Fractional Frequency Reuse (FFR), which was introduced by 3GPP is considered the powerful technique to improve user performance. However, implementation of FFR is a challenge due to strong dependence between base stations (BSs) in terms of resource allocations. This paper studies a modified and flexible FFR scheme that allows all BSs works independently. The analytical and simulation results prove that the modified FFR scheme outperforms the conventional FFR.

This letter proposes a transmission scheme called spatial vector (SV), which is effective for Nakagami-m fading multiple-input multiple-output channels. First, the analytical error rate of SV is derived for Nakagami-m fading MIMO channels. Next, an example of SV called integer SV (ISV) is introduced. The error performance was evaluated over Nakagami-m fading from m = 1 to m = 50 and compared with spatial modulation (SM), enhanced SM, and quadrature SM. The results show that for m > 1, ISV outperforms the SM schemes and is robust to m variations.

In this letter, we investigate tight analytical and asymptotic upper bounds for bit error rate (BER) of constitutional codes over exponentially correlated Nakagami-m fading channels. Specifically, we derive the BER expression depending on an exact closed-form formula for pairwise error event probabilities (PEEP). Moreover, the corresponding asymptotic analysis in high signal-to-noise ratio (SNR) regime is also explored, which is verified via numerical results. This allows us to have explicit insights on the achievable coding gain and diversity order.

In this paper, we investigate a cooperative communication system comprised of a source, a destination, and multiple decode-and-forward (DF) relays in the presence of a potential malicious eavesdropper is within or without the coverage area of the source. Based on the more general Nakagami-m fading channels, we analyze the security performance of the single-relay selection and multi-relay selection schemes for protecting the source against eavesdropping. In the single-relay selection scheme, only the best relay is chosen to assist in the source transmission. Differing from the single-relay selection, multi-relay selection scheme allows multiple relays to forward the source to the destination. We also consider the classic direct transmission as a benchmark scheme to compare with the two relay selection schemes. We derive the exact closed-form expressions of outage probability (OP) and intercept probability (IP) for the direct transmission, the single-relay selection as well as the multi-relay selection scheme over Nakagami-m fading channel when the eavesdropper is within and without the coverage area of the source. Moreover, the security-reliability tradeoff (SRT) of these three schemes are also analyzed. It is verified that the SRT of the multi-relay selection consistently outperforms the single-relay selection, which of both the single-relay and multi-relay selection schemes outperform the direct transmission when the number of relays is large, no matter the eavesdropper is within or without the coverage of the source. In addition, as the number of DF relays increases, the SRT of relay selection schemes improve notably. However, the SRT of both two relay selection approaches become worse when the eavesdropper is within the coverage area of the source.

In this paper, we analyze the impact of channel estimation errors in an amplify-and-forward (AF)-based two-way relaying network (TWRN) where adaptive modulation (AM) is employed in individual relaying path. In particular, the performance degradation caused by channel estimation error is investigated over Nakagami-m fading channels. We first derive an end-to-end signal-to-noise ratio (SNR), a cumulative distribution function, and a probability density function in the presence of channel estimation error for the AF-based TWRN with adaptive modulation (TWRN-AM). By utilizing the derived SNR statistics, we present accurate expressions of the average spectral efficiency and bit error rates with an outage-constraint in which transmission does not take place during outage events of bidirectional communications. Based on our derived analytical results, an optimal power allocation scheme for TWRN-AM is proposed to improve the average spectral efficiency by minimizing system outages.

In this paper, we derive two simple asymptotic closed-form formulas for the average bit error probability (BEP) of differential quaternary phase shift keying (DQPSK) with Gray encoding and a simple asymptotic approximation for the average symbol error probability (SEP) of doubly-differential quaternary phase shift keying (DDQPSK) in Nakagami-m fading channels. Compared with the existing BEP/SEP expressions, the derived concise formulas are much more effective in evaluating the asymptotic properties of DQPSK/DDQPSK with various Nakagami fading parameters, the accuracy of which is verified by extensive numerical results.

Subcarrier mapping (SCM) is considered to be crucial for capacity-maximization in orthogonal frequency division multiplexing (OFDM) relaying networks and has been investigated extensively. However, no study has examined its exact or approximate close-form analysis under Nakagami-m fading. This paper considers the ordered subcarrier pairing schemes, i.e., worst-to-best (WTB) SCM and best-to-best (BTB) SCM, for the analysis of bit error rate (BER) and capacity of a dual-hop OFDM amplify-and-forward (AF) relay system. The system-analysis is presented for Nakagami-m fading with emphasis on two special cases: one-sided Gaussian fading ($(m=rac{1}{2})$) and Rayleigh fading (m=1). Close-form expressions for the probability density function (PDF) and moment generating function (MGF) of end-to-end SNR are derived while considering fixed gain AF relays. The classical MGF and PDF based approaches are used to compare the BER performance of the system with WTB SCM and BTB SCM schemes. Close-form expressions for the upper bound on ergodic capacity are derived by analyzing Jensen's inequality. Accurate analysis is presented for integer m while the non-integer m values allow the derivations of approximate expressions. The accuracy of the suggested approximation is verified analytically as well as numerically. The simulation results validate the analysis in Nakagami-m fading channel.

We analyze the outage probability of the multiuser two-way relay network (TWRN) where the N-th best mobile user (MU) out of M MUs and the base station (BS) exchange messages with the aid of an amplify-and-forward relay. In the analysis, we focus on the practical unbalanced Nakagami-m fading between the MUs-relay link and the relay-BS link. We also consider both perfect and outdated channel state information (CSI) between the MUs and the relay. We first derive tight closed-form lower bounds on the outage probability. We then derive compact expressions for the asymptotic outage probability to explicitly characterize the network performance in the high signal-to-noise ratio regime. Based on our asymptotic results, we demonstrate that the diversity order is determined by both Nakagami-m fading parameters, M, and N when perfect CSI is available. When outdated CSI is available, the diversity order is determined by Nakagami-m fading parameters only. In addition, we quantify the contributions of M, N, and the outdated CSI to the outage probability via the array gain.

We derive a closed-form expression for the outage probability (OP), which is an important performance metric used to measure the probability that the target error rate performance of wireless systems exceeds a specified value, of multiple-input multiple-output (MIMO) amplify-and-forward (AF) relaying systems with best antenna selection under independent, but not necessarily identical distributed Nakagami-m fading. To gain further insights on the performance, the asymptotic approximation for OP, which reveals the diversity gain, is presented. We show that the diversity gain is solely determined by the fading severity parameters and increases with number of antennas at all nodes.

The end-to-end performance of dual-hop multiple-input multiple-output (MIMO) decouple-and-forward relaying with orthogonal space-time block code (OSTBC) transmission over Nakagami-m fading is analyzed. By considering the multiple antennas at all nodes, we derive exact closed-form and asymptotic expressions for the outage probability and symbol error rate, which enables us to evaluate the exact performance and reveals the diversity gains of the considered system. In addition, the closed-form approximation and asymptotic expressions for the ergodic capacity are also derived. We show that OSTBC transmission over relay systems yields a unit order of multiplexing gain despite the fact that full diversity order, which is equal to the minimum fading severity between the two hops, is achieved.

Cooperative relay selection, in which one of multiple relays is selected to retransmit the source signal to the destination, has received considerable attention in recent years, because it is a simple way to obtain cooperative diversity in wireless networks. The exact expression of outage probability for a decode-and-forward cooperative relay selection with multiple source and destination antennas over Rayleigh fading channels was recently derived in [9]. In this letter, we derive the exact expressions of outage probability and diversity-multiplexing tradeoff over independent and non-identically distributed Nakagami-m fading channels as an extension of [9]. We then analyze the effects of various parameters such as fading conditions, number of relays, and number of source and destination antennas on the outage probability.

This paper presents a novel 2-D (2-dimension) receiver that adopts the reception scheme to promote OFDM-DS-CDMA (orthogonal frequency division multiplexing multi-carrier coded-division multiple-access) system performance. The system model includes spread coding and a system block diagram of the 2-D receiver shown graphically with 3-D (three dimensions) plots. The analytical calculation of system performance for an OFDM-DS-CDMA system combined with the proposed receiver equipment is investigated. To evaluate the results from the channel fading effect is considered over the correlated fading environments. The correlated-Nakagami-m statistical distribution is taken into account in the evaluation. The results show that the number of users, the number of subcarriers and the fading channel correlation generally affect OFDM-DS-CDMA systems. The system is also influenced by the Doppler shift and the signal propagation environment (fading parameter).

In this letter, a study on the end-to-end outage performance of dual-hop non-regenerative relaying in the presence of co-channel interference is presented. We assume that both the desired and the interfering signals are subjected to Nakagami-m fading. Exact analytical expressions, as well as tight lower bounds of the end-to-end outage probability, are derived. An asymptotic expression for the outage probability at high values of Signal-to-Interference Ratio is also presented. Furthermore, we also propose the optimal power allocation for high values of Signal-to-Interference Ratio. Extensive numerically evaluation and computer simulation results are presented to verify the validity and the accuracy of the proposed analysis.

This letter provides a tight upper bound on the bit error rate (BER) over the Nakagami-m fading channel for the dual carrier modulation (DCM) scheme, which is adopted by the multi-band orthogonal frequency division multiplexing (MB-OFDM) ultra-wideband (UWB) system. Its tightness is verified with the existing result for Rayleigh fading channel, i.e., for m=1, which would be also valid for a more general fading environment.

This letter presents structurally simpler symbol error rate (SER) expressions for Transmit Antenna Selection/Maximal-Ratio Combining (TAS/MRC) scheme in independent Nakagami-m fading channels in a comparison with those in the literature. First, the SER is derived as a single infinite series of simple functions for arbitrary m. For integer m, the SER can be attained as a closed-form expression with a double finite series. Moreover, simple asymptotic SER expressions suggest that the TAS/MRC scheme can achieve a full diversity order at high SNR. Numerical and simulation results verify the conciseness of the derived expressions.

Performance analysis of a dual-hop semi-blind amplify-and-forward (AF) relay system in mixed Nakagami-m and Rician fading channels, is proposed. We derived the closed-form expression for the cumulative distribution function (CDF) of the equivalent end-to-end signal to noise ratio (SNR), based on which the exact outage probability and symbol error probability (SEP) are investigated. The theoretical analysis is validated by Monte Carlo simulation results.

In this letter, a dual-hop wireless communication network with opportunistic amplify and forward (O-AF) relay is investigated over independent and non-identically distributed Nakagami-m fading channels. Employing Maclaurin series expansion around zero to derive the approximate probability density function of the normalized instantaneous signal-to-noise ratio (SNR), the asymptotic symbol error rate (SER) and outage probability expressions are presented. Simulation results indicate that the derived expressions well match the results of Monte-Carlo simulations at medium and high SNR regions. By comparing the O-AF with all AF relaying analyzed previously, it can be concluded that the former has significantly better performance than the latter in many cases.

A simple closed-form approximation for the outage capacity of Transmit Antenna Selection/Maximal-Ratio Combining (TAS/MRC) systems over independent and identically distributed (i.i.d) Nakagami-m fading channels is derived while the fading index is a positive integer. When the Nakagami-m fading index is not an integer, the approximate outage capacity is derived as a single infinite series of Gamma function. Computer simulations verify the accuracy of the approximate results.

In this letter, we derive an exact bit error rate (BER) expression for downlink multi-carrier code division multiple access (MC-CDMA) systems with orthogonal restoring combining (ORC) in Nakagami-m fading channel. A simple approximated expression is also provided. For uncoded and coded MC-CDMA systems, the BER expressions are calculated based on the moment generating function (MGF) of the combined fading random variable. The derived analytic expressions are verified by simulation results.

In this paper, we consider a dual-hop wireless cooperative network with amplify-and-forward (AF) relaying. The output signal-to-noise ratio (SNR) at the destination of the AF cooperative networks is in the form of the sum of harmonic mean of the source-relay channel SNR and the relay-destination channel SNR. Instead of deriving the exact probability density function (PDF) of the output SNR, we study the series expansion of this PDF around zero. This result is then applied to evaluate the performance of the AF cooperative systems over Nakagami-m fading channels, and closed-form high-SNR approximations of the average symbol error rate (SER) and the outage probability are derived. Next, we investigate the optimal power allocation (OPA) among the source node and the relays to minimize the approximate SER as well as the outage probability. It is shown that the optimal power allocation depends on the channel m parameters and the ratio of the source-relay channel gain to the relay-destination gain. In addition to the optimal power allocation, we also propose a low complexity sub-optimal power allocation (SubOPA) scheme. The performance improvement with optimal and sub-optimal power allocation is analyzed and validated by numeric results. It is shown that equal power allocation is near optimal when the relays are close to the source, while significant performance improvement is observed by both the optimal and sub-optimal power allocation schemes when the relays are close to the destination.