Training-based Transmission Research Articles

Interleaved Training and Training-Based Transmission Design for Hybrid Massive Antenna Downlink

In this paper, we study the beam-based training design jointly with the transmission design for hybrid massive antenna single-user (SU) and multiple-user (MU) systems where outage probability is adopted as the performance measure. For SU systems, we propose an interleaved training design to concatenate the feedback and training procedures, thus making the training length adaptive to the channel realization. Exact analytical expressions are derived for the average training length and the outage probability of the proposed interleaved training. For MU systems, we propose a joint design for the beam-based interleaved training, beam assignment, and MU data transmissions. Two solutions for the beam assignment are provided with different complexity-performance tradeoff. Analytical results and simulations show that for both SU and MU systems, the proposed joint training and transmission designs achieve the same outage performance as the traditional full-training scheme but with significant saving in the training overhead.

Jamming Energy Allocation in Training-Based Multiple Access Systems

We consider the problem of jamming attack in a multiple access channel with training-based transmission. First, we derive upper and lower bounds on the maximum achievable ergodic sum-rate which explicitly shows the impact of jamming during both the training phase and the data transmission phase. Then, from the jammer's design perspective, we analytically find the optimal jamming energy allocation between the two phases that minimizes the derived bounds on the ergodic sum-rate. Numerical results demonstrate that the obtained optimal jamming design reduces the ergodic sum-rate of the legitimate users considerably in comparison to fixed power jamming.

On an Achievable Rate of Large Rayleigh Block-Fading MIMO Channels With No CSI

Training-based transmission over Rayleigh block-fading multiple-input multiple-output (MIMO) channels is investigated. As a training method a combination of a pilot-assisted scheme and a biased signaling scheme is considered. The achievable rates of successive decoding (SD) receivers based on the linear minimum mean-squared error (LMMSE) channel estimation are analyzed in the large-system limit, by using the replica method under the assumption of replica symmetry. It is shown that negligible pilot information is best in terms of the achievable rates of the SD receivers in the large-system limit. The obtained analytical formulas of the achievable rates can improve the existing lower bound on the capacity of the MIMO channel with no channel state information (CSI), derived by Hassibi and Hochwald, for all signal-to-noise ratios (SNRs). The comparison between the obtained bound and a high SNR approximation of the channel capacity, derived by Zheng and Tse, implies that the high SNR approximation is unreliable unless quite high SNR is considered. Energy efficiency in the low SNR regime is also investigated in terms of the power per information bit required for reliable communication. The required minimum power is shown to be achieved at a positive rate for the SD receiver with no CSI, whereas it is achieved in the zero-rate limit for the case of perfect CSI available at the receiver. Moreover, numerical simulations imply that the presented large-system analysis can provide a good approximation for not so large systems. The results in this paper imply that SD schemes can provide a significant performance gain in the low-to-moderate SNR regimes, compared to conventional receivers based on one-shot channel estimation.

Optimizing Training-Based Transmission Against Smart Jamming

We consider training-based transmissions over multiple-input-multiple-output (MIMO) fading channels in the presence of jamming. Each transmission block consists of a training phase and a data transmission phase. From an information-theoretic viewpoint, we study the optimal energy allocation between the two phases for both the legitimate user of the channel and the jammer. For a fixed jamming strategy, we derive a closed-form solution of the optimal transmit energy allocation for the legitimate user and show that the optimal training length is equal to the number of transmit antennas. On the other hand, if the jammer has optimized its strategy, the best choice for the training length is shown to be larger than the number of transmit antennas and approaches half of the block length at low signal-to-jamming-and-noise ratio (SJNR). From the jammer's perspective, we derive closed-form solutions of the optimal jamming energy allocation. Numerical results demonstrate 30%-50% performance gains by using optimal designs in various scenarios. We also model the energy allocation problem as a zero-sum game and prove the existence and uniqueness of the Nash equilibrium when the training length is fixed. Furthermore, we extend our analysis to the case where the channel state information (CSI) is available at the transmitter. We show that many results found for systems with no transmitter CSI are also valid for systems with full transmitter CSI.

On the Capacity of Frequency-Selective Channels in Training-Based Transmission Schemes

Communication systems transmitting over frequency-selective channels generally employ an equalizer to recover the transmitted sequence corrupted by intersymbol interference (ISI). Most practical systems use a training sequence to learn the channel impulse response and thereby design the equalizer. An important issue is determining the optimal amount of training: too little training and the channel is not learned properly, too much training and there is not enough time available to transmit data before the channel changes and must be learned anew. We use an information-theoretic approach to find the optimal parameters in training-based transmission schemes for channels described by a block-fading model. The optimal length of the training interval is found by maximizing a lower bound on the training-based channel capacity. When the transmitter is capable of providing two distinct transmission power levels (one for training and one for data transmission), the optimal length of the training interval is shown to be equal to the length of the channel. Further, we show that at high SNR, training-based schemes achieve the capacity of block-fading frequency selective channels, whereas at low SNR, they are highly suboptimal.