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This paper considers the secrecy outage performance of a multiple-relay assisted non-orthogonal multiple access (NOMA) network over Nakagami- $m$ fading channels. Two time slots are utilized to transmit signals from the base station to destination. At the first time slot, the base station broadcasts the superposition signal of the two users to all decode-and-forward relays by message mapping strategy. Subsequently, the selected relay transmits superposition signal to the two users via power-domain NOMA technology. Three relay selection schemes, i.e., optimal single relay selection (OSRS) scheme, two-step single relay selection (TSRS) scheme, and optimal dual relay selection (ODRS) scheme are proposed and the secrecy outage performance is analyzed. As a benchmark, we also examine the secrecy outage performance of the NOMA systems with traditional multiple relay forwarding (TMRF) scheme in which all the relay that successfully decode signals from the source forward signals to the NOMA users with equal power. Considering the correlation between the secrecy capacity of two users and different secrecy requirement for two NOMA users, the analytical expressions for the security outage probability (SOP) of the proposed OSRS, TSRS, and ODRS schemes along with the TMRF scheme are derived and validated via simulations. To get more insights, we also derive the analytical expressions for the asymptotic SOP for all the schemes with fixed and dynamic power allocations. Furthermore, the secrecy diversity order (SDO) and secrecy array gain of cooperative NOMA systems are obtained. The results demonstrate that our proposed schemes can significantly enhance the secrecy performance compared to the TMRF scheme and that all the schemes with fixed power allocation obtain zero SDO and the OSRS scheme with dynamic power allocation obtains the same SDO as TMRF.

In this paper, we establish a framework for enabling ultra-reliable and low-latency communications in the control and non-payload communications (CNPC) links of the unmanned aerial vehicle (UAV) communication systems. We first derive the available range of the CNPC links between UAVs and a ground control station. The available range is defined as the maximal horizontal communication distance within which the round-trip delay and the overall packet loss probability can be ensured with a required probability. To exploit the macro-diversity gain of the distributed multi-antenna systems (DAS) and the array gain of the centralized multi-antenna systems (CAS), we consider a modified DAS (M-DAS), where the ground control station is equipped with the distributed access points (APs), and each AP can have multiple antennas. We then show that the available range can be maximized by judiciously optimizing the altitude of UAVs, the duration of the uplink and downlink phases, and the antenna configuration. To solve the non-convex problem, we propose an algorithm that can converge to the optimal solution in DAS and CAS, and then extend it into more general M-DAS. The simulation and numerical results validate our analysis and show that the available range of M-DAS can be significantly larger than those of the DAS and CAS.

In this paper, a comprehensive design and analysis of multiple-input multiple-output (MIMO) full-duplex (FD) relaying systems in a multi-cell environment are investigated, where a multi-antenna amplify-and-forward (AF) FD relay station serves multiple half-duplex (HD) multi-antenna users. The pivotal obstacles of loopback self-interference (LI) and multiple co-channel interferers (CCI) at the relay and destination when employing FD relaying in cellular networks are addressed. In contrast to the HD relaying mode, the CCI in the FD relaying mode is predicted to double since the uplink and downlink communications are simultaneously scheduled via the same channel. In this paper, the optimal layout of transmit (receive) precoding (decoding) weight vectors which maximizes the overall signal-to-interefernce-plusnoise ratio (SINR) is constructed by a suitable optimization problem, then a closed-form sub-optimal formula based on null space projection is presented. The proposed hop-by-hop rank- 1 zero-forcing (ZF) beamforming vectors are based on added ZF constraints used to suppress the LI and CCI channels at the relay and destination, i.e., the source and relay perform transmit ZF beamforming, while the relay and destination employ receive ZF combining. To this end, unified accurate expressions for the outage probability and ergodic capacity are derived in closed-form. In addition, simpler tight lower-bound formulas for the outage probability and ergodic capacity are presented. Moreover, the asymptotic approximations for outage probability is considered to gain insights into system behavior in terms of the diversity order and array gain. Numerical and simulation results show the accuracy of the presented exact analytical expressions and the tightness of the lower-bound expressions. The case of hopby- hop maximum-ratio transmission/maximal-ratio combining beamforming is included for comparison purposes. Furthermore, our results show that while multi-antenna terminals improve the system performance, the detrimental effect of CCI on FD relaying is clearly seen. Therefore, our findings unveil that MIMO FD relaying could significantly improve the system performance compared to its conventional MIMO HD relaying counterpart.

Owing to abundant spectrum resources, millimeter wave (mmwave) communication promises to provide Gbps data rates, which, however, may be restricted by large path-loss. Thus, antenna arrays are commonly used along with beam alignment (BA) as an important step to achieve the array gain. Efficient BA relies on the beam training codebook design. In this paper, we propose a new hierarchical codebook to achieve uniform BA performance with low overhead. To better elaborate on the design principle, a single-path channel model is considered first to frame the proposal. The codebook design is formulated as an optimization problem, where the ripple in the main/side lobes is constrained such that each training beam is close to the ideal one with a flat magnitude response and a narrow transition band. Then, we propose an efficient algorithm to find such a beam training codebook. Furthermore, we derive closed-form expressions of the BA misalignment probability or error rate of the proposed beam training codebook. Our results reveal that using the proposed codebook, the error rate of tree-search-based BA exponentially decreases with the SNR for a given channel, and linearly decreases in the log–log coordinate axis for a fading channel. We further propose a power allocation scheme used in different training stages to further improve the BA performance. Finally, the proposed framework is extended to the more complex case of multi-path channels. Numerical results confirm the effectiveness of the proposed training codebook and power allocation scheme as well as the accuracy of the performance analysis.

Massive multiple-input multiple-output (massive MIMO) has been studied to improve the throughput in cellular communication systems via spatial degrees of freedom and array gain. However, in massive MIMO systems, due to the hardware cost considerations, it is infeasible to install a radio frequency (RF) chain for each antenna. To deploy massive MIMO within reasonable hardware cost, hybrid precoding is proposed in which the signal is processed by a low-dimensional digital baseband precoder and a high-dimensional analog RF precoder. On the other hand, cooperative transmission is another way to enhance system throughput, in which base stations (BSs) can jointly transmit to a user. In this paper, we first investigate the hybrid precoder design for cooperative multiuser massive MIMO systems. We propose hybrid precoding algorithms for two performance metrics: weighted sum rate and max-min fairness. We also propose a low complexity user pairing for both precoder designs. Numerical results show that the proposed hybrid precoding algorithms outperform existing hybrid precoding algorithms for non-cooperative transmissions, and perform closely compared with existing digital precoding algorithms for cooperative transmissions, when the number of users does not exceed the total number of RF chains of the BSs in cooperative (i.e., the largest possible channel rank). In summary, this paper provides a hybrid precoder design guideline for existing and developing cellular communication systems, including Long Term Evolution-Advanced and the fifth generation cellular systems.

—The integration of cooperative transmission into satellite networks is regarded as an effective strategy to increase the energy efficiency as well as the coverage of satellite communications. This paper investigates the performance of an amplifyand-forward (AF) hybrid satellite-terrestrial relay network (HSTRN), where the links of the two hops undergo Shadowed- Rician andRayleigh fadingdistributions, respectively.By assuming that a single antenna relay is used to assist the signal transmission between the multi-antenna satellite and multi-antenna mobile terminal, and multiple interferers corrupt both the relay and destination, we first obtain the equivalent end-to-end signal-to-interference-plus-noise ratio (SINR) of the system. Then, an approximate yet very accurate closed-form expression for the ergodic capacity of the HSTRN is derived. The analytical lower bound expressions are also obtained to efficiently evaluate the outage probability (OP) and average symbol error rate (ASER) of the system. Furthermore, the asymptotic OP and ASER expressions are developed at high signal-to-noise ratio (SNR) to reveal the achievable diversity order and array gain of the considered HSTRN. Finally, simulation results are provided to validate of the analytical results, and show the impact of various parameters on the system performance.

We consider the multi-user MIMO broadcast channel with $M$ single-antenna users and $N$ transmit antennas under the constraint that each antenna emits signals having constant envelope (CE). The motivation for this is that CE signals facilitate the use of power-efficient RF power amplifiers. Analytical and numerical results show that, under certain mild conditions on the channel gains, for a fixed $M$, array gain is achievable even under the stringent per-antenna CE constraint (essentially, for a fixed $M$, at sufficiently large $N$ the total transmitted power can be reduced with increasing $N$ while maintaining a fixed information rate to each user). Simulations for the i.i.d. Rayleigh fading channel show that the total transmit power can be reduced linearly with increasing $N$ (i.e., an O(N) array gain). We also propose a precoding scheme which finds near-optimal CE signals to be transmitted, and has O(MN) complexity. Also, in terms of the total transmit power required to achieve a fixed desired information sum-rate, despite the stringent per-antenna CE constraint, the proposed CE precoding scheme performs close to the sum-capacity achieving scheme for an average-only total transmit power constrained channel., Comment: Submitted to IEEE Transactions on Communications

We propose and analyze transmit antenna selection (TAS) to enhance physical layer security in a wiretap channel with NA antennas at the transmitter, NB antennas at the receiver, and NE antennas at the eavesdropper. We focus on the practical scenario where the transmitter does not have any channel state information (CSI) of the eavesdropper's channel. The transmitter selects a single antenna that maximizes the instantaneous signal-to-noise ratio (SNR) at the receiver. The receiver and the eavesdropper employ either maximal-ratio combining (MRC) or selection combining (SC) to combine the received signals. For the proposed protocols, we derive new closed-form expressions for the probability of non-zero secrecy capacity. We consider Nakagami-m fading with non-identical fading parameters of the main channel, mB, and of the eavesdropper's channel, mE. Next, we derive new closed-form expressions for the exact secrecy outage probability, based on which the e-outage secrecy capacity is characterized. Based on the exact expressions, we derive the asymptotic secrecy outage probability which accurately reveals the secrecy diversity order and the secrecy array gain. We confirm that the proposed protocols achieve identical secrecy diversity orders of NANBmB. An interesting conclusion is reached that this diversity order is independent of NE and mE. Furthermore, we prove that under the proposed protocols, the secrecy outage probability and the e-outage secrecy capacity improve with increasing NA.

A comprehensive performance analysis framework for dual-hop multiple-input multiple-output (MIMO) amplify-and-forward (AF) relay networks with hop-by-hop beamforming (i.e. both source and relay perform beamforming) is presented. The system performance degradation due to practical transmission impairments (i) feedback delays, (ii) channel estimation errors and (iii) spatially-correlated fading is quantified. To this end, closed-form expressions for the cumulative distribution function of the end-to-end signal-to-noise ratio, its moment generating function, the outage probability, and the average bit error rate (BER) are derived. The asymptotic high SNR approximations of the outage probability and average BER are derived to obtain valuable system-design insights such as the diversity order and array gain. In order to illustrate the usefulness of our analysis, four applications, which employ dual-hop MIMO relaying with hop-by-hop beamforming, are also presented and analyzed. Furthermore, our analyses are validated through Monte-Carlo simulations.

In this paper, we first derive an optimal precoder for amplify-and-forward (AF) multiple-antenna relay systems with single-antenna source and destination terminals by maximizing the output signal-to-noise ratio (SNR). Then, the resulting maximum SNR expression and its approximation at high transmission SNR are analyzed to obtain their statistical properties for independently identically distributed (i.i.d.) Rayleigh fading channels. Based on the properties of the approximate maximum SNR, the average symbol error probability (ASEP) is investigated, leading to an explicit diversity order and array gain. The ergodic achievable rate is also studied, giving a tight closed-form upper bound. The theoretical analysis is finally validated by Monte Carlo simulations.

We develop a unified framework for the symbol error rate (SER) of distributed transmit antenna selection with receiver maximal-ratio combining (TAS/MRC) in multiple-input multiple-output (MIMO) relay networks. We focus on nonregenerative relaying with NS, NR, and ND antennas at the source, relay, and destination, respectively. We consider the general fading scenario of Nakagami-m fading with distinct m fading parameters in the source-to-relay and the relay-to-destination links. We present new analytical expressions for the statistics of the end-to-end signal-to-noise ratio (SNR). Specifically, we derive exact expressions and first order expansions for the cumulative distribution function and moment generating function of the end-to-end SNR. Based on these, we derive new closed-form expressions for the asymptotic SER under M-ary phase-shift keying (M-PSK) and M-ary quadrature amplitude modulation (M-QAM). Our asymptotic solutions accurately identify the diversity order and the array gain as two key design components of the network.

In wireless mesh networks, it is desirable to utilize overlapping coverage of multiple parallel relays to assist the source-destination transmission. In this letter, we consider selection diversity (SD) to select the strongest link amongst the direct and N amplify-and-forward (AF) relay links. We derive new closed-form expressions for the symbol error rate (SER) in independent but not necessarily identically distributed (i.n.d.) Rayleigh fading relay channels. Our results are given as both lower bound and asymptotic expressions based on an accurate upper bound on the signal-to-noise ratio (SNR) of the relay links. Our asymptotic results provide key performance parameters such as the array gain and diversity order, which prove that a full N+1 diversity order is achieved. We show that SD can offer an array gain advantage over maximal-ratio combining which entails all the relays to transmit. Numerical results are shown to validate the analysis.

This paper provides a systematic characterization of Zero-Forcing (ZF) detectors over multiple-input multiple-output (MIMO) channels that experience both small and large-scale fading. In particular, we consider the generic K distribution (Rayleigh/gamma distribution) to model the composite fading fluctuations and also assume the general case of semi-correlated small-scale fading. In the following, novel exact analytical expressions for the achievable sum rate are derived, followed by asymptotic expressions in the high and low Signal-to-Noise ratio (SNR) regimes. In these limiting cases, two common and insightful affine expansions are studied followed by new, closed-form upper and lower bounds on the sum rate that remain tight for all SNRs. In the second part of the paper, we present exact tractable expressions along with first-order expansions for the symbol error rate (SER) and outage probability; we also quantify the performance of ZF detectors in terms of diversity order and array (or coding) gain. The implications of the model parameters on the ZF detector performance are investigated via Monte-Carlo simulations which also validate the theoretical analysis.

This paper investigates the symbol error rate (SER) performance of the multiple-input multiple-output (MIMO) multi-channel beamforming (MB) in the general double-scattering channel. We derive an asymptotic expansion on the marginal eigenvalue distribution of the MIMO channel matrix, and apply the result to get an approximate expression on the average SER at high signal-to-noise ratio (SNR). Two parameters pertaining to the SER, i.e., the diversity gain and the array gain, are analyzed. Our results show that it suffices for the double-scattering channel to have only limited scatterers, if the same diversity gain as the Rayleigh channel is desired; however, once the number of scatterers is below a certain level, the array gain in the double-scattering channel will vary with the SNR logarithmically.

This letter advocates the performance of a multiuser relay network (MRN) equipped with a single amplify-and-forward (AaF) relay over Rayleigh fading environments. We derive new expressions for the cumulative distribution function (CDF) of the highest instantaneous end-to-end signal-to-noise ratio (SNR) taking into consideration the two cases of fixed gain relays and variable gain relays. Relying on these statistical results, we derive new expressions for the outage probability and symbol error rate (SER), both of which are obtained in exact closed form. Furthermore, we derive simple asymptotic outage probability and SER. Our asymptotic results confirm that opportunistic scheduling has no impact on the diversity order. We further prove that the array gain is what determines the SNR advantage of opportunistic scheduling over the single user scenario.

This paper considers orthogonal space-time block coded transmission for a multiple-input multiple-output channel (MIMO) with non-coherent amplify-and-forward (AF) relaying in Rayleigh fading. We first characterize the statistical properties of the instantaneous signal-to-noise ratio (SNR) at the destination, by deriving new exact closed form expressions for the moment generating function, cumulants, and first and second moments. These results show a reciprocity relationship between the number of antennas at the relay and destination. The probability density function and cumulative distribution function of the SNR are also derived for certain system configurations, and for various asymptotic regimes. We then investigate the system performance by presenting new analytical expressions for the symbol error rate, outage probability, amount of fading, as well as the diversity order and array gain. Our results indicate that the proposed scheme can achieve the maximum diversity order of the non-coherent AF MIMO relay channel.

This paper analyzes the performance of multiuser optimum combining systems. We consider the practical scenario where the desired user undergoes Rician fading, and the received signals are corrupted by Rayleigh-faded interference and noise. We derive new closed-form expressions for the symbol error rate, ergodic capacity, level crossing rate, and average fade duration. These results are given as either accurate approximations or asymptotic (eg. high signal-to-noise ratio (SNR)) expressions, and are based on new closed-form statistical properties which we derive for the signal-to-interference noise ratio (SINR). Specifically, we derive exact first order expansions and accurate gamma approximations for the SINR distribution, as well as simplified exact expressions for the moments. We also present closed-form expressions for key performance parameters such as the diversity order and array gain, wideband slope, and high SNR power offset, and analyze the impact of the Rician K-factor, which is shown in all cases to yield a performance improvement.

This paper analyzes MIMO systems with multichannel beamforming in Ricean fading. Our results apply to a wide class of multichannel systems which transmit on the eigenmodes of the MIMO channel. We first present new closed-form expressions for the marginal ordered eigenvalue distributions of complex noncentral Wishart matrices. These are used to characterize the statistics of the signal to noise ratio (SNR) on each eigenmode. Based on this, we present exact symbol error rate (SER) expressions. We also derive closed-form expressions for the diversity order, array gain, and outage probability. We show that the global SER performance is dominated by the subchannel corresponding to the minimum channel singular value. We also show that, at low outage levels, the outage probability varies inversely with the Ricean K-factor for cases where transmission is only on the most dominant subchannel (i.e. a singlechannel beamforming system). Numerical results are presented to validate the theoretical analysis., Comment: 26 pages, 5 figures, to appear in IEEE Transactions on Communications

We develop a model for a large array ground receiver system for use in deep space communications, and analyze the resulting array channel capacity. The model includes effects of array geometry, time-dependent spacecraft orbital trajectory, point and extended interference sources, and elevation- dependent noise and atmospheric channel variations. Channel capacity is expressed as a simple quadratic form dependent upon covariance matrices characterizing the source, interference, and additive noise. This formulation facilitates inclusion of array and channel characteristics into the model, as well as comparison of optimal, suboptimal and equivalent single-antenna configurations on achievable throughput. Realistic examples of ground array channel capacity calculations are presented, demonstrating the impact of array geometry, planetary interference sources, and array combining algorithm design upon the achievable data throughput.

Multiple input multiple output (MIMO) relay networks are wireless communication systems comprising of multiple nodes, each of which is equipped with multiple antennas. Information theories have shown that using multiple nodes to simultaneously relay a message can improve the capacity of source-to-destination communications. In this paper, we propose new relaying schemes for MIMO relay networks. The major concept behind the proposed schemes is to transform each of the MIMO relay channels into an equivalent triangular channel with positive real diagonal entries. By doing so, the resultant MIMO relay channel can simultaneously offer both distributed array gain (diversity gain obtained among relay nodes) and intranode array gain (diversity gain realized by multiple antennas of individual relay node) while maintaining the maximum spatial multiplexing gain (number of parallel data pipes). Based on this concept, three relaying schemes are derived that perform QR decomposition and phase control. Numerical results confirm that at least one of the proposed schemes outperforms the amplify-and-forward and the zero-forcing relaying schemes under various conditions. Moreover, we show that ratios of noise power level at relay and destination node have a great impact on capacities.

In this paper, we analyze a multiple-input multiple-output (MIMO) array consisting of two circular microstrip antennas, designed to exploit pattern diversity. We analytically derive the spatial correlation coefficients of this array as a function of the mode excited, for realistic clustered MIMO channel models. We compare the performance of the circular patch array (CPA) against an array of two spaced dipoles. In particular, we compute a theoretical tradeoff to predict when the pattern diversity provided by the CPA is more effective than space diversity from the uniform linear array (ULA), based on the eigenvalues of the spatial correlation matrix. Through simulations, we show that CPAs yield better performance or satisfy more restrictive size constraints than ULAs in clustered MIMO channels, depending on the element spacing of the ULA. These results make the CPA an attractive solution for miniaturized MIMO arrays for portable devices or access points.

In this paper, we present a cross-layer analytical framework to jointly investigate antenna diversity and multiuser scheduling under the generalized Nakagami fading channels. We derive a unified capacity formula for the multiuser scheduling system with different multiple-input multiple-output antenna schemes, including: 1) selective transmission/selective combining (ST/SC); 2) maximum ratio transmission/maximum ratio combining (MRT/MRC); 3) ST/MRC; and 4) space-time block codes (STBC). Our analytical results lead to the following four observations regarding the interplay of multiuser scheduling and antenna diversity. First, the higher the Nakagami fading parameter, the lower the multiuser diversity gain for all the considered antenna schemes. Second, from the standpoint of multiuser scheduling, the multiple antennas with the ST/SC method can be viewed as virtual users to amplify multiuser diversity order. Third, the boosted array gain of the MRT/MRC scheme can compensate the detrimental impact of the reduced amount of fading gain on multiuser scheduling, thereby resulting in greater capacity than the ST/SC method. Last, employing the STBC scheme together with multiuser diversity may cause capacity loss due to the reduced amount of fading gain, but without the supplement of array gain.

Orthogonal space-time block codes (OSTBCs) can obtain full diversity advantage with a simple, but optimal, receiver. Unfortunately, OSTBCs lack in array gain compared with beamforming techniques and suffer a rate loss for more than two transmit antennas. One simple method for improving the array gain and adapting OSTBCs to any number of transmit antennas is antenna-subset selection, where the OSTBC is transmitted on a subset of the transmit antennas. In this letter, we analyze the symbol-error rate performance of antenna-subset selection combined with OSTBCs.

The assignment of interference power in the Numerical Results section of the paper entitled “Capacity of Large Array Receivers for Deep-Space Communications in the Presence of Interference” (IEEE Transactions on Communications, February 2008, pp. 194-200) is on a perantenna basis, whereas the received signal power is defined in terms of the entire array. The reason for this normalization is that the signal source is a distant spacecraft, hence appears as a point source to both the individual antenna elements and to the entire array. This means that the signal power remains constant over the entire spacecraft trajectory (ignoring atmospheric attenuation), hence a single value can be assigned for each plot. This however is not the case for interference power collected from nearby extended sources (such as Mars) that are resolved by the array, because the effective shape of the array beam is determined by the projection of the array layout onto the source direction vector, which is a function of time. Therefore, the interference power collected by the array varies over the spacecraft trajectory, but remains constant for the antenna elements that do not resolve the interference: hence it is more convenient to assign interference power on a perantenna basis. In particular, we should emphasize that in the text describing Fig. 2b in the Numerical Results section, the interference power per antenna is set equal to the source power over the array, hence the total interference power collected by the array is N times that of the signal power, where N is the number of antenna elements. Similarly, the summed interference power per antenna in Fig. 3a is nominally one fifth of the signal power. Although not discussed specifically in the text, this same normalization was used to compute the array capacity results of Figs. 4a and 4b.