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Industry and academia have been working towards the evolution from Centralized massive Multiple-Input Multiple-Output (CmMIMO) to Distributed mMIMO (DmMIMO) architectures. Instead of splitting a coverage area into many cells, each served by a single Base Station equipped with several antennas, the whole coverage area is jointly covered by several Access Points (AP) equipped with few or single antennas. Nevertheless, when choosing between deploying more APs with few or single antennas or fewer APs equipped with many antennas, one observes an inherent trade-off between the beamforming and macro-diversity gains that has not been investigated in the literature. Given a total number of antenna elements and total downlink power, under a channel model that takes into account a probability of Line-of-Sight (LoS) as a function of the distance between the User Equipments (UEs) and APs, our numerical results show that there exists a ``sweet spot" on the optimal number of APs and of antenna elements per AP which is a function of the physical dimensions of the coverage area., Comment: 6 pages, 3 figures. Manuscript submitted to the IEEE Wireless Communications and Networking Conference (WCNC) 2024, Dubai, United Arab Emirates

In wiretap channels the eavesdropper's channel state information (CSI) is commonly assumed to be known at transmitter, fully or partially. However, under perfect secrecy constraint the eavesdropper may not be motivated to feedback any correct CSI. In this paper we consider a more feasible problem for the transmitter to have eavesdropper's CSI. That is, the fast fading multiple-antenna Gaussian broadcast channels (FMGBC-CM) with confidential messages, where both receivers are legitimate users such that they both are willing to feedback accurate CSI to maintain their secure transmission, and not to be eavesdropped by the other. We assume that only the statistics of the channel state information are known by the transmitter. We first show the necessary condition for the FMGBC-CM not to be degraded to the common wiretap channels. Then we derive the achievable rate region for the FMGBC-CM where the channel input covariance matrices and the inflation factor are left unknown and to be solved. After that we provide an analytical solution to the channel input covariance matrices. We also propose an iterative algorithm to solve the channel input covariance matrices and the inflation factor. Due to the complicated rate region formulae in normal SNR, we resort to low SNR analysis to investigate the characteristics of the channel. Finally, numerical examples show that under perfect secrecy constraint both users can achieve positive rates simultaneously, which verifies our derived necessary condition. Numerical results also elucidate the effectiveness of the analytic solution and proposed algorithm of solving the channel input covariance matrices and the inflation factor under different conditions., Comment: 31 pages

This paper considers the multi-antenna multiple access relay channel (MARC), in which multiple users transmit messages to a common destination with the assistance of a relay. In a variety of MARC settings, the dynamic decode and forward (DDF) protocol is very useful due to its outstanding rate performance. However, the lack of good structured codebooks so far hinders practical applications of DDF for MARC. In this work, two classes of structured MARC codes are proposed: 1) one-to-one relay-mapper aided multiuser lattice coding (O-MLC), and 2) modulo-sum relay-mapper aided multiuser lattice coding (MS-MLC). The former enjoys better rate performance, while the latter provides more flexibility to tradeoff between the complexity of the relay mapper and the rate performance. It is shown that, in order to approach the rate performance achievable by an unstructured codebook with maximum-likelihood decoding, it is crucial to use a new K-stage coset decoder for structured O-MLC, instead of the one-stage decoder proposed in previous works. However, if O-MLC is decoded with the one-stage decoder only, it can still achieve the optimal DDF diversity-multiplexing gain tradeoff in the high signal-to-noise ratio regime. As for MS-MLC, its rate performance can approach that of the O-MLC by increasing the complexity of the modulo-sum relay-mapper. Finally, for practical implementations of both O-MLC and MS-MLC, practical short length lattice codes with linear mappers are designed, which facilitate efficient lattice decoding. Simulation results show that the proposed coding schemes outperform existing schemes in terms of outage probabilities in a variety of channel settings., Comment: 32 pages, 5 figures

In this paper we consider the secure transmission over the fast fading multiple antenna Gaussian broadcast channels with confidential messages (FMGBC-CM), where a multiple-antenna transmitter sends independent confidential messages to two users with information theoretic secrecy and only the statistics of the receivers' channel state information are known at the transmitter. We first use the same marginal property of the FMGBC-CM to classify the non-trivial cases, i.e., those not degraded to the common wiretap channels. We then derive the achievable rate region for the FMGBC-CM by solving the channel input covariance matrices and the inflation factor. Due to the complicated rate region formulae, we resort to low SNR analysis to investigate the characteristics of the channel. Finally, the numerical examples show that under the information-theoretic secrecy requirement both users can achieve positive rates simultaneously., Comment: 6 pages, conference, 5 figures

Wyner-Ziv coding (WZC) is a compression technique using decoder side information, which is unknown at the encoder, to help the reconstruction. In this paper, we propose and implement a new WZC structure, called residual WZC, for the quadratic-Gaussian Wyner-Ziv problem where side information can be arbitrarily distributed. In our two-stage residual WZC, the source is quantized twice and the input of the second stage is the quantization error (residue) of the first stage. The codebook of the first stage quantizer must be simultaneously good for source and channel coding, since it also acts as a channel code at the decoder. Stemming from the non-ideal quantization at the encoder, a problem of channel decoding beyond capacity is identified and solved when we design the practical decoder. Moreover,by using the modified reinforced belief-propagation quantization algorithm, the low-density parity check code (LDPC), whose edge degree is optimized for channel coding, also performs well as a source code. We then implement the residual WZC by an LDPC and a low density generator matrix code (LDGM). The simulation results show that our practical construction approaches the Wyner-Ziv bound. Compared with previous works, our construction can offer more design lexibility in terms of distribution of side information and practical code rate selection., Comment: To appear, IEEE International Symposium on Information Theory (ISIT) Jul, 2012, corrected reference [13]

In this paper we consider the secure transmission in fast Rayleigh fading channels with full knowledge of the main channel and only the statistics of the eavesdropper's channel state information at the transmitter. For the multiple-input, single-output, single-antenna eavesdropper systems, we generalize Goel and Negi's celebrated artificial-noise (AN) assisted beamforming, which just selects the directions to transmit AN heuristically. Our scheme may inject AN to the direction of the message, which outperforms Goel and Negi's scheme where AN is only injected in the directions orthogonal to the main channel. The ergodic secrecy rate of the proposed AN scheme can be represented by a highly simplified power allocation problem. To attain it, we prove that the optimal transmission scheme for the message bearing signal is a beamformer, which is aligned to the direction of the legitimate channel. After characterizing the optimal eigenvectors of the covariance matrices of signal and AN, we also provide the necessary condition for transmitting AN in the main channel to be optimal. Since the resulting secrecy rate is a non-convex power allocation problem, we develop an algorithm to efficiently solve it. Simulation results show that our generalized AN scheme outperforms Goel and Negi's, especially when the quality of legitimate channel is much worse than that of eavesdropper's. In particular, the regime with non-zero secrecy rate is enlarged, which can significantly improve the connectivity of the secure network when the proposed AN assisted beamforming is applied., Comment: 28 pages, 7 figures, submitted to IEEE Transactions on Wireless Communications

We consider the interference-mitigation based cognitive radio where the primary and secondary users can coexist at the same time and frequency bands, under the constraint that the rate of the primary user (PU) must remain the same with a single-user decoder. To meet such a coexistence constraint, the relaying from the secondary user (SU) can help the PU's transmission under the interference from the SU. However, the relayed signal in the known dirty paper coding (DPC) based scheme is interfered by the SU's signal, and is not "clean". In this paper, under the half-duplex constraints, we propose two new transmission schemes aided by the clean relaying from the SU's transmitter and receiver without interference from the SU. We name them as the clean transmitter relaying (CT) and clean transmitter-receiver relaying (CTR) aided cognitive radio, respectively. The rate and multiplexing gain performances of CT and CTR in fading channels with various availabilities of the channel state information at the transmitters (CSIT) are studied. Our CT generalizes the celebrated DPC based scheme proposed previously. With full CSIT, the multiplexing gain of the CTR is proved to be better (or no less) than that of the previous DPC based schemes. This is because the silent period for decoding the PU's messages for the DPC may not be necessary in the CTR. With only the statistics of CSIT, we further prove that the CTR outperforms the rate performance of the previous scheme in fast Rayleigh fading channels. The numerical examples also show that in a large class of channels, the proposed CT and CTR provide significant rate gains over the previous scheme with small complexity penalties., Comment: 30 pages

For the multiuser multiple-input multiple-output (MIMO) downlink channel, the users feedback their channel state information (CSI) to help the base station (BS) schedule users and improve the system sum rate. However, this incurs a large aggregate feedback bandwidth which grows linearly with the number of users. In this paper, we propose a novel scheme to reduce the feedback load in a downlink orthogonal space division multiple access (SDMA) system with zero-forcing receivers by allowing the users to dynamically determine the number of feedback bits to use according to multiple decision thresholds. Through theoretical analysis, we show that, while keeping the aggregate feedback load of the entire system constant regardless of the number of users, the proposed scheme almost achieves the optimal asymptotic sum rate scaling with respect to the number of users (also known as the multiuser diversity). Specifically, given the number of thresholds, the proposed scheme can achieve a constant portion of the optimal sum rate achievable only by the system where all the users always feedback, and the remaining portion (referred to as the sum rate loss) decreases exponentially to zero as the number of thresholds increases. By deriving a tight upper bound for the sum rate loss, the minimum number of thresholds for a given tolerable sum rate loss is determined. In addition, a fast bit allocation method is discussed for the proposed scheme, and the simulation results show that the sum rate performances with the complex optimal bit allocation method and with the fast algorithm are almost the same. We compare our multi-threshold scheme to some previously proposed feedback schemes. Through simulation, we demonstrate that the proposed scheme can reduce the feedback load and utilize the limited feedback bandwidth more effectively than the existing feedback methods., Comment: 25 pages, 10 figures

The Dynamic Decode-and-Forward (DDF) protocol and the Hybrid DDF and Amplified-and-Forward (HDAF) protocol for the multiple-access relay channel (MARC) with quasi static fading are evaluated using the Zheng-Tse diversity-multiplexing tradeoff (DMT). We assume that there are two users, one half-duplex relay, and a common destination, each equipped with single antenna. For the Rayleigh fading, the DDF protocol is well known and has been analyzed in terms of the DMT with infinite block length. By carefully dealing with properties specific to finite block length, we characterize the finite block length DMT which takes into account the fact that the event of decoding error at the relay causes the degradation in error performance when the block length is finite. Furthermore, we consider the situation where the destination does not have a priori knowledge of the relay decision time at which the relay switches from listening to transmitting. By introducing a decision rejection criterion such that the relay forwards message only when its decision is reliable, and the generalized likelihood ratio test (GLRT) at the destination that jointly decodes the relay decision time and the information message, our analysis show that the optimal DMT is achievable as if there is no decoding error at the relay and the relay decision time is known at the destination. Therefore, infinite block length and additional overhead for communicating the decision time are not needed for the DDF to achieve the optimal DMT. To further improve the DMT, we propose the HDAF protocol which take advantages of both the DDF and the Amplified-and-Forward protocols by judiciously choosing which protocol to use. Our result shows that the HDAF protocol outperforms the original DDF in the DMT perspective. Finally, a variant of the HDAF protocol with lower implementation complexity without sacrificing the DMT performance is devised., Comment: 28 pages, 2 figures

This paper considers feedback load reduction for multiuser multiple input multiple output (MIMO) broadcast channel where the users' channel distributions are not homogeneous. A cluster-based feedback scheme is proposed such that the range of possible signal-to-noise ratio (SNR) of the users are divided into several clusters according to the order statistics of the users' SNRs. Each cluster has a corresponding threshold, and the users compare their measured instantaneous SNRs with the thresholds to determine whether and how many bits they should use to feed back their instantaneous SNRs. If a user's instantaneous SNR is lower than a certain threshold, the user does not feed back. Feedback load reduction is thus achieved. For a given number of clusters, the sum rate loss using the cluster-based feedback scheme is investigated. Then the minimum number of clusters given a maximum tolerable sum rate loss is derived. Through simulations, it is shown that, when the number of users is large, full multiuser diversity can be achieved by the proposed feedback scheme, which is more efficient than the conventional schemes., Comment: 6 pages, 4 figures

In this paper, system design for the multi-input multi-output (MIMO) relay broadcast channel with individual signal-to-interference-plus-noise ratio (SINR) constraints at the mobile stations (MS) is considered. By exploring the structure of downlink (DL) uplink (UL) duality at either the base station (BS) or the relay station (RS), we propose two schemes of joint power allocation and beamforming design at the BS and the RS. The problem of existence of feasible solutions under practical power constraints at the BS and the RS with given SINR targets is considered first. Then the problem of sum power minimization is considered. Each design problem can be solved efficiently using optimal joint power allocation and beamforming under the framework of convex optimization. We also show that with subchannel pairing at the RS, the transmission power can be reduced by channel compensation at either hop. Finally, an extension to more general multi-hop applications is provided to further improve the power efficiency., Comment: 30 pages, 12 figures, 2 tables

The cognitive interference channel with unidirectional destination cooperation (CIFC-UDC) is a variant of the cognitive interference channel (CIFC) where the cognitive (secondary) destination not only decodes the information sent from its sending dual but also helps enhance the communication of the primary user. This channel is an extension of the original CIFC to achieve a win-win solution under the coexistence condition. The CIFC-UDC comprises a broadcast channel (BC), a relay channel (RC), as well as a partially cooperative relay broadcast channel (PCRBC), and can be degraded to any one of them. In this paper, we propose a new achievable rate region for the dis-crete memoryless CIFC-UDC which improves the previous re-sults and includes the largest known rate regions of the BC, the RC, the PCRBC and the CIFC. A new outer bound is presented and proved to be tight for two classes of the CIFC-UDCs, result-ing in the characterization of the capacity region., Comment: submitted to ISIT 2011

The cognitive interference channel with unidirectional destination cooperation (CIFC-UDC) is a cognitive interference channel (CIFC) where the cognitive (secondary) destination not only decodes the information sent from its sending dual but also helps enhance the communication of the primary user. This channel model is an extension of the original CIFC to achieve a win-win solution under the coexistence condition. From an information-theoretic perspective, the CIFC-UDC comprises a broadcast channel (BC), a relay channel (RC) and a partially cooperative relay broadcast channel (PCRBC), and can be degraded to any one of them. Our main result is the establishment of a new unified achieva-ble rate region for the CIFC-UDC which is the largest known to date and can be explicitly shown to include the previous result proposed by Chu and the largest known rate regions for the BC, the RC and the PCRBC. In addition, an interesting viewpoint on the unidirectional destination cooperation in the CIFC-UDC is discussed: to enable the decoder of the primary user to perform interference mitigation can be considered as a complementary idea to the interference mitigation via Gel'fand-Pinsker precod-ing in the CIFC proposed by Devroye et al. Henceforth, by com-bing these two ideas, the interferences caused at both the desti-nations can be alleviated. Lastly, an outer bound is presented and proved to be tight for a class of the CIFC-UDC, resulting in the characterization of the capacity region for this class., Comment: 18 pages, 3 figures

In this paper, we propose a novel adaptive modulation and coding (AMC) algorithm dedicated to reduce the feedback frequency of the channel state information (CSI). There have been already plenty of works on AMC so as to exploit the bandwidth more efficiently with the CSI feedback to the transmitter. However, in some occasions, frequent CSI feedback is not favorable in these systems. This work considers finite-state Markov chain (FSMC) based channel prediction to alleviate the feedback while maximizing the overall throughput. We derive the close-form of the frame error rate (FER) based on channel prediction using limited CSI feedback. In addition, instead of switching settings according to the CSI, we also provide means to combine both CSI and FER as the switching parameter. Numerical results illustrate that the average throughput of the proposed algorithm has significant performance improvement over fixed modulation and coding while the CSI feedback being largely reduced.

We analytically study a carrier sense multiple access (CSMA)-based network. In the network, the nodes have their own average throughput demands for transmission to a common base station. The CSMA is based on the request-to-send (RTS)/clear-to-send (CTS) handshake mechanism. Each node individually chooses its probability of transmitting an RTS packet, which specifies the length of its requested data transmission period. The RTS packets transmitted by different nodes in the same time slot interfere with one another, and compete to be received by the base station. If a node's RTS has the received signal to interference plus noise ratio (SINR) higher than the capture ratio, it will be successfully received. The node will then be granted the data transmission period. The transmission probabilities of RTS packets of all nodes will determine the average throughput and power consumption of each node. The set of all possible throughput demands of nodes that can be supported by the network is called the feasible throughput region. We characterize the feasible throughput region and provide an upper bound on the total power consumption for any throughput demands in the feasible throughput region. The upper bound corresponds to one of three points in the feasible throughput region depending on the fraction of time occupied by the RTS packets., Comment: submitted to IEEE Transactions on Communications

Zheng and Tse have shown that over a quasi-static channel, there exists a fundamental tradeoff, known as the diversity-multiplexing gain (D-MG) tradeoff. In a realistic system, to avoid inefficiently operating the power amplifier, one should consider the situation where constraints are imposed on the peak to average power ratio (PAPR) of the transmitted signal. In this paper, the D-MG tradeoff of multi-antenna systems with PAPR constraints is analyzed. For Rayleigh fading channels, we show that the D-MG tradeoff remains unchanged with any PAPR constraints larger than one. This result implies that, instead of designing codes on a case-by-case basis, as done by most existing works, there possibly exist general methodologies for designing space-time codes with low PAPR that achieve the optimal D-MG tradeoff. As an example of such methodologies, we propose a PAPR reduction method based on constellation shaping that can be applied to existing optimal space-time codes without affecting their optimality in the D-MG tradeoff. Unlike most PAPR reduction methods, the proposed method does not introduce redundancy or require side information being transmitted to the decoder. Two realizations of the proposed method are considered. The first is similar to the method proposed by Kwok except that we employ the Hermite Normal Form (HNF) decomposition instead of the Smith Normal Form (SNF) to reduce complexity. The second takes the idea of integer reversible mapping which avoids the difficulty in matrix decomposition when the number of antennas becomes large. Sphere decoding is performed to verify that the proposed PAPR reduction method does not affect the performance of optimal space-time codes., Comment: submitted to IEEE Transactions on Signal Processing

In this paper, a point-to-point Orthogonal Frequency Division Multiplexing (OFDM) system with a decode-and-forward (DF) relay is considered. The transmission consists of two hops. The source transmits in the first hop, and the relay transmits in the second hop. Each hop occupies one time slot. The relay is half-duplex, and capable of decoding the message on a particular subcarrier in one time slot, and re-encoding and forwarding it on a different subcarrier in the next time slot. Thus each message is transmitted on a pair of subcarriers in two hops. It is assumed that the destination is capable of combining the signals from the source and the relay pertaining to the same message. The goal is to maximize the weighted sum rate of the system by jointly optimizing subcarrier pairing and power allocation on each subcarrier in each hop. The weighting of the rates is to take into account the fact that different subcarriers may carry signals for different services. Both total and individual power constraints for the source and the relay are investigated. For the situations where the relay does not transmit on some subcarriers because doing so does not improve the weighted sum rate, we further allow the source to transmit new messages on these idle subcarriers. To the best of our knowledge, such a joint optimization inclusive of the destination combining has not been discussed in the literature. The problem is first formulated as a mixed integer programming problem. It is then transformed to a convex optimization problem by continuous relaxation, and solved in the dual domain. Based on the optimization results, algorithms to achieve feasible solutions are also proposed. Simulation results show that the proposed algorithms almost achieve the optimal weighted sum rate, and outperform the existing methods in various channel conditions., Comment: 33 pages, 11 figures

In this paper we aim to solve the multiuser multi-input multi-output (MIMO) downlink beamforming problem where one multi-antenna base station broadcasts data to many users. Each user is assigned multiple data streams and has multiple antennas at its receiver. Efficient solutions to the joint transmit-receive beamforming and power allocation problem based on iterative methods are proposed. We adopt the group maximum signal-to-interference-plus-noise-ratio (SINR) filter bank (GSINR-FB) as our beamformer which exploits receiver diversity through cooperation between the data streams of a user. The data streams for each user are subject to an average SINR constraint, which has many important applications in wireless communication systems and serves as a good metric to measure the quality of service (QoS). The GSINR-FB also optimizes the average SINR of its output. Based on the GSINR-FB beamformer, we find an SINR balancing structure for optimal power allocation which simplifies the complicated power allocation problem to a linear one. Simulation results verify the superiority of the proposed algorithms over previous works with approximately the same complexity., Comment: 29 pages, 7 figures

The Nash equilibrium point of the transmission probabilities in a slotted ALOHA system with selfish nodes is analyzed. The system consists of a finite number of heterogeneous nodes, each trying to minimize its average transmission probability (or power investment) selfishly while meeting its average throughput demand over the shared wireless channel to a common base station (BS). We use a game-theoretic approach to analyze the network under two reception models: one is called power capture, the other is called signal to interference plus noise ratio (SINR) capture. It is shown that, in some situations, Braess-like paradoxes may occur. That is, the performance of the system may become worse instead of better when channel state information (CSI) is available at the selfish nodes. In particular, for homogeneous nodes, we analytically present that Braess-like paradoxes occur in the power capture model, and in the SINR capture model with the capture ratio larger than one and the noise to signal ratio sufficiently small., Comment: 30 pages, 5 figures

Linear-assignment Gel'fand-Pinsker coding (LA-GPC) is a coding technique for channels with interference known only at the transmitter, where the known interference is treated as side-information (SI). As a special case of LA-GPC, dirty paper coding has been shown to be able to achieve the optimal interference-free rate for interference channels with perfect channel state information at the transmitter (CSIT). In the cases where only the channel distribution information at the transmitter (CDIT) is available, LA-GPC also has good (sometimes optimal) performance in a variety of fast and slow fading SI channels. In this paper, we design the filters in nested-lattice based coding to make it achieve the same rate performance as LA-GPC in multiple-input multiple-output (MIMO) channels. Compared with the random Gaussian codebooks used in previous works, our resultant coding schemes have an algebraic structure and can be implemented in practical systems. A simulation in a slow-fading channel is also provided, and near interference-free error performance is obtained. The proposed coding schemes can serve as the fundamental building blocks to achieve the promised rate performance of MIMO Gaussian broadcast channels with CDIT or perfect CSIT, Comment: submitted to IEEE Transactions on Communications, Feb, 2009

In this paper, we present the cognitive radio system design with partial channel state information known at the transmitter (CSIT).We replace the dirty paper coding (DPC) used in the cognitive radio with full CSIT by the linear assignment Gel'fand-Pinsker coding (LA-GPC), which can utilize the limited knowledge of the channel more efficiently. Based on the achievable rate derived from the LA-GPC, two optimization problems under the fast and slow fading channels are formulated. We derive semianalytical solutions to find the relaying ratios and precoding coefficients. The critical observation is that the complex rate functions in these problems are closely related to ratios of quadratic form. Simulation results show that the proposed semi-analytical solutions perform close to the optimal solutions found by brute-force search, and outperform the systems based on naive DPC. Asymptotic analysis also shows that these solutions converge to the optimal ones solved with full CSIT when the K-factor of Rician channel approaches infinity. Moreover, a new coding scheme is proposed to implement the LA-GPC in practice. Simulation results show that the proposed practical coding scheme can efficiently reach the theoretical rate performance., Comment: resubmitted to IEEE Transaction on Wireless Communications, May 2009