Performance analysis of MIMO beamforming with imperfect feedback

Orthogonal frequency-division multiple access (OFDMA) systems divide the available bandwidth into orthogonal subchannels and exploit multiuser diversity and frequency selectivity to achieve high spectral efficiencies. However, they require a significant amount of channel state feedback for scheduling and rate adaptation and are sensitive to feedback delays. We develop a comprehensive analysis for OFDMA system throughput in the presence of feedback delays as a function of the feedback scheme, frequency-domain scheduler, and rate adaptation rule. Also derived are expressions for the outage probability, which captures the inability of a subchannel to successfully carry data due to the feedback scheme or feedback delays. Our model encompasses the popular best- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> and threshold-based feedback schemes and the greedy, proportional fair, and round-robin schedulers that cover a wide range of throughput versus fairness tradeoff. It helps quantify the different robustness of the schedulers to feedback overhead and delays. Even at low vehicular speeds, it shows that small feedback delays markedly degrade the throughput and increase the outage probability. Further, given the feedback delay, the throughput degradation depends primarily on the feedback overhead and not on the feedback scheme itself. We also show how to optimize the rate adaptation thresholds as a function of feedback delay.

We study a practical version of the broadcast channel (BC) where the channel state information at the transmitter (CSIT) is available only for some of the users, dubbing the system as mixed CSIT. We start with the simplest instance of such a heterogeneous BC where a multi-antenna transmitter base-station (BS) is trying to communicate data to two single-antenna user equipments (UE), having the perfect CSIT about UE1 and no CSIT about UE2. We propose a very simple transmission strategy at the BS for such a system and compare its performance with the interference alignment solution proposed elsewhere which achieves full degrees-of-freedom (DOF) when channel coherence lengths and switching instants abide by certain restrictions. Then with an additional receive antenna granted to UE2 (whose CSIT is not available) and keeping the same CSIT perspective, achievable rates for two users are derived and compared with earlier schemes. Analytical and simulation results show that this additional receive antenna brings significant gains in the system with the same transmission strategy and without any extra requirement of channel training or feedback.

In this paper, we investigate the ergodic performance of rate-splitting multiple access (RSMA) with finite blocklength (FBL) in high mobility communication systems to meet the ultra-reliable and low-latency (URLLC) requirements. Considering the imperfect channel state information at the transmitter (CSIT) originating from the high mobility of vehicles and the time delay of channel feedback, we analyze the statistical properties of signal-to-interference-plus-noise ratios (SINRs) for common and private streams at the desired vehicle. Next, we derive the closed-form expression for the ergodic sum-rate in FBL RSMA systems considering an arbitrary number of transmit antennas, number of vehicles, vehicle speeds, blocklengths, and block error rates (BLERs). Compared to other benchmarks, such as FBL non-orthogonal multiple access (NOMA) and space division multiple access (SDMA), the proposed scheme holds its optimum performance to meet the stringent BLER requirement while maintaining a prominent reduction in blocklength.

This paper presents capacity limits of novel position aware adaptive cellular communication systems exploiting channel state information (CSI) at the transmitter (CSIT). The position aware adaptive communication systems are benchmarked against state-of-the-art adaptive modulation and coding (AMC) systems that use only feedback or predict CSIT in addition to the feedback CSI. We analyze the position aware adaptive communication systems both with perfect and imperfect position information. Numerical results demonstrate that position aware adaptive systems operate close to the channel capacity over a large range of feedback delays and channel variability with perfect position information. Further, position aware adaptive communication systems can outperform state-of-the-art AMC systems for Gaussian distributed position errors with standard deviations smaller than 2.5 m by more than 0.6 bits/s/Hz.

In this paper, we analyze the performance of a dual-hop system with partial relay selection and feedback delay over Nakagami-m fading channels in the presence of multiple identical interferers at the destination. Based on the new closed-form expressions for the cumulative distribution function of the effective signal-to-interference plus noise ratio, we present closed-form expressions for the outage probability and average symbol error rate (SER) for both fixed and CSI-assisted gain relaying systems. To gain further insights, the asymptotic outage probability and average symbol error rates at the high signal to noise ratio regimes are examined. Our results reveal that increasing the number of relays does not provide any extra diversity gain due to the presence of the feedback delay. Specifically, we show that feedback delay as well as CCI only affect the coding gain of the system. The accuracy of the analytical results are supported Monte-Carlo simulations.

Average packet error probability (PEP) is an important error statistic for wireless communication system designers. In this paper, we address the problem of analytically quantifying the effect of channel estimation errors, feedback delay and channel vector quantization on the PEP of transmit beamforming multiple-input-single-output (MISO) systems in a spatially independent slow-fading wireless channel environment. We develop an accurate characterization of estimation errors as well as errors due to feedback delay, and tools relevant for deriving analytical expressions for the PEP. The modeling highlights the distinction between errors that arise due to channel estimation from those that arise due to feedback delay and represents an important departure from past work. Analytical expressions are derived for the PEP with BPSK signaling. The derived approximated closed-form analytical expression is complemented by simulations.

본 논문에서는 시변 다중 입출력 (multiple-input multiple-output) 방송(broadcast) 채널에서 피드백 양자화와 지연을 고려한 협력 빔형성 (coordinated beamforming: CBF) 시스템을 제안한다. 다중 데이터 스트림을 전송하는 CBF 시스템에 피드백 양자화 기법을 적용하고, 구현 복잡도와 피드백 오버헤드 측면에서 효율적인 CBF 시스템을 제시한다. 또한, 실제적인 무선통신 환경에서 발생하는 피드백 지연에 의한 오류를 최소화하기 위하여 사용자 단말에 선형 채널 예측기를 적용한다. 선형 예측기로 Wiener 필터를 이용하여 피드백 지연시간 후의 미래 채널을 예측하교 이를 토대로 피드백 정보를 생성함으로써 지연된 피드백 정보를 이용하는 CBF 시스템의 성능을 향상시킨다. 모의실험을 통해 다양한 도플러 (Doppler) 주파수의 MIMO 방송 채널에서 양자화와 Wiener 필터를 적용한 CBF 시스템의 향상된 심볼 오율과 합 전송률 성능을 확인한다. In this paper we propose a coordinated beamforming(CBF) scheme considering the effects of feedback quantization and delay in time-varying multiple-input multiple-output(MIMO) broadcast channels. By equal power allocation per data stream, the proposed CBF scheme transmits multiple data streams per user terminals without additional feedback overhead when quantized feedback information is used. The proposed CBF scheme also applies a linear channel predictor to each user terminals to prevent errors due to feedback delays that are not evitable in practical wireless systems. Each user terminal utilizes Wiener filter to predict future channel responses and generates feedback information based on the predicted channels. Consequently the proposed CBF scheme adapting Wiener filter improves system performances compared with the conventional scheme using delayed feedback.

We consider the block diagonalization (BD) and user selection based on limited feedback in multiple antenna broadcast channels. With limited feedback, due to the imperfect channel state information at the transmitter (CSIT), BD cannot completely eliminate multiuser interference, and the throughput is correspondingly lower than that achieved with perfect CSIT. Nevertheless, the achievable multiuser diversity gain can be the same, such that limited-feedback-based BD can achieve an optimal throughput growth as the number of users increases. To show this, we first propose a channel quality indicator (CQI) for user selection. The CQI is designed to accurately estimate an achievable rate of each user and is given by an expected rate, where the expectation is solely taken over precoding matrices which cannot be known at the feedback stage. With the proper CQI, user selection can benefit from a large number of users in the system. As a result, we show that the BD can achieve an asymptotically optimal growth in throughput with the proposed CQI, based solely on a finite-rate feedback of channel information.

Multicell cooperative processing (MCP) can overcome the detrimental effects of inter-cell interference (ICI). However, since mobile terminals (MTs) need to estimate and feed back channel state information (CSI) related to several cooperative base stations (BSs), reductions in CSI feedback overhead and delay are more demanding in MCP enabled networks. In this paper, a novel overlaid-pilot based CSI feedback scheme for multicell cooperative networks is proposed. MTs directly overlay the received downlink pilot data of all the cooperative BSs on the uplink pilot data and then broadcast it to the cooperative BSs. Each cooperative BS can recover multiple CSIs from the overlaid pilot by a presented overlaid-pilot based channel estimation algorithm. Because the overlaid pilot is fed back on the uplink pilot channel, no extra uplink channel is occupied and the downlink CSI feedback process is with zero-overhead regardless of the number of cooperative BSs. In addition, as it just needs one broadcast to feed back multiple CSIs to BSs, the feedback delay is decreased significantly. Numerical simulations show that the performance of the proposed CSI feedback scheme outperforms the traditional feedback scheme.

Recent information theoretic results suggest that precoding on the multi-user downlink MIMO channel with delayed channel state information at the transmitter (CSIT) could lead to data rates much beyond the ones obtained without any CSIT, even in extreme situations when the delayed channel feedback is made totally obsolete by a feedback delay exceeding the channel coherence time. This surprising result is based on the ideas of interference forwarding and alignment which allow the receivers to reconstruct an information allowing them to cancel out the interference completely, making it an optimal scheme in the infinite SNR regime. In this paper, we formulate a similar problem, yet at finite SNR. We propose a new construction for the precoder which matches the previous results at infinite SNR yet reaches a useful tradeoff between interference alignment and signal enhancement at finite SNR, allowing for significant performance improvements in practical settings.

In this paper, we consider MIMO beamforming in the presence of Rayleigh product channels. Based on a derived largest eigenvalue distribution, the key performance metrics of the beamforming system are obtained, assuming perfect channel knowledge at the transmitter and receiver. Using the closed-form expressions, we gain insights into the behavior of MIMO beamforming systems in scenarios of practical interest.

In this paper, the effect of feedback delay and channel gain difference (CGD) on the performance of distributed transmit diversity (DTD) systems are analyzed over Rayleigh fading channels. We derive new expressions for the average error rate of DTD in the absence of receiver phase compensation (RPC), which is useful for a large number of modulation schemes. Furthermore, we analyze the effect of feedback delay and CGD on DTD compared to spatially correlated co-located transmit diversity (CTD) systems. Analytical results enable us to verify the fact that in DTD without RPC as CGD between antennas increases the performance degrades. Via extensive performance evaluations for various cases, we quantitatively analyze the sensitivity of the performance gap between CTD and DTD in absence of RPC according to feedback delay. The results show that, in without RPC case DTD is robust to feedback delay compared to correlated CTD. We also present Monte Carlo simulation results as verification of our analytical results.

Link adaptation allows the transmitter to adapt to changing channel conditions. Critical to the design of link adaptation is the accuracy of channel state information at the transmitter. In this paper, we investigate the effect of imperfect channel state information and feedback delay on the performance of a multiple-input multiple-output zero-forcing receiver with adaptive power allocation. A closed-form approximate upper bound on bit error rate is derived for M-ary phase shift keying and M-ary quadrature amplitude modulation and it is valid for arbitrary numbers of transmit and receive antennas. Comparison with Monte Carlo simulations is also provided, showing that the results derived from this analytical bound are useful for system design

In our earlier work, we described an optimization problem and corresponding scheduling algorithm aimed at obtaining maximum throughput guarantees in wireless networks. To further improve the short-term performance, we also proposed two adaptive versions of the optimal algorithm. Results from the simulations showed that the adaptive algorithms perform significantly better than other well-known scheduling algorithms in networks based on Mobile WiMAX, HSDPA, LTE and WINNER I. However, there were several idealistic assumptions in that analysis, the most important of which is that each user estimates its carrier-to-noise ratio (CNR) perfectly, and there is no feedback delay. In practice however, the channel estimation is not perfect, and there is always some delay in the feedback channel. In this paper, we assume that a maximum a posteriori (MAP) predictor is employed for the CNR, so that the system takes the feedback delay and the channel noise into account. We then investigate the effect of imperfect channel prediction and delay on the throughput guarantees promised to all the users in the wireless network. A procedure to reduce the probability of outage in case of imperfect channel prediction is also proposed.

In this study, the bit error rate (BER) performance of multiple-input-multiple-output (MIMO) hierarchical quadrature amplitude modulation systems employing maximum ratio transmission (MRT-HQAM) is investigated under the effects of imperfect channel state information (ICSI) due to the channel estimation error and feedback delay. Theoretical expressions for the BER performance of the MRT-HQAM systems are derived using the two common ICSI models that exist in the current literature, specifically when studying the MIMO beam-forming systems with ICSI, where the error term due to the ICSI is assumed to contribute to either the noise component or to the signal component. The BER results for the two ICSI models are presented and then compared. In addition, various antenna configurations are studied to illustrate the performance gains achievable with additional antennas, and to identify the ideal antenna configuration for a given number of antennas. Moreover, the hierarchical modulation parameter is varied to determine the varying levels of sensitivity of the hierarchical layers in the presence of ICSI. The theoretical BER expressions provided for both ICSI models are verified by simulation results.