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Secure degrees of freedom of the multiple access wiretap channel with no eavesdropper CSI,’’ presented at the
 IEEE Int. Symp. Inf. Theory, Hong Kong
, 2015
"... Abstract—We consider the Kuser Gaussian multiple access wiretap channel (MACWT), where no eavesdropper channel state information (CSI) is available at the transmitters. We show that the exact sum secure degrees of freedom (s.d.o.f.) of this channel model is K−1 K. This result shows that, under the ..."
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Abstract—We consider the Kuser Gaussian multiple access wiretap channel (MACWT), where no eavesdropper channel state information (CSI) is available at the transmitters. We show that the exact sum secure degrees of freedom (s.d.o.f.) of this channel model is K−1 K. This result shows that, under the condition of no eavesdropper CSI, the MACWT acts like a singletransmitter K − 1 helper wiretap channel. We further show that, when a subset of the transmitters have eavesdropper CSI, then higher sum s.d.o.f. can be achieved, and the system can be operated as a MACWT for the users with eavesdropper CSI, with the remaining users acting as helpers. In particular, if m of the K transmitters have eavesdropper CSI, we show that m(K−1) m(K−1)+1 sum s.d.o.f. can be achieved, showing the benefits of having the eavesdropper CSI at the transmitters. I.
Secure Degrees of Freedom Region of the TwoUser MISO Broadcast Channel with Alternating CSIT∗
, 2015
"... The two user multipleinput singleoutput (MISO) broadcast channel with confidential messages (BCCM) is studied in which the nature of channel state information at the transmitter (CSIT) from each user can be of the form Ii, i = 1, 2 where I1, I2 ∈ {P,D,N}, and the forms P, D and N correspond to p ..."
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The two user multipleinput singleoutput (MISO) broadcast channel with confidential messages (BCCM) is studied in which the nature of channel state information at the transmitter (CSIT) from each user can be of the form Ii, i = 1, 2 where I1, I2 ∈ {P,D,N}, and the forms P, D and N correspond to perfect and instantaneous, completely delayed, and no CSIT, respectively. Thus, the overall CSIT can alternate between 9 possible states corresponding to all possible values of I1I2, with each state occurring for λI1I2 fraction of the total duration. The main contribution of this paper is to establish the secure degrees of freedom (s.d.o.f.) region of the MISO BCCM with alternating CSIT with the symmetry assumption, where λI1I2 = λI2I1. The main technical contributions include developing a) novel achievable schemes for MISO BCCM with alternating CSIT with security constraints which also highlight the synergistic benefits of interstate coding for secrecy, b) new converse proofs via local statistical equivalence and channel enhancement; and c) showing the interplay between various aspects of channel knowledge and their impact on s.d.o.f. 1
1Achievable Rates of FDD Massive MIMO Systems with Spatial Channel Correlation
"... Abstract—It is well known that the performance of frequencydivisionduplex (FDD) massive MIMO systems with i.i.d. channels is disappointing compared with that of timedivisionduplex (TDD) systems, due to the prohibitively large overhead for acquiring channel state information at the transmitter (C ..."
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Abstract—It is well known that the performance of frequencydivisionduplex (FDD) massive MIMO systems with i.i.d. channels is disappointing compared with that of timedivisionduplex (TDD) systems, due to the prohibitively large overhead for acquiring channel state information at the transmitter (CSIT). In this paper, we investigate the achievable rates of FDD massive MIMO systems with spatially correlated channels, considering the CSIT acquisition dimensionality loss, the imperfection of CSIT and the regularizedzeroforcing linear precoder. The achievable rates are optimized by judiciously designing the downlink channel training sequences and user CSIT feedback codebooks, exploiting the multiuser spatial channel correlation. We compare our achievable rates with TDD massive MIMO systems, i.i.d. FDD systems, and the joint spatial division and multiplexing (JSDM) scheme, by deriving the deterministic equivalents of the achievable rates, based on the onering model and the Laplacian model. It is shown that, based on the proposed eigenspace channel estimation schemes, the rategap between FDD systems and TDD systems is significantly narrowed, even approached under moderate number of base station antennas. Compared to the JSDM scheme, our proposal achieves dimensionalityreduction channel estimation without channel preprojection, and higher throughput for moderate number of antennas and moderate to large channel coherence block length, though at higher computational complexity. Index Terms—Massive MIMO systems, Frequencydivisionduplex, Spatial channel correlation, Training sequences design,
Settling conjectures on the collapse of degrees of freedom under finite precision csit
 in Proceedings of Globecom
, 2014
"... states that the degrees of freedom (DoF) of a two user broadcast channel, where the transmitter is equipped with 2 antennas and each user is equipped with 1 antenna, must collapse under finite precision channel state information at the transmitter (CSIT). That this conjecture, which predates interfe ..."
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states that the degrees of freedom (DoF) of a two user broadcast channel, where the transmitter is equipped with 2 antennas and each user is equipped with 1 antenna, must collapse under finite precision channel state information at the transmitter (CSIT). That this conjecture, which predates interference alignment, has remained unresolved, is emblematic of a pervasive lack of understanding of the degrees of freedom of wireless networks— including interference and X networks—under channel uncertainty at the transmitter(s). In this work we prove that the conjecture is true in all nondegenerate settings (e.g., where the probability density function of unknown channel coefficients exists and is bounded). The DoF collapse even when perfect channel knowledge for one user is available to the transmitter. This also settles a related recent conjecture by Tandon et al. Reminiscent of Korner and Marton’s work on the images of a set, the key to our proof is a bound on the number of codewords that can cast the same image (within noise distortion) at the undesired receiver, while remaining resolvable at the desired receiver. We are also able to generalize the result to arbitrary number of users, including the K user interference channel. Remarkably, for the K user interference channel, this work and the earlier work by Cadambe and Jafar reveal two contrasting sides of the same coin. Both works close a gap between the best previously known DoF inner bound of 1 and the best previously known DoF outer bound of K/2. However, while Cadambe and Jafar do so in the optimistic direction, showing that K/2 is optimal under perfect CSIT, here we close the gap in the pessimistic direction, showing that 1 DoF is optimal under finite precision CSIT. I.
Secure degrees of freedom of the interference channel with no eavesdropper CSI
 in IEEE Inf. Theory Workshop
, 2015
"... Abstract—We consider the Kuser interference channel with an external eavesdropper, with no eavesdropper’s channel state information at the transmitters (CSIT). We determine the exact sum secure degrees of freedom (s.d.o.f.) for this channel by providing a new alignment based achievable scheme and ..."
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Abstract—We consider the Kuser interference channel with an external eavesdropper, with no eavesdropper’s channel state information at the transmitters (CSIT). We determine the exact sum secure degrees of freedom (s.d.o.f.) for this channel by providing a new alignment based achievable scheme and a matching converse. Our results show that the lack of eavesdropper’s CSIT does not have a significant impact on the optimal s.d.o.f. of the interference channel with an external eavesdropper, especially when the number of users is large. I.
Secrecy for MISO broadcast channels via alternating CSIT
 In IEEE ICC
, 2015
"... broadcast channel with confidential messages (BCCM) is studied in which the nature of channel state information at the transmitter (CSIT) from each user can be of the form Ii, i = 1, 2 where I1, I2 ∈ {P,D,N}, and the forms P, D and N correspond to perfect and instantaneous, completely delayed, and ..."
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broadcast channel with confidential messages (BCCM) is studied in which the nature of channel state information at the transmitter (CSIT) from each user can be of the form Ii, i = 1, 2 where I1, I2 ∈ {P,D,N}, and the forms P, D and N correspond to perfect and instantaneous, completely delayed, and no CSIT, respectively. Thus, the overall CSIT can alternate over time between 9 possible states corresponding to all possible values of I1I2, with each state occurring for λI1I2 fraction of the total duration. The main contribution of this paper is to establish the secure degrees of freedom (s.d.o.f.) region of the MISO BCCM with alternating CSIT with the symmetry assumption λI1I2 = λI2I1. The results highlight the synergistic benefits of coding across CSIT states for secrecy and the interplay between various aspects of channel knowledge and its impact on s.d.o.f. I.
Secure Degrees of Freedom of Onehop Wireless Networks with No Eavesdropper CSIT∗
, 2015
"... We consider three channel models: the wiretap channel withM helpers, the Kuser multiple access wiretap channel, and the Kuser interference channel with an external eavesdropper, when no eavesdropper's channel state information (CSI) is available at the transmitters. In each case, we establish ..."
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We consider three channel models: the wiretap channel withM helpers, the Kuser multiple access wiretap channel, and the Kuser interference channel with an external eavesdropper, when no eavesdropper's channel state information (CSI) is available at the transmitters. In each case, we establish the optimal sum secure degrees of freedom (s.d.o.f.) by providing achievable schemes and matching converses. We show that the unavailability of the eavesdropper's CSIT does not reduce the s.d.o.f. of the wiretap channel with helpers. However, there is loss in s.d.o.f. for both the multiple access wiretap channel and the interference channel with an external eavesdropper. In particular, we show that in the absence of eavesdropper's CSIT, the Kuser multiple access wiretap channel reduces to a wiretap channel with (K − 1) helpers from a sum s.d.o.f. perspective, and the optimal sum s.d.o.f. reduces from K(K−1)K(K−1)+1 to K−1 K. For the interference channel with an external eavesdropper, the optimal sum s.d.o.f. decreases from K(K−1)2K−1 to K−1 2 in the absence of the eavesdropper's CSIT. Our results show that the lack of eavesdropper's CSIT does not have a signicant impact on the optimal s.d.o.f. for any of the three channel models, especially when the number of users is large. This implies that physical layer security can be made robust to the unavailability of eavesdropper CSIT at high signal to noise ratio (SNR) regimes by careful modication of the achievable schemes as demonstrated in this paper. 1
Secrecy for MISO Broadcast Channels with Heterogeneous CSIT
"... Abstract—We consider the twouser multipleinput singleoutput (MISO) broadcast channel with confidential messages (BCCM), in which the nature of channel state information at the transmitter (CSIT) from each user can be of the form P, D and N, corresponding to perfect and instantaneous, completely d ..."
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Abstract—We consider the twouser multipleinput singleoutput (MISO) broadcast channel with confidential messages (BCCM), in which the nature of channel state information at the transmitter (CSIT) from each user can be of the form P, D and N, corresponding to perfect and instantaneous, completely delayed, and no CSIT, respectively. We focus on the cases with heterogeneous CSIT from the users, that is, the states PD, PN and DN. The main contribution of this paper is to establish the exact secure degrees of freedom (s.d.o.f.) regions of the MISO BCCM in all of these three heterogeneous states. The results highlight the impact of availability of CSIT on the s.d.o.f. region. I.