- Open Access
Performance analysis of space shift keying (SSK) modulation with multiple cooperative relays
© Mesleh et al.; licensee Springer. 2012
- Received: 17 February 2012
- Accepted: 28 August 2012
- Published: 18 September 2012
In this article, space shift keying (SSK) modulation is used to study a wireless communication system when multiple relays are placed between the transmitter and the receiver. In SSK, the indices of the transmit antennas form the constellation symbols and no other data symbol are transmitted. The transmitter and the receiver communicate through a direct link and the existing relays. In this study, two types of relays are considered. Conventional amplify and forward relays in which all relays amplify their received signal and forward it to the destination in a round-robin fashion. In addition, decode and forward relays in which the relays that correctly detect the source signal will forward the corresponding fading gain to the destination in pre-determined orthogonal time slots are studied. The optimum decoder for both communication systems is derived and performance analysis are conducted. The exact average bit error probability (ABEP) over Rayleigh fading channels is obtained in closed-form for a source equipped with two transmit antennas and arbitrary number of relays. Furthermore, simple and general asymptotic expression for the ABEP is derived and analyzed. Numerical results are also provided, sustained by simulations which corroborate the exactness of the theoretical analysis. It is shown that both schemes perform nearly the same and the advantages and disadvantages of each are discussed.
- Amplify and forward
- Decode and forward
- Cooperative communication
- Performance analysis
Cooperative communication creates collaboration through distributed transmission/processing by allowing different nodes in a wireless network to share resources. The information for each user is sent out not only by the user, but also by other collaborating users. This includes a family of configurations in which the information can be shared among transmitters and relayed to reach final destination in order to improve the system’s overall capacity and coverage [1, 2]. Recently, cooperative technologies have also made their way toward next generation wireless standards, such as IEEE 802.16 (WiMAX)  or LTE , and have been incorporated into many modern wireless applications, such as cognitive radio and secret communications.
Multiple-input multiple-output (MIMO) technique is also one of the major contributions to the progress in wireless communications in recent years and has been considered in many recent standards such as LTE, WiMAX, WINNER , and others. Cooperative MIMO techniques promise a significant enhancement in spectral efficiency and network coverage for future wireless communication systems (, and references therein). The use of multiple antennas at the transmitter and the receiver in a MIMO system may not be feasible in all applications due to size, cost, and hardware considerations . Therefore, multiple relays can be used as a virtual antenna array to emulate MIMO communications.
Space shift keying (SSK) is a MIMO technique which activates a single transmit-antenna during each time instant and uses the activated antenna index to implicitly convey information . The fundamental idea of SSK is originally proposed in , which was further developed into spatial modulation (SM) in [10, 11]. Activating single transmit-antenna at a time eliminates inter-channel interference, avoids the need for inter-antenna synchronization, and creates a robust system to channel estimation errors since the probability of error is determined by the differences between channels associated with the different transmit antennas rather than the actual channel realization. Thereby, SSK is shown to have lower complexity and enhanced error performance with moderate number of transmit antennas as compared to other conventional MIMO techniques such as space–time coding  and vertical Bell laboratories layered space–time . However, the diversity potential of MIMO systems is not fully exploited in conventional SSK where only receive diversity gain through the multiple receive antennas is achieved but no transmit diversity. Therefore, several recent attempts were made to develop systems based on the SSK concept that achieves both transmit and receive diversity [14–18].
In this article, a source and a destination in a wireless communication system adopting SSK modulation communicates through a direct link and through a set of multiple relays. Conventional amplify and forward (AF) relays as well as decode and forward (DF) relays are considered. In conventional AF system, all existing relays amplify their received signals from the source and forward them to the destination in a round-robin fashion. While in DF system, only the relays that decode the source signals correctly participate in the retransmission process in a predetermined orthogonal time slots. The receiver, in turn, assumes full channel knowledge and estimates the activated transmit antenna to retrieve the transmitted information bits.
However, and though important, the use of SSK in cooperative MIMO is very limited. Recently, the application of SM in a dual-hop non-cooperative scenario is proposed in  and significant performance gains are reported as compared to non-cooperative DF system. Also, performance analyses of SSK with single AF relay are reported in . In , a coherent versus non-coherent DF space–time shift keying system is proposed where a matrix dispersion approach is used to activate one of the relays similar to activating transmit antennas in SSK. In , a space–time SSK aided AF relaying is employed to avoid the need for a large number of transmit antennas and mitigate the effects of deep fading. Also, based on the concept of SSK, an information-guided transmission scheme is proposed in  for multi-relay channel and the achievable data rate is analyzed.
With respect to current literature, our contributions are threefold: (i) the optimum receiver ML detectors for the signal received via single or multiple relays and through a direct link in AF and DF systems are derived, (ii) the end-to-end average error probability for the systems under study are computed in closed-form without resorting to Monte Carlo numerical simulations, and (iii) approximate and accurate expressions for the average error probability are also obtained to illustrate the impact of fading parameters on the systems under study.
The remainder of this article is organized as follows: AF and DF systems with optimum receiver detector are discussed in “System model and optimum receiver design” section. Performance analysis for conventional AF relaying is given in “Performance analysis of conventional AF relaying system” section and for DF system in “DF system performance analysis” section. Numerical and analytical results are discussed in “Numerical analysis and discussion” section and a conclusion at the last section.
where is the channel complex path gain between transmit antenna ℓ and the receive antenna with |f ℓ | and being the amplitude and the phase of the channel; and ns−dis the AWGN at the receiver input with similar characteristics as .
In the second transmission phase, the relays participate in retransmitting the source message to the destination. Based on the relays type, two systems are discussed in what follows.
Conventional AF relaying
where denotes the channel complex path gain between the relay m and the receiver, is the amplification factor at the relay m, and is the AWGN with both real and imaginary parts having a double-sided power spectral density equal to N0/2.
where Re(·) denotes the real part of complex number, T s is the symbol time, (·)∗ is the complex conjugate, and .
Again, the receiver is assumed to have full CSI. Therefore, the optimum ML detector, assuming perfect time synchronization, is similar to Equations (5) and (6) except that the summation considers only the relays that belong to set C.
Conditional error probability
where , , , and .
where , which when conditioned upon the fading channels is a random variable with zero-mean and a variance of .
where , , and with being the m th relay output energy.
Average error probability using moment generation function-based approach
In what follows, the average error probability will be computed by exploiting the moment-generation function (MGF)-based approach for performance analysis of digital communication systems over fading channels.
where E1(·) is the exponential integral function.
Asymptotic analysis at high SNR analysis
A diversity gain of M is clearly seen in the above equation.
Arbitrary number of transmit antennas
where is the number of error bits when choosing instead of ℓ as the transmitting antenna index and is the pairwise error probability (PEP) of deciding on given that x ℓ was transmitted. The PEP for two transmit antennas can be computed as in (18) and substituted in (22) to obtain the error probability for an arbitrary number of transmit antennas.
Conditional error probability
Average error probability
where P s =E s /N0.
with , where and .
Asymptotic analysis: high SNR approximation
where ψ(1) denotes the digamma function.
We have introduced an accurate analysis of the performance of SSK modulation over Rayleigh fading channels with arbitrary number of relays. Conventional AF relays as well as DF relays are considered in the study. A simple asymptotic expression for the error probability has been derived as well. Numerical results have validated the accuracy of the proposed analytical derivations. Also, it is shown that the complexity and the spectral efficiency of the two proposed schemes can be traded off while maintaining almost identical performance. Optimizing the transmitted power and the relays positions as well as comparing to other cooperative MIMO techniques will be considered in future works.
The authors gratefully acknowledge the support for this study from SNCS Research center at University of Tabuk under the grant from the Ministry of Higher Education in Saudi Arabia.
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