Karim Banawan

In this thesis, we consider the application of collaborative MIMO and Turbo equalization techniques for the uplink of the LTE-advanced. Collaborative MIMO involves sharing 2 users or more the same resource block. The scheme will increase spectral efficiency for the uplink mode. The main contributions of the thesis are distributed over chapter 4,5 and 6. In chapter 4,we have proposed 2 ordering techniques for the SIC detector for the multiuser SC-FDMA based system. We also propose a novel initial guess based maximum likelihood receiver and simplified version of it relying on QR-transform. In chapter 5 ,We propose three precoding schemes to the collaborative MIMO system. Which are SFBC precoding which doesn’t require CSI, SVD precoding which require full CSI and codebook precoding which requires partial CSI. In chapter 6 we moved to turbo equalizer which uses a recursive equalization/decoding algorithm. So we applied turbo equalization for precoded/unprecoded collaborative MIMO system.

—We consider the problem of private information retrieval (PIR) over a distributed storage system. The storage system consists of N non-colluding databases, each storing an MDS-coded version of M messages. In the PIR problem, the user wishes to retrieve one of the available messages without revealing the message identity to any individual database. We derive the information-theoretic capacity of this problem, which is defined as the maximum number of bits of the desired message that can be privately retrieved per one bit of downloaded information. We show that the PIR capacity in this case is C = 1 + K N + K 2 N 2 + · · · + K M −1 N M −1 −1 = (1 + Rc + R 2 c + · · · + R M −1 c) −1 = 1−Rc 1−R M c , where Rc is the rate of the (N, K) code used. The capacity is a function of the code rate and the number of messages only regardless of the explicit structure of the storage code. The result implies a fundamental tradeoff between the optimal retrieval cost and the storage cost. The result generalizes the achievability and converse results for the classical PIR with replicating databases to the case of coded databases.

—We consider the broadcast channel with confidential messages (BCCM) over N parallel Gaussian channels. The transmitter aims at maximizing the sum-rate. The system has two combating jammers, each aiming to enhance the secure rate to one receiver only, while hurting the other receiver by sending Gaussian jamming signals. We cast the problem as an extensive-form game and derive the optimal jamming policy. We show that the jamming strategy is a form of generalized water-filling, and provide theoretical insights on the optimal solution. We provide simulation results to show the convergence of the rate and power allocations, and study the effect of increasing the available power of the transmitter and/or the jammers.

—We consider the multiple access wiretap channel (MAC-WTC), where multiple legitimate users wish to have secure communication with a legitimate receiver in the presence of an eavesdropper. The exact secure degrees of freedom (s.d.o.f.) region of this channel is known. Achieving this region requires users to follow a certain protocol altruistically and transmit both message-carrying and cooperative jamming signals in an optimum manner. In this paper, we consider the case when a subset of users deviate from this optimum protocol. We consider two kinds of deviation: when some of the users stop transmitting cooperative jamming signals, and when a user starts sending intentional jamming signals. For the first scenario, we investigate possible responses of the remaining users to counteract such deviation. For the second scenario, we use an extensive-form game formulation for the interactions of the deviating and well-behaving users. We prove that a deviating user can drive the s.d.o.f. to zero; however, the remaining users can exploit its intentional jamming signals as cooperative jamming signals against the eavesdropper and achieve an optimum s.d.o.f.

We consider the multiple-input multiple-output (MIMO) wiretap channel under a minimum receiver-side power constraint in addition to the usual maximum transmitter-side power constraint. This problem is motivated by energy harvesting communications with wireless energy transfer, where an added goal is to deliver a minimum amount of energy to a receiver in addition to delivering secure data to another receiver. In this paper, we characterize the exact secrecy capacity of the MIMO wiretap channel under transmitter and receiver-side power constraints. We first show that solving this problem is equivalent to solving the secrecy capacity of the wiretap channel under a double-sided correlation matrix constraint on the channel input. We show the converse by extending the channel enhancement technique to our case. We present two achievable schemes that achieve the secrecy capacity: the first achievable scheme uses a Gaussian codebook with a fixed mean, and the second achievable scheme uses artificial noise (or cooperative jamming) together with a Gaussian codebook. The role of the mean or the artificial noise is to enable energy transfer without sacrificing from the secure rate. This is the first instance of a channel model where either the use of a mean signal or the use of channel prefixing via artificial noise is strictly necessary for the MIMO wiretap channel. We then extend our work to consider a maximum receiver-side power constraint instead of a minimum receiver-side power constraint. This problem is motivated by cognitive radio applications, where an added goal is to decrease the received signal energy (interference temperature) at a receiver. We further extend our results to: requiring receiver-side power constraints at both receivers; considering secrecy constraints at both receivers to study broadcast channels with confidential messages; and removing the secrecy constraints to study the classical broadcast channel.

— We consider a channel with N parallel sub-bands. There is a single user that can access exactly k channels, while maintaining some minimum rate at each accessed channel. The transmission takes place in the presence of a jammer which can access at most m channels. We cast the problem as an extensive-form game and derive the optimal power allocation strategies for both the user and the jammer. We present extensive simulation results regarding convergence of rates, effect of changing the number of accessed bands for the user and the jammer, and the minimum rate constraint.

—We investigate the secure degrees of freedom (s.d.o.f.) of two new channel models: broadcast channel with combating helpers and interference channel with selfish users. In the first model, over a classical broadcast channel with confidential messages (BCCM), there are two helpers, each associated with one of the receivers. In the second model, over a classical interference channel with confidential messages (ICCM), there is a helper and users are selfish. The goal of introducing these channel models is to investigate various malicious interactions that arise in networks, including active adversaries. By casting each problem as an extensive-form game and applying recursive real interference alignment, we show that, for the first model, the combating intentions of the helpers are neutralized and the full s.d.o.f. is retained; for the second model, selfishness precludes secure communication and no s.d.o.f. is achieved.

We consider the two-user multiple-input multiple-output (MIMO) interference channel with confidential messages (ICCM). We determine the exact sum secure degrees of freedom (s.d.o.f.) for the symmetric case of M antennas at both transmitters and N antennas at both receivers. We develop the converse by combining the broadcast channel with confidential messages (BCCM) cooperative upper bound, decodability upper bound for the IC with no secrecy constraints, and extensions of the secrecy penalty and role of a helper lemmas. We propose a novel achievable scheme for the 2 × 2 ICCM, which combines asymptotic real interference alignment with spatial interference alignment. Using this scheme, we provide achievable schemes for any M and N by proper vector space operations.

We consider the multiple-input multiple-output (MIMO) wiretap channel under a minimum receiver-side power constraint in addition to the usual maximum transmitter-side power constraint. This problem is motivated by energy harvesting communications with wireless energy transfer, where an added goal is to deliver a minimum amount of energy to a receiver in addition to delivering secure data to another receiver. In this paper, we characterize the exact secrecy capacity of the MIMO wiretap channel under transmitter and receiver-side power constraints. We first show that solving this problem is equivalent to solving the secrecy capacity of a wiretap channel with a double-sided correlation matrix constraint on the channel input. We show the converse by extending the channel enhancement technique to our case. We present two achievable schemes that achieve the secrecy capacity: the first achievable scheme uses a Gaussian codebook with a fixed mean, and the second achievable scheme uses artificial noise (or cooperative jamming) together with a Gaussian codebook. The role of the mean or the artificial noise is to enable energy transfer without sacrificing from the secure rate. This is the first instance of a channel model where either the use of a mean signal or use of channel prefixing via artificial noise is strictly necessary in the MIMO wiretap channel.

We consider the problem of single-round private information retrieval (PIR) from N replicated databases. We consider the case when B databases are outdated (unsyn-chronized), or even worse, adversarial (Byzantine), and therefore, can return incorrect answers. In the PIR problem with Byzantine databases (BPIR), a user wishes to retrieve a specific message from a set of M messages with zero-error, irrespective of the actions performed by the Byzantine databases. We consider the T-privacy constraint in this paper, where any T databases can collude, and exchange the queries submitted by the user. We derive the information-theoretic capacity of this problem, which is the maximum number of correct symbols that can be retrieved privately (under the T-privacy constraint) for every symbol of the downloaded data. We determine the exact BPIR capacity to be C = N −2B N · 1− T N−2B 1−(T N−2B) M , if 2B + T < N. This capacity expression shows that the effect of Byzantine databases on the retrieval rate is equivalent to removing 2B databases from the system, with a penalty factor of N −2B N , which signifies that even though the number of databases needed for PIR is effectively N − 2B, the user still needs to access the entire N databases. The result shows that for the unsyn-chronized PIR problem, if the user does not have any knowledge about the fraction of the messages that are mis-synchronized, the single-round capacity is the same as the BPIR capacity. Our achievable scheme extends the optimal achievable scheme for the robust PIR (RPIR) problem to correct the errors introduced by the Byzantine databases as opposed to erasures in the RPIR problem. Our converse proof uses the idea of the cut-set bound in the network coding problem against adversarial nodes.

We consider the problem of multi-message private information retrieval (MPIR) from N non-communicating replicated databases. In MPIR, the user is interested in retrieving P messages out of M stored messages without leaking the identity of the retrieved messages. The information-theoretic sum capacity of MPIR C P s is the maximum number of desired message symbols that can be retrieved privately per down-loaded symbol. For the case P ≥ M 2 , we determine the exact sum capacity of MPIR as C P s = 1 1+ M −P P N. The achievable scheme in this case is based on downloading MDS-coded mixtures of all messages. For P ≤ M 2 , we develop lower and upper bounds for all M, P, N. These bounds match if the total number of messages M is an integer multiple of the number of desired messages P , i.e., M P ∈ N. In this case, C P s = 1− 1 N 1−(1 N) M/P. The achievable scheme in this case generalizes the single-message capacity achieving scheme to have unbalanced number of stages per round of download. For all the remaining cases, the difference between the lower and upper bound is at most 0.0082, which occurs for M = 5, P = 2, N = 2. Our results indicate that joint retrieval of desired messages is more efficient than successive use of single-message retrieval schemes.

We consider the problem of private information retrieval (PIR) over a distributed storage system. The storage system consists of N non-colluding databases, each storing a coded version of M messages. In the PIR problem, the user wishes to retrieve one of the available messages without revealing the message identity to any individual database. We derive the information-theoretic capacity of this problem, which is defined as the maximum number of bits of the desired message that can be privately retrieved per one bit of downloaded information. We show that the PIR capacity in this case is C = 1 + K N + K 2 N 2 + · · · + K M −1 N M −1 −1 = (1 + R c + R 2 c + · · · + R M −1 c) −1 = 1−Rc 1−R M c , where R c is the rate of the (N, K) code used. The capacity is a function of the code rate and the number of messages only regardless of the explicit structure of the storage code. The result implies a fundamental tradeoff between the optimal retrieval cost and the storage cost. The result generalizes the achievability and converse results for the classical PIR with replicating databases to the case of coded databases.