Analysis of Adaptive Modulation with Antenna Selection under Channel Prediction Errors Shiva Prakash, Student Member, IEEE, Ian McLoughlin, Senior Member, IEEE Abstract—The performance of an adaptive modulation system in Rayleigh fading channels exploiting spatial diversity through transmit antenna selection is analysed for the case of delay constrained networks. The system combines maximal ratio com- bining at the receiver and a transmit antenna selection system which switches between available antennas and modulation schemes at the transmitter. In a practical system, a delay between the channel being sampled at the receiver and acted upon by the transmitter will tend to degrade system performance. In this paper, a channel prediction scheme is employed at the receiver to provide estimates of future best transmission states, which includes selecting the best transmission antenna as well as the best supported M-QAM modulation scheme. The Shannon capacity for optimal rate and constant power is derived and presented, and used as a benchmark to evaluate the spectral efficiency of the discrete rate system optimised for instantaneous BER (bit error rate) and constant power constraint. I. I NTRODUCTION By exploiting spatial diversity, MIMO (Multiple input mul- tiple output) technology has been shown to provide capacity gain without incurring power or bandwidth cost [1]. Further gains can be achieved by adapting to the varying channel fluctuations, by adjusting parameters such as constellation size, transmit power and code rate to match changes in the channel [2], [3], [4], [5]. However, the performance of adaptive modulated schemes is limited by CSI (channel state information) imperfections particularly in the form of delay in the feedback channel, which causes outdated channel infor- mation at the transmitter, thus reducing capacity. The use of imperfect channel estimates for SISO channels is investigated in [6], [7] while the effect of feed back delay in adaptive modulation (AM) systems over a Nakagami fading SISO has been considered in [8], showing the degradation of BER (bit error rate) with feedback delay. To mitigate the effect of feedback delay, channel prediction has been employed for use in SISO channels using a pilot symbol aided modulation (PSAM) technique [9], while [10], [11], [12], [13] consider multiple antenna schemes. This paper investigates the issues relating to degraded CSI for an un-coded TAS/MRC (transmit antenna selection with maximal ratio combing) system with prediction, which adaptively adjusts modulation format based upon outdated CSI, in order to maximise spectral efficiency at a target BER. The predicted future CSI is used at the receiver to select the best switching parameters for transmis- sion. Although the use of a feedback channel is necessary, in practice only a low bandwidth channel is required since it is simply the indices of the best predicted antenna and rate that need to be fed back. TAS [14], is beneficial in reducing Fig. 1. A (Nt ;1,Nr ) transceiver block diagram employing both adaptive modulation and transmit antenna selection with MRC. number of transmit chains and has been shown to achieve full diversity as if all the transmit antennas were used (at high SNR), outperforming STC (space time codes) of the same spectral efficiency. The performance of non-adaptive TAS is usually limited by the quality of the channel knowledge, which is an index to the best antenna which offers the highest SNR gain amongst all transmit antennas. Large delays render the feedback information useless, effectively creating an open- loop system. In [15], channel prediction was applied to a non- adaptive TASP/MRC (predicted TAS/MRC) system, where the effects due to delay is mitigated by predicting the antenna index at the receiver, several coherence intervals ahead. In this paper we consider an adaptively modulated TASP/MRC system, optimised for instantaneous BER (I-BER) constraint under constant power. In Section II, we describe the TASP system model, the channel prediction scheme and fading PDF (probability density function) of the system. In Section III, we derive the closed form expression for the Shannon capacity bound for optimal rate and constant power for the TAS/MRC scheme under prediction, and use it as a benchmark to compare our different transmission schemes. In Section IV, we analytically describe the TASP/MRC AM system. In Section V, we consider the I-BER constraint with constant power scheme, and derive optimal switching boundaries for the AM system. Section VI discusses the performance analysis in terms of average BER and spectral efficiency, comparing it with nonadaptive TASP/MRC schemes. Section VII has the conclusion. Notation used in the paper: (.) H stands for conjugate transpose, E[.] stands for expectation, I P stands for identity matrix of size P . II. SYSTEM MODEL AND ASSUMPTIONS We consider a point-to-point MIMO adaptive system as shown in Fig. 1, equipped with N t transmit and N r receive antennas. The transmitter is capable of switching between different M-QAM (M-Quadrature amplitude modulation) con- stellations as well as selecting a single best antenna based on