We consider orthogonal frequency division multiplexing (OFDM) in a multiple input single output (MISO) system. In the presence of spatially uncorrelated time-varying frequency selective channel, we use subcarrier by subcarrier antenna selection using delayed feedback. We derive closed-form expressions for the pdf of the received SNR and BER for MQAM constellation. The expressions have been obtained as a function of the correlation (ρ) between perfect channel state information (CSI) and delayed CSI, where 0 ≤ ρ ≤ 1. We have verified our analytical expressions by comparing them with simulation results. We have also reduced the BER expression for some special cases and compared them with the results available in the literature. We conclude that the diversity gain of the considered system is reduced to one for ρ
Orthogonal frequency division multiplexing (OFDM) is used in wireless standards for high speed data transmission in frequency selective channels. Using OFDM, multiple data streams can be transmitted in parallel without inter symbol interference. Moreover, if each subchannel is narrow enough then the multipath fading can be characterized as flat fading. Thus, OFDM enhances spectral efficiency by increasing data rate, however it results in poor BER performance due to flat fading nature of effective channel. Therefore, spatial diversity with multiple antennas, popularly known as multiple input multiple output (MIMO) systems, is used to mitigate the effect of fading. Hence, the use of OFDM in MIMO systems has been proposed as an efficient solution to meet the current demand of high data rate with reliable communication in wireless standards such as LTE [1], IEEE 802.11 (WLAN) and IEEE 802.16 (WiMAX) [2].
However, combination of MIMO and OFDM has some inherent bottlenecks also. One of them is that MIMO systems require channel state information (CSI) at the transmitter for precoding or transmit beamforming [3]. In case of frequency division duplex (FDD), this required CSI can be conveyed to the transmitter by employing dedicated feedback channel. Unfortunately, in MIMO—OFDM systems, the amount of CSI data grows linearly with number of subcarriers and number of antennas, which makes this combination difficult in a practical wireless system. Therefore, various techniques have been proposed to reduce the feedback data in MIMO–OFDM systems. For example, [4] has exploited time and frequency correlations between subcarriers to reduce feedback for precoding and beamforming. In [5], opportunistic scheduling and beamforming schemes have been proposed in multi-user environment. In [6], [7], [8] and [9], finite rate transmit beamforming has been considered with limited feedback.
The other popular technique to reduce feedback data is transmit antenna selection. Performance analysis of MIMO systems with antenna selection is well documented in literature, a few of them are [10] and [11]. However, most of them have considered flat fading channels. The benefit of antenna selection in MIMO systems is that the diversity gain of reduced MIMO systems (with antenna selection) is the same as the diversity gain of full MIMO systems (without antenna selection). Moreover, in MIMO-OFDM systems, antenna selection reduces inter carrier interference also. In [12], [13], [14], [15] and [16], subcarrier by subcarrier antenna selection using perfect CSI at the transmitter in MIMO–OFDM systems has been considered. However, since wireless channels are time varying and the feedback link introduces non zero delay, it is difficult to provide perfect CSI at the transmitter, even if we assume perfectly estimated CSI at the receiver and a noiseless feedback link. Therefore, in [17], [18] and [19], performance analysis of different MIMO systems with antenna selection using delayed CSI at the transmitter has been done in flat fading channels.
In this paper, we consider subcarrier by subcarrier transmit antenna selection using delayed CSI in MISO–OFDM systems for frequency selective channel. We assume perfect CSI for all the subcarriers at the receiver and delayed feedback link. For MQAM constellation, we derive closed-form expressions for the pdf of received SNR and for the BER as a function of correlation (ρ) between perfect CSI and delayed CSI. We reduce the expression of BER for some special cases and compare them with the prevailing results in literature. We also present simulation results of the considered system and compare the analytical results with them. Moreover, we have also presented simulation results for spectral efficiency (R) of the considered system and shown the degradation in R due to decreasing the value of ρ.
The rest of the paper is organized as follows. Section 2 describes the channel and system models. In Section 3 we present the detailed performance analysis and some special cases have been discussed in Section 4. In Section 5, we present the results and the paper is concluded in Section 6.
Notations : Bold upper (lower) letters denote matrices (column vectors). The transpose, hermitian, absolute value, norm and expectation are denoted by (·)T, (·)*, | · |, ∥· ∥ and E [·] respectively. We use Q(·)Q(·) and J0(·)J0(·) to denote the Gaussian Q-function and the zeroth order Bessel's function of the first kind respectively.
We considered subcarrier by subcarrier transmit antenna selection with delayed CSI in MISO–OFDM systems in frequency selective channel. We derived closed-form expressions for the pdf of received SNR and the BER, assuming MQAM constellation, as a function of correlation (ρ) between CSI at the receiver and (delayed) CSI at the transmitter. We have presented simulation results and found a close match with their analytical counterparts. We conclude that the diversity gain of the considered system is reduced to one, irrespective of multiple transmit antennas, while not selecting perfect antenna (i.e. ρ < 1) for each subcarrier. However, we have some coding gain with respect to SISO system for ρ < 1, the coding gain reduces with decreasing ρ. We have also discussed some special cases of the considered system and compared them with the prevailing results in the literature. Moreover, we have also presented simulation results for spectral efficiency (R) and we observed reduction in R with decreasing ρ.
