Antenna Selection in Interference-Constrained Underlay Cognitive Radios: SEP-Optimal Rule and Performance Benchmarking

In the underlay mode of cognitive radio, secondary users are allowed to transmit when the primary is transmitting, but under tight interference constraints that protect the primary. However, these constraints limit the secondary system performance. Antenna selection (AS)-based multiple antenna techniques, which exploit spatial diversity with less hardware, help improve secondary system performance. We develop a novel and optimal transmit AS rule that minimizes the symbol error probability (SEP) of an average interference-constrained multiple-input-single-output secondary system that operates in the underlay mode. We show that the optimal rule is a non-linear function of the power gain of the channel from the secondary transmit antenna to the primary receiver and from the secondary transmit antenna to the secondary receive antenna. We also propose a simpler, tractable variant of the optimal rule that performs as well as the optimal rule. We then analyze its SEP with L transmit antennas, and extensively benchmark it with several heuristic selection rules proposed in the literature. We also enhance these rules in order to provide a fair comparison, and derive new expressions for their SEPs. The results bring out new inter-relationships between the various rules, and show that the optimal rule can significantly reduce the SEP.

Antenna selection in spatial modulation systems

Novel transmit antenna selection techniques are conceived for Spatial Modulation (SM) systems and their symbol error rate (SER) performance is investigated. Specifically, low-complexity Euclidean Distance optimized Antenna Selection (EDAS) and Capacity Optimized Antenna Selection (COAS) are studied. It is observed that the COAS scheme gives a better SER performance than the EDAS scheme. We show that the proposed antenna selection based SM systems are capable of attaining a significant gain in signal-to-noise ratio (SNR) compared to conventional SM systems, and also outperform the conventional MIMO systems employing antenna selection at both low and medium SNRs.

Channel training signal design for reciprocal multiple antenna systems with beamforming

Fast and efficient channel estimation is key to achieving high data rate performance in mobile and vehicular communication systems, where the channel is fast time-varying. To this end, this work proposes and optimizes channel-dependent training schemes for reciprocal Multiple-Input Multiple-Output (MIMO) channels with beamforming (BF) at the transmitter and receiver. First, assuming that Channel State Information (CSI) is available at the receiver, a channel-dependent Reverse Channel Training (RCT) signal is proposed that enables efficient estimation of the BF vector at the transmitter with a minimum training duration of only one symbol. In contrast, conventional orthogonal training requires a minimum training duration equal to the number of receive antennas. A tight approximation to the capacity lower bound on the system is derived, which is used as a performance metric to optimize the parameters of the RCT. Next, assuming that CSI is available at the transmitter, a channel-dependent forward-link training signal is proposed and its power and duration are optimized with respect to an approximate capacity lower bound. Monte Carlo simulations illustrate the significant performance improvement offered by the proposed channel-dependent training schemes over the existing channel-agnostic orthogonal training schemes.

Training for Antenna Selection in Time-Varying Channels: Optimal Selection, Energy Allocation, and Energy Efficiency Evaluation

Single receive antenna selection (AS) is a popular method for obtaining diversity benefits without the additional costs of multiple radio receiver chains. Since only one antenna receives at any time, the transmitter sends a pilot multiple times to enable the receiver to estimate the channel gains of its N antennas to the transmitter and select an antenna. In time-varying channels, the channel estimates of different antennas are outdated to different extents. We analyze the symbol error probability (SEP) in time-varying channels of the N-pilot and (N+1)-pilot AS training schemes. In the former, the transmitter sends one pilot for each receive antenna. In the latter, the transmitter sends one additional pilot that helps sample the channel fading process of the selected antenna twice. We present several new results about the SEP, optimal energy allocation across pilots and data, and optimal selection rule in time-varying channels for the two schemes. We show that due to the unique nature of AS, the (N+1)-pilot scheme, despite its longer training duration, is much more energy-efficient than the conventional N-pilot scheme. An extension to a practical scenario where all data symbols of a packet are received by the same antenna is also investigated.

Joint Antenna Selection and Frequency-Domain Scheduling in OFDMA Systems with Imperfect Estimates from Dual Pilot Training Scheme

Transmit antenna selection (AS) has been adopted in contemporary wideband wireless standards such as Long Term Evolution (LTE). We analyze a comprehensive new model for AS that captures several key features about its operation in wideband orthogonal frequency division multiple access (OFDMA) systems. These include the use of channel-aware frequency-domain scheduling (FDS) in conjunction with AS, the hardware constraint that a user must transmit using the same antenna over all its assigned subcarriers, and the scheduling constraint that the subcarriers assigned to a user must be contiguous. The model also captures the novel dual pilot training scheme that is used in LTE, in which a coarse system bandwidth-wide sounding reference signal is used to acquire relatively noisy channel state information (CSI) for AS and FDS, and a dense narrow-band demodulation reference signal is used to acquire accurate CSI for data demodulation. We analyze the symbol error probability when AS is done in conjunction with the channel-unaware, but fair, round-robin scheduling and with channel-aware greedy FDS. Our results quantify how effective joint AS-FDS is in dispersive environments, the interactions between the above features, and the ability of the user to lower SRS power with minimal performance degradation.

A Markov Decision Theoretic Approach to Pilot Allocation and Receive Antenna Selection

This paper considers antenna selection (AS) at a receiver equipped with multiple antenna elements but only a single radio frequency chain for packet reception. As information about the channel state is acquired using training symbols (pilots), the receiver makes its AS decisions based on noisy channel estimates. Additional information that can be exploited for AS includes the time-correlation of the wireless channel and the results of the link-layer error checks upon receiving the data packets. In this scenario, the task of the receiver is to sequentially select (a) the pilot symbol allocation, i.e., how to distribute the available pilot symbols among the antenna elements, for channel estimation on each of the receive antennas; and (b) the antenna to be used for data packet reception. The goal is to maximize the expected throughput, based on the past history of allocation and selection decisions, and the corresponding noisy channel estimates and error check results. Since the channel state is only partially observed through the noisy pilots and the error checks, the joint problem of pilot allocation and AS is modeled as a partially observed Markov decision process (POMDP). The solution to the POMDP yields the policy that maximizes the long-term expected throughput. Using the Finite State Markov Chain (FSMC) model for the wireless channel, the performance of the POMDP solution is compared with that of other existing schemes, and it is illustrated through numerical evaluation that the POMDP solution significantly outperforms them.

SEP-optimal antenna selection for average interference constrained underlay cognitive radios

In the underlay mode of cognitive radio, secondary users can transmit when the primary is transmitting, but under tight interference constraints, which limit the secondary system performance. Antenna selection (AS)-based multiple antenna techniques, which require less hardware and yet exploit spatial diversity, help improve the secondary system performance. In this paper, we develop the optimal transmit AS rule that minimizes the symbol error probability (SEP) of an average interference-constrained secondary system that operates in the underlay mode. We show that the optimal rule is a non-linear function of the power gains of the channels from secondary transmit antenna to primary receiver and secondary transmit antenna to secondary receive antenna. The optimal rule is different from the several ad hoc rules that have been proposed in the literature. We also propose a closed-form, tractable variant of the optimal rule and analyze its SEP. Several results are presented to compare the performance of the closed-form rule with the ad hoc rules, and interesting inter-relationships among them are brought out.

Multi-port network modeling of stub loaded Microstrip ring antenna for dual-band operations

A square ring microstrip antenna can be modified for dual-band operations by appropriately attaching an open ended stub. The input impedance of this antenna is analyzed here using multi-port network modeling (MNM) approach. The coupled feed is included by defining additional terms in the model. A prototype antenna is fabricated and tested to validate these computations.

Optimal Joint Antenna Selection and Power Adaptation in Underlay Cognitive Radios

Transmit antenna selection (AS) is a popular, low hardware complexity technique that improves the performance of an underlay cognitive radio system, in which a secondary transmitter can transmit when the primary is on but under tight constraints on the interference it causes to the primary. The underlay interference constraint fundamentally changes the criterion used to select the antenna because the channel gains to the secondary and primary receivers must be both taken into account. We develop a novel and optimal joint AS and transmit power adaptation policy that minimizes a Chernoff upper bound on the symbol error probability (SEP) at the secondary receiver subject to an average transmit power constraint and an average primary interference constraint. Explicit expressions for the optimal antenna and power are provided in terms of the channel gains to the primary and secondary receivers. The SEP of the optimal policy is at least an order of magnitude lower than that achieved by several ad hoc selection rules proposed in the literature and even the optimal antenna selection rule for the case where the transmit power is either zero or a fixed value.

Antenna selection for time-varying channels based on slepian subspace projections

Single receive antenna selection (AS) allows single-input single-output (SISO) systems to retain the diversity benefits of multiple antennas with minimum hardware costs. We propose a single receive AS method for time-varying channels, in which practical limitations imposed by next-generation wireless standards such as training, packetization and antenna switching time are taken into account. The proposed method utilizes low-complexity subspace projection techniques spanned by discrete prolate spheroidal (DPS) sequences. It only uses Doppler bandwidth knowledge, and does not need detailed correlation knowledge. Results show that the proposed AS method outperforms ideal conventional SISO systems with perfect CSI but no AS at the receiver and AS using the conventional Fourier estimation/prediction method. A closed-form expression for the symbol error probability (SEP) of phase-shift keying (MPSK) with symbol-by-symbol receive AS is derived.

Using an Office Inkjet Printer to Define the Formation of Copper Films on Paper

A low-cost fabrication process for forming conductive copper lines on paper is presented. An office inkjet printer was used to deposit desired patterns of silver nitrate and tannic acid solutions sequentially on paper. Silver nitrate was instantaneously reduced in situ on paper by tannic acid at room temperature to form silver nanoparticles, which acted as catalysts for the subsequent electroless deposition of copper. The copper films were 1.8 mu m thick, and the sheet resistance of the copper film on paper was 9 Omega/square. A dual monopole ultrawide band antenna was fabricated on paper and its performance was equivalent to that of a similar antenna fabricated on a copper-film covered Kapton substrate using conventional lithographic processes. The paper-based conductive copper films fabricated using the facile process presented herein will aid the development of low-cost flexible circuits and sensors.

Antenna Selection with Power Adaptation in Interference-Constrained Cognitive Radios

The performance of an underlay cognitive radio (CR) system, which can transmit when the primary is on, is curtailed by tight constraints on the interference it can cause to the primary receiver. Transmit antenna selection (AS) improves the performance of underlay CR by exploiting spatial diversity but with less hardware. However, the selected antenna and its transmit power now both depend on the channel gains to the secondary and primary receivers. We develop a novel Chernoffbound based optimal AS and power adaptation (CBBOASPA) policy that minimizes an upper bound on the symbol error probability (SEP) at the secondary receiver, subject to constraints on the average transmit power and the average interference to the primary. The optimal antenna and its power are presented in an insightful closed form in terms of the channel gains. We then analyze the SEP of CBBOASPA. Extensive benchmarking shows that the SEP of CBBOASPA for both MPSK and MQAM is one to two orders of magnitude lower than several ad hoc AS policies and even optimal AS with on-off power control.

An Eigen Approach to Transmit Beamforming in Wireless Networks With Single Antenna Receivers

In this paper, we propose an eigen framework for transmit beamforming for single-hop and dual-hop network models with single antenna receivers. In cases where number of receivers is not more than three, the proposed Eigen approach is vastly superior in terms of ease of implementation and computational complexity compared with the existing convex-relaxation-based approaches. The essential premise is that the precoding problems can be posed as equivalent optimization problems of searching for an optimal vector in the joint numerical range of Hermitian matrices. We show that the latter problem has two convex approximations: the first one is a semi-definite program that yields a lower bound on the solution, and the second one is a linear matrix inequality that yields an upper bound on the solution. We study the performance of the proposed and existing techniques using numerical simulations.

Quantifying the Transmit Diversity Order of Euclidean Distance Based Antenna Selection in Spatial Modulation

In this letter, we quantify the transmit diversity order of the SM system operating in a closed-loop scenario. Specifically, the SM system relying on Euclidean distance based antenna subset selection (EDAS) is considered and the achievable diversity gain is evaluated. Furthermore, the resultant trade-off between the achievable diversity gain and switching gain is studied. Simulation results confirm our theoretical results. Specifically, at a symbol error rate of about 10(-4) the signal-to-noise ratio gain achieved by EDAS is about 7 dB in case of 16-QAM and about 5 dB in case of 64-QAM.

Training-Based Antenna Selection for PER Minimization: A POMDP Approach

This paper considers the problem of receive antenna selection (AS) in a multiple-antenna communication system having a single radio-frequency (RF) chain. The AS decisions are based on noisy channel estimates obtained using known pilot symbols embedded in the data packets. The goal here is to minimize the average packet error rate (PER) by exploiting the known temporal correlation of the channel. As the underlying channels are only partially observed using the pilot symbols, the problem of AS for PER minimization is cast into a partially observable Markov decision process (POMDP) framework. Under mild assumptions, the optimality of a myopic policy is established for the two-state channel case. Moreover, two heuristic AS schemes are proposed based on a weighted combination of the estimated channel states on the different antennas. These schemes utilize the continuous valued received pilot symbols to make the AS decisions, and are shown to offer performance comparable to the POMDP approach, which requires one to quantize the channel and observations to a finite set of states. The performance improvement offered by the POMDP solution and the proposed heuristic solutions relative to existing AS training-based approaches is illustrated using Monte Carlo simulations.