Unlike in conventional modulation where information bits are conveyed only through symbols from modulation alphabets defined in the complex plane (e.g., quadrature amplitude modulation (QAM), phase shift keying (PSK)), in index modulation (IM), additional information bits are conveyed through indices of certain transmit entities that get involved in the transmission. Transmit antennas in multi-antenna systems and subcarriers in multi-carrier systems are examples of such transmit entities that can be used to convey additional information bits through indexing. In this paper, we introduce generalized space and frequency index modulation, where the indices of active transmit antennas and subcarriers convey information bits. We first introduce index modulation in the spatial domain, referred to as generalized spatial index modulation (GSIM). For GSIM, where bits are indexed only in the spatial domain, we derive the expression for achievable rate as well as easy-to-compute upper and lower bounds on this rate. We show that the achievable rate in GSIM can be more than that in spatial multiplexing, and analytically establish the condition under which this can happen. It is noted that GSIM achieves this higher rate using fewer transmit radio frequency (RF) chains compared to spatial multiplexing. We also propose a Gibbs sampling based detection algorithm for GSIM and show that GSIM can achieve better bit error rate (BER) performance than spatial multiplexing. For generalized space-frequency index modulation (GSFIM), where bits are encoded through indexing in both active antennas as well as subcarriers, we derive the achievable rate expression. Numerical results show that GSFIM can achieve higher rates compared to conventional MIMO-OFDM. Also, BER results show the potential for GSFIM performing better than MIMO-OFDM.Index Terms-Multi-antenna systems, multi-carrier systems, spatial index modulation, space-frequency index modulation, achievable rate, transmit RF chains, detection.

Abstract-Single-carrier frequency division multiple access (SC-FDMA) has become a popular alternative to orthogonal frequency division multiple access (OFDMA) in multiuser communication on the uplink. This is mainly due to the low peakto-average power ratio (PAPR) of SC-FDMA compared to that of OFDMA. Long-term evolution (LTE) uses SC-FDMA on the uplink to exploit this PAPR advantage to reduce transmit power amplifier backoff in user terminals. In this paper, we show that SC-FDMA can be beneficially used for multiuser communication on the downlink as well. We present SC-FDMA transmit and receive signaling architectures for multiuser communication on the downlink. The benefits of using SC-FDMA on the downlink are that SC-FDMA can achieve ) significantly better bit error rate (BER) performance at the user terminal compared to OFDMA, and ) improved PAPR compared to OFDMA which reduces base station (BS) power amplifier backoff (making BSs more green). SC-FDMA receiver needs to do joint equalization, which can be carried out using low complexity equalization techniques. For this, we present a local neighborhood search based equalization algorithm for SC-FDMA. This algorithm is very attractive both in complexity as well as performance. We present simulation results that establish the PAPR and BER performance advantage of SC-FDMA over OFDMA in multiuser SISO/MIMO downlink as well as in large-scale multiuser MISO downlink with tens to hundreds of antennas at the BS.

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