Quantized Equal Gain Transmission Research Articles

On the Power Amplifier Nonlinearity in MIMO Transmit Beamforming Systems

In this paper, single-carrier multiple-input multiple-output (MIMO) transmit beamforming (TB) systems in the presence of high-power amplifier (HPA) nonlinearity are investigated. Specifically, due to the suboptimality of the conventional maximal ratio transmission/maximal ratio combining (MRT/MRC) under HPA nonlinearity, we propose the optimal TB scheme with the optimal beamforming weight vector and combining vector, for MIMO systems with nonlinear HPAs. Moreover, an alternative suboptimal but much simpler TB scheme, namely, quantized equal gain transmission (QEGT), is proposed. The latter profits from the property that the elements of the beamforming weight vector have the same constant modulus. The performance of the proposed optimal TB scheme and QEGT/MRC technique in the presence of the HPA nonlinearity is evaluated in terms of the average symbol error probability and mutual information with the Gaussian input, considering the transmission over uncorrelated quasi-static frequency-flat Rayleigh fading channels. Numerical results are provided and show the effects on the performance of several system parameters, namely, the HPA parameters, numbers of antennas, quadrature amplitude modulation modulation order, number of pilot symbols, and cardinality of the beamforming weight vector codebook for QEGT.

다중 안테나 시스템에서 양자화된 동 이득 전송 기법의 코드북 검색 복잡도 감쇄 기법

Reduced complexity codebook searching for Quantized Equal Gain Transmission(QEGT) is proposed over MIMO-OFDM systems. QEGT codebook is divided into M groups of Q index members. Each group has a representative index. At the 1st stage only the representative indices are searched then the best index is selected. At the 2nd stage the optimum index is determined only among the group of the selected representative index. This strategy reduces the overall index search algorithm comparing to the conventional methods. Monte-Carlo simulation shows that the searching complexity is reduced, but the link-level performance is still almost the same as the conventional methods when the number of transmission antennas are 3 to 7.

On MIMO beamforming systems using quantized feedback

We propose the Hadamard matrix as a codebook for multiple-input multiple-output (MIMO) beamforming systems, and show that a quantized equal gain transmission (QEGT) scheme using the Hadamard codebook has the same symbol error probability performance as a receiver selection diversity combining scheme operating in independent generalized Rayleigh fading channels. We show that a MIMO beamforming system using quantized feedback over Rician fading channels can be analyzed by considering a corresponding receiver selection combining scheme operating in single-input multiple-output (SIMO) systems over correlated generalized Rician fading channels. Also, we propose a greedy cophasing scheme for MIMO beamforming systems using quantized feedback. The greedy cophasing scheme provides 3.2 dB power gain over an orthogonal space-time block code when the number of transmit antennas is four, the number of receive antennas is one, and the number of feedback bits is three.

MISO 빔포밍 시스템에서 효율적인 QEGT 코드북 탐색 기법

본 논문은 Rayleigh 플랫 페이딩 채널에서 MISO 빔포밍 시스템의 효율적인 양자화된 동 이득 전송 코드북 인덱스 탐색 기법을 제안한다. 코드북의 사이즈가 선형적으로 증가함에 따라 비트 오율 성능은 증가하지만, 최적의 가중치 벡터를 찾는 시간은 지수적으로 증가한다. 따라서 본 논문에서 새로운 간단한 메트릭을 이용하여 2개에서 5개의 후보 벡터들만 찾아내는 빠른 탐색 기법을 제안한다. 후보 벡터들에는 기존의 정확한 탐색 기법을 적용하여 최적의 벡터를 찾아낸다. 제안하는 기법은 전반적인 탐색 시간을 줄이면서도 비트 오율에는 거의 영향을 주지 않는다. 더욱이 코드북의 사이즈가 증가함에 따라 탐색 시간도 기존의 기법에 비해 매우 감소된다. This paper presents an efficient Quantized Equal Gain Transmission(QEGT) codebook index searching technique for MISO beamforming system in a Rayleigh flat fading channel. The searching time for the optimum weight vector among the codebook vectors increases exponentially when the codebook size increases linearly, although the bit error rate decreases. So, newly defined simple metric is proposed for fast searching, which determines a few candidates. Then the conventional method combined with accurate search algorithm selects the optimal index. This strategy significantly reduces the overall search time, while maintaining almost the same bit error rate performance. Furthermore, as the codebook size increases, the search time is considerably decreased compared to that of the conventional approach.

Quantization Methods for Equal Gain Transmission With Finite Rate Feedback

We consider the design and analysis of quantizers for equal gain transmission (EGT) systems with finite rate feedback-based communication in flat-fading multiple input single output (MISO) systems. EGT is a beamforming technique that maximizes the MISO channel capacity when there is an equal power-per-antenna constraint at the transmitter, and requires the feedback of t-1 phase angles, when there are t antennas at the transmitter. In this paper, we contrast two popular approaches for quantizing the phase angles: vector quantization (VQ) and scalar quantization (SQ). On the VQ side, using the capacity loss with respect to EGT with perfect channel information at transmitter as performance metric, we develop a criterion for designing the beamforming codebook for quantized EGT (Q-EGT). We also propose an iterative algorithm based on the well-known generalized Lloyd algorithm, for computing the beamforming vector codebook. On the analytical side, we study the performance of Q-EGT and derive closed-form expressions for the performance in terms of capacity loss and outage probability in the case of i.i.d. Rayleigh flat-fading channels. On the SQ side, assuming uniform scalar quantization and i.i.d. Rayleigh flat-fading channels, we derive the high-resolution performance of quantized EGT and contrast the performance with that of VQ. We find that although both VQ and SQ achieve the same rate of convergence (to the capacity with perfect feedback) as the number of feedback bits B increases, there exists a fixed gap between the two