signal or control channel and extracting information from it about whether the PU's Signal to Interference plus Noise power Ratio has increased or decreased. In addition to introducing the OBNSLA, the paper provides a thorough convergence analysis of this algorithm. The OBNSLA is shown to have a linear convergence rate and an asymptotic quadratic convergence rate.

  • blind Null Space learning for mimo underlay cognitive radio with primary user interference adaptation
    IEEE Transactions on Wireless Communications, 2013
    Co-Authors: Yair Noam, Andrea Goldsmith
    Abstract:

    This paper proposes a blind technique that enables a MIMO cognitive radio Secondary User (SU) to transmit in the same band simultaneously with a Primary User (PU) by utilizing separate spatial dimensions than the PU. Specifically, the SU transmits in the Null Space of the interference channel to the PU. The SU learns this Null Space without burdening the PU with any knowledge or explicit cooperation with the SU. The only condition required is that during the learning period, the SU is allowed to inflict "non-harmful" interference to the PU. The SU measures a monotonic function of this interference in order to learn the Null Space. Specifically, during the learning interval, the SU learns the Null Space by iteratively modifying the spatial orientation of its transmitted signal and measures the effect of this modification on the monotonic function that it observes. We provide simulation results demonstrating that the algorithm converges rapidly and is robust to quantization noise and other sources of interference.

Yair Noam - One of the best experts on this subject based on the ideXlab platform.

  • Null Space learning in cooperative mimo cellular networks using interference feedback
    IEEE Transactions on Wireless Communications, 2015
    Co-Authors: Alexandros Manolakos, Yair Noam, Andrea Goldsmith
    Abstract:

    We present schemes for acquiring the Null Space of the interference channel between a User Equipment (UE) and an interfering Base Station Group (BSG) in Cooperative Multi-point cellular networks, whose only required network information is the interference levels at the UE. Specifically, the interfering BSG transmits a sequence of learning signals which inflicts interference on a UE served by a neighboring BSG. The UE treats interference as noise, measures its overall interference plus noise power, and feeds this value back to its serving BSG. Then, the latter distributes this information to the interfering BSG, from which it learns the Null Space of the interfering channel. We also present a Null Space tracking algorithm, whose performance includes an inherent tradeoff between the accuracy of the Null Space learning and the inflicted interference during learning, and characterize analytically and via simulations its performance under channel variations and noisy measurements. The proposed algorithms do not affect the transmission protocol between the UE and the serving BSG, do not add any signaling to the control channel between them, and do not require any protocol changes from the UE side.

  • Null Space learning with interference feedback for spatial division multiple access
    IEEE Transactions on Wireless Communications, 2014
    Co-Authors: Yair Noam, Alexandros Manolakos, Andrea Goldsmith
    Abstract:

    We propose a learning technique for MIMO communication systems to perform spatial division multiple access with minimal cooperation between users. In the proposed technique, each user (in a two-user receiver-transmitter pair) learns the Null Space of the interference channel to the other user by transmitting a learning signal and observing an affine function of the other user's interference plus noise power. The only requirement is that each system broadcasts, through a low-rate control channel, a periodic beacon that is a function of its noise plus interference power, which in practice is typically known by each system's receiver and transmitter. Thus, the learning can be made by the two users' transmitters without affecting the communication protocol between each user's receiver and transmitter. The proposed learning scheme is particularly attractive for underlay cognitive radio, where only the secondary user (SU), which must not interfere with the primary user (PU), has to learn the Null Space. In this case, the PU can broadcast the scheme's beacon without being aware of the SU. Furthermore, if the PU uses a power control mechanism which maintains a constant signal to interference plus noise ratio, the SU can learn the Null Space even without a beacon, i.e., without any cooperation with the PU.

  • Interference due to Null Space mismatch in cooperative multipoint MIMO cellular networks
    2014 IEEE International Conference on Communications (ICC), 2014
    Co-Authors: Alexandros Manolakos, Yair Noam, Andrea J. Goldsmith
    Abstract:

    Cooperative Multi-Point (CoMP) has emerged as a new paradigm to improve both average cell and cell edge throughput in cellular networks. However, the performance is significantly degraded due to Out-of-Group Interference (OGI). One way to mitigate OGI is to restrict the interfering signal to lie inside the Null Space of the unintended receiver. Yet, accurately tracking this Null Space is a challenge in time-varying channels. In this work, we address the effect of Null Space variations on the OGI mitigation. A measure for accuracy of Null Space estimates is proposed and bounds are derived on the residual average worst-case interference. We define the Null Space Update Rate as the inverse of the Null Space Coherence Time; i.e., the time it takes a Null Space estimate to become outdated relative to an interference threshold on the unintended receiver. In the case of Rayleigh fading channels, we derive a bound on the Null Space Coherence Time in closed form, and compare the performance of a given Null Space tracking algorithm against this bound. Both Monte Carlo simulations and the analytical bounds show that the worst-case interference levels are sensitive to Null Space variations, independent of the Null Space learning algorithm employed.

  • ICC - Interference due to Null Space mismatch in cooperative multipoint MIMO cellular networks
    2014 IEEE International Conference on Communications (ICC), 2014
    Co-Authors: Manolakos Alexandros, Yair Noam, Andrea Goldsmith
    Abstract:

    Cooperative Multi-Point (CoMP) has emerged as a new paradigm to improve both average cell and cell edge throughput in cellular networks. However, the performance is significantly degraded due to Out-of-Group Interference (OGI). One way to mitigate OGI is to restrict the interfering signal to lie inside the Null Space of the unintended receiver. Yet, accurately tracking this Null Space is a challenge in time-varying channels. In this work, we address the effect of Null Space variations on the OGI mitigation. A measure for accuracy of Null Space estimates is proposed and bounds are derived on the residual average worst-case interference. We define the Null Space Update Rate as the inverse of the Null Space Coherence Time; i.e., the time it takes a Null Space estimate to become outdated relative to an interference threshold on the unintended receiver. In the case of Rayleigh fading channels, we derive a bound on the Null Space Coherence Time in closed form, and compare the performance of a given Null Space tracking algorithm against this bound. Both Monte Carlo simulations and the analytical bounds show that the worst-case interference levels are sensitive to Null Space variations, independent of the Null Space learning algorithm employed.

  • one bit Null Space learning for mimo underlay cognitive radio
    Information Theory and Applications, 2013
    Co-Authors: Yair Noam, Andrea Goldsmith
    Abstract:

    We present a new algorithm, called the One-Bit Null Space Learning Algorithm (OBNSLA), for MIMO cognitive radio Secondary Users (SU) to learn the Null Space of the interference channel to the Primary User (PU). The SU observes a binary function that indicates whether the interference it inflicts on the PU has increased or decreased in comparison to the SU's previous transmitted signal. This function is obtained by listening to the PU's transmitted signal or control channel and extracting information from it about whether the PU's Signal to Interference plus Noise power Ratio has increased or decreased. In addition to introducing the OBNSLA, the paper provides a thorough convergence analysis of this algorithm. The OBNSLA is shown to have a linear convergence rate and an asymptotic quadratic convergence rate.

Bruno Siciliano - One of the best experts on this subject based on the ideXlab platform.

  • Null Space impedance control with disturbance observer
    Intelligent Robots and Systems, 2012
    Co-Authors: Hamid Sadeghian, Mehdi Keshmiri, Luigi Villani, Bruno Siciliano
    Abstract:

    In this paper a new approach for the Null-Space impedance control of a kinematically redundant robot is proposed. The approach is useful for the case where the robot experience an external interaction on the body, especially in the presence of humans. The proposed algorithm guarantees safe and dependable physical interaction of the robot body with the environment, thanks to the Null-Space impedance control. At the same time, the correct execution of the task assigned to the end effector is ensured by a disturbance observer. The algorithm does not require joint torque measurements. The performance of the proposed controller is verified through simulations on 7R KUKA lightweight robot arm.

  • IROS - Null-Space impedance control with disturbance observer
    2012 IEEE RSJ International Conference on Intelligent Robots and Systems, 2012
    Co-Authors: Hamid Sadeghian, Mehdi Keshmiri, Luigi Villani, Bruno Siciliano
    Abstract:

    In this paper a new approach for the Null-Space impedance control of a kinematically redundant robot is proposed. The approach is useful for the case where the robot experience an external interaction on the body, especially in the presence of humans. The proposed algorithm guarantees safe and dependable physical interaction of the robot body with the environment, thanks to the Null-Space impedance control. At the same time, the correct execution of the task assigned to the end effector is ensured by a disturbance observer. The algorithm does not require joint torque measurements. The performance of the proposed controller is verified through simulations on 7R KUKA lightweight robot arm.

Alexandros Manolakos - One of the best experts on this subject based on the ideXlab platform.

  • Null Space learning in cooperative mimo cellular networks using interference feedback
    IEEE Transactions on Wireless Communications, 2015
    Co-Authors: Alexandros Manolakos, Yair Noam, Andrea Goldsmith
    Abstract:

    We present schemes for acquiring the Null Space of the interference channel between a User Equipment (UE) and an interfering Base Station Group (BSG) in Cooperative Multi-point cellular networks, whose only required network information is the interference levels at the UE. Specifically, the interfering BSG transmits a sequence of learning signals which inflicts interference on a UE served by a neighboring BSG. The UE treats interference as noise, measures its overall interference plus noise power, and feeds this value back to its serving BSG. Then, the latter distributes this information to the interfering BSG, from which it learns the Null Space of the interfering channel. We also present a Null Space tracking algorithm, whose performance includes an inherent tradeoff between the accuracy of the Null Space learning and the inflicted interference during learning, and characterize analytically and via simulations its performance under channel variations and noisy measurements. The proposed algorithms do not affect the transmission protocol between the UE and the serving BSG, do not add any signaling to the control channel between them, and do not require any protocol changes from the UE side.

  • Null Space learning with interference feedback for spatial division multiple access
    IEEE Transactions on Wireless Communications, 2014
    Co-Authors: Yair Noam, Alexandros Manolakos, Andrea Goldsmith
    Abstract:

    We propose a learning technique for MIMO communication systems to perform spatial division multiple access with minimal cooperation between users. In the proposed technique, each user (in a two-user receiver-transmitter pair) learns the Null Space of the interference channel to the other user by transmitting a learning signal and observing an affine function of the other user's interference plus noise power. The only requirement is that each system broadcasts, through a low-rate control channel, a periodic beacon that is a function of its noise plus interference power, which in practice is typically known by each system's receiver and transmitter. Thus, the learning can be made by the two users' transmitters without affecting the communication protocol between each user's receiver and transmitter. The proposed learning scheme is particularly attractive for underlay cognitive radio, where only the secondary user (SU), which must not interfere with the primary user (PU), has to learn the Null Space. In this case, the PU can broadcast the scheme's beacon without being aware of the SU. Furthermore, if the PU uses a power control mechanism which maintains a constant signal to interference plus noise ratio, the SU can learn the Null Space even without a beacon, i.e., without any cooperation with the PU.

  • Interference due to Null Space mismatch in cooperative multipoint MIMO cellular networks
    2014 IEEE International Conference on Communications (ICC), 2014
    Co-Authors: Alexandros Manolakos, Yair Noam, Andrea J. Goldsmith
    Abstract:

    Cooperative Multi-Point (CoMP) has emerged as a new paradigm to improve both average cell and cell edge throughput in cellular networks. However, the performance is significantly degraded due to Out-of-Group Interference (OGI). One way to mitigate OGI is to restrict the interfering signal to lie inside the Null Space of the unintended receiver. Yet, accurately tracking this Null Space is a challenge in time-varying channels. In this work, we address the effect of Null Space variations on the OGI mitigation. A measure for accuracy of Null Space estimates is proposed and bounds are derived on the residual average worst-case interference. We define the Null Space Update Rate as the inverse of the Null Space Coherence Time; i.e., the time it takes a Null Space estimate to become outdated relative to an interference threshold on the unintended receiver. In the case of Rayleigh fading channels, we derive a bound on the Null Space Coherence Time in closed form, and compare the performance of a given Null Space tracking algorithm against this bound. Both Monte Carlo simulations and the analytical bounds show that the worst-case interference levels are sensitive to Null Space variations, independent of the Null Space learning algorithm employed.

  • blind Null Space tracking for mimo underlay cognitive radio networks
    Global Communications Conference, 2012
    Co-Authors: Alexandros Manolakos, Yair Noam, Konstantinos Dimou, Andrea Goldsmith
    Abstract:

    Blind Null Space Learning [1] has recently been proposed for fast and accurate learning of the Null-Space associated with the channel matrix between a secondary transmitter and a primary receiver. In this paper we propose a channel tracking enhancement of the algorithm, namely the Blind Null Space Tracking algorithm, that allows transmission of information to the Secondary Receiver while simultaneously learning the Null-Space of the time-varying target channel. Specifically, the enhanced algorithm initially performs a sweep in order to acquire the Null Space. Then, it performs modified Jacobi rotations such that the induced interference is kept lower than a given threshold P Th with probability p while information is transmitted to the secondary receiver simultaneously. The learning process is performed based on sensing whether the transmit power of the primary user has increased or decreased between adaptations. We present simulation results indicating that the proposed approach has strictly better performance over the Blind Null Space Learning algorithm for channels with independent Rayleigh fading at a low Doppler frequency.

Gameiro Atílio - One of the best experts on this subject based on the ideXlab platform.

  • One-bit Null-Space cognitive interference alignment for heterogeneous networks
    IEEE, 1
    Co-Authors: Castanheira Daniel, Silva Adão, Gameiro Atílio
    Abstract:

    To increase capacity and offload traffic from the current macro cell cellular system, small cells have been deployed extensively. In the current deployments small cells coexist with their respective macro cells in the same spectrum, due to the difficulty and costs involved in acquiring new spectrum licenses. This leads to considerable interference between the two systems. In this context, we propose an underlay cognitive interference alignment technique to remove the interference from the small cell to the macro cell system. In the proposed scheme the small cells sense the unused resources in the Space dimension of the macro cell, i.e. its Null Space, and precode their signals such that they lie in the sensed Null Space. We demonstrate that only the sign of the Null Space components is necessary to obtain close to full Null Space information performance. This results in less overhead in the sensing process making the system more efficient and practically feasible

  • Null-Space cognitive precoding for heterogeneous networks
    Institution of Engineering and Technology (IET), 1
    Co-Authors: Castanheira Daniel, Silva Adão, Gameiro Atílio
    Abstract:

    Small-cells are considered as an effective solution to increase capacity and offload traffic from, the current macro-cell cellular system. Owing to the difficulty and costs involved in acquiring new spectrum licenses, small-cells are expected to coexist with their respective macro-cells, in the same spectrum. This leads to considerable interference between the two systems. Optimum performance, at the macro-cell, is achieved when the small-cell terminals transmit their information over the Null- Space of the macro-cell link. However, availability, at the small-cell terminals, of the macro-cell channel Null-Space information requires full-cooperation and thus a high overhead of information exchange. In this study, the cognitive precoding schemes are designed under a limited inter-system information exchange and the constraint that the performance of the macro-cell link is kept close to the case where no small-cell network does exist. Two techniques are considered: a two-bit quantisation precoded and a dual Space-frequency coding precoded approach. It is demonstrated that the first achieves a performance close to the full cooperation approach recently proposed, but with very low information exchange requirements. For the second, it is show that both the systems are able to coexist without any inter-system cooperation and with a performance close to the non-coexistence scenario