An equivalent model for a multiple-input-multiple-output communication system with space-time block codes (STBCs) is proposed based on a revealed connection between STBCs and Euclidean codes. Examples of distance spectra, signal constellations, and signal coordinate diagrams of Euclidean codes equivalent to simplest orthogonal STBCs are given. A new asymptotic upper bound for the symbol error rate (SER) of STBCs, based on the distance spectra of the equivalent Euclidean codes, is derived, and new general design criteria for signal constellations of the optimal code are proposed. Some bounds relating distance properties, dimensionality, and cardinality of STBCs with constituent signals of equal energy are given, and new signal constellations with cardinalities of 8 and 16 for Alamouti's code are designed. A general methodology for performance analysis of STBCs is revisited. As an example of the application of this methodology, an exact evaluation of the SER of an orthogonal STBC is given. Namely, a new expression for the SER of Alamouti's code with binary phase shift keying signals is derived.

The exact average capacities of rate adaptive single-relay selection decode-and-forward dual-hop relaying for block Rayleigh fading with two cooperation schemes, called parallel channel cooperation and repetition-based cooperation (RC), are obtained. General, dissimilar fading channels and the effect of the source-destination link are considered. Accurate approximations to the average capacity in the RC case are derived for large and small signal-to-noise ratio (SNR) regimes. The approximations characterize the cooperative power gain of the system, and show that the power gain almost increases with half the logarithm of the number of relays, and that the capacity is logarithmic in SNR in both large and small SNR scenarios. In the scenarios with the SD link, the power gain in dB is always positive. In the scenarios without the SD link, the gain is positive only for more than 3 to 5 relays. The small SNR power gain is greater than the large SNR power gain for any number of relays.

Three low complexity, single-parameter, selection cooperation protocols, called P-n, P-γ, and P-t, are introduced for dual-hop relaying networks. The protocols are based on information accumulation, and can potentially be implemented using rateless codes. The expected transmission time is analyzed for the three protocols for block fading channels. As a baseline for performance comparison, a rate optimal protocol, called P-o, is proposed. In the single-relay case, all the protocols, if used with their optimized parameter which is trivially obtained, coincide with P-o. Large signal-to-noise ratio (SNR) approximations to the optimal parameters in the multirelay case, which have good accuracy in large SNR regimes, and satisfactory accuracy for smaller values of SNR, are derived. The dependence of the optimal parameters on the network parameters is numerically studied for Rayleigh fading. The average rate and average source transmission time (ASTT) of the schemes are compared with one another and other comparable previous relaying schemes through numerical examples. It is observed that the suboptimal schemes exhibit near-optimal rate and ASTT performances. As a general rule, P-o and P-γ have the best performances. The P-n scheme has a larger rate, but a larger or smaller ASTT, compared to P-t. Increasing the number of relays ultimately causes diminishing returns in the average rate and ASTT.

The capacity of rate adaptive, power nonadaptive, multibranch, multihop, decode-and-forward relaying networks is analyzed for ergodically fading channels. Different cases of superimposed, selection, and orthogonal relaying are investigated. Parallel channel coding and repetition coding are considered for each case. Closed-form expressions for the maximum instantaneous achievable rates are obtained for each case. The distribution functions of the maximum instantaneous achievable rates for a source-relay-symmetric (S-R-sym.), relay-destination-symmetric (R-D-sym.) case are evaluated. The ergodic capacity of rate adaptive, power nonadaptive, multibranch, dual-hop networks in the S-R-sym., R-D-sym. case with no-source-destination-link assumption is derived for Rayleigh fading. It is observed that parallel channel coding gain can attain as much as 1 bit improvement for the examples considered. Increasing the number of branches deteriorates the performance of the orthogonal relaying scheme, but improves the performances of the other schemes albeit with diminishing returns. The performances of all schemes degrade rapidly as the number of hops per branch increases, such that no scheme is more energy efficient than direct transmission for more than three hops per branch.

Exact statistics of the local signal-to-noise ratios (SNRs) of the best relay in decode-and-forward (DF) opportunistic relaying (ORe) are derived. It is observed that although the different links are assumed to suffer independent fadings, the best-relay local SNRs are dependent. Both joint and marginal statistics are determined for the general case of nonidentical SNR distributions, and a source-relay-symmetric (S-R-sym.), relay-destination-symmetric (R-D-sym.) case. Both general fading and Rayleigh fading cases are considered. Using the statistics derived, exact, closed-form expressions for the outage probability and ergodic capacity of DF ORe are calculated in the S-R-sym., RD-sym., Rayleigh fading case. The exact results for the outage probability show almost linearly increasing diversity order with the number of relays. The exact results for the ergodic capacity show a multiplexing gain almost equaling one half and a power gain increasing with the number of relays that exhibits diminishing returns.

Selection amplify-and-forward (SAF) relaying, which has been shown to be optimal under the constraints of localized channel information at the relays and a constant relay power allocation (PA) template, is shown to be globally strictly suboptimal. A necessary condition for the outage optimality of the SAF PA, and an exponentially vanishing upper bound on the probability of the SAF optimality are derived.

Selection cooperation is proposed for rateless coded relaying by developing a novel low-complexity protocol that exploits all source-destination, source-relay, and relay-destination link qualities for relay selection. The source or any decoding relay having a link to the destination with a gain greater than a preset threshold is a candidate for collaboration. When the number of candidates reaches a preset value, the best of them is selected for passing the source data to the destination. The source and relays are informed of the selected node by a broadcast feedback from the destination. Limited feedback is required only between the destination and the other nodes and merely for declaring success in decoding or selecting the next transmitting node. The system power and complexity are independent of the system parameters. Also, the system dispenses with internode synchronization at carrier or symbol levels, multireception combining, multiaccess interference, and multiuser detection. Assuming independent fading on different links, a general performance analysis of the new system is presented valid for any individual link fading model. It is shown through numerical results that the novel scheme is considerably more energy efficient, for diverse input conditions, than a more complex commensurate scheme previously proposed. Also, the energy efficiency is enhanced as the number of relays increases, such that despite an increase in the capacity, the energy expenditure diminishes.

An amplify-and-forward relaying network where the source is orthogonal to all the relays but the relays are nonorthogonal (SORNAF) is studied. The problem of relay power optimization in a SORNAF relaying scheme is formulated as a nonconcave fractional program. Selection amplify-and-forward (SAF) relaying is a possible power allocation strategy previously proposed for the SORNAF scheme. A necessary condition for the optimality of the SAF power allocation is derived in terms of instantaneous channel coefficients, based on which, an upper bound on the SAF optimality probability is calculated. The upper bound approaches zero almost exponentially as the number of relays increases, showing that SAF relaying is asymptotically strictly suboptimal. A suboptimal power allocation, which is significantly superior to the SAF algorithm in terms of outage performance, is also proposed for SORNAF relaying.

The achievable rates of three decode-and-forward half-duplex (DFHD) and two decode-and-forward full-duplex (DFFD) protocols are studied under a peak power constraint (PPC) and an average power constraint (APC). Two of the DFHD and one of the DFFD protocols are known. One new, much simpler, DFHD protocol, and one new DFFD protocol are proposed. The fairness in comparing the protocols in terms of energy cost is formulated, and the protocols are compared to each other in a power-fair regime. The two previously proposed DFHD protocols, one of which is superior to the other under the PPC, are found to have almost the same performances when compared power-fairly. The proposed protocols are built upon the water filling principle and power optimization such that, although inferior to their predecessors in a PPC regime, they can slightly surpass them under the APC. The protocols considered here take advantage of the previously proposed opportunistic relaying (ORe) concept. The original ORe is not directly applicable to the rateless schemes. However, it is shown that the ORe, after a novel modification, is compatible with, and implementable in the rateless protocols. The ORe brings about practical benefits and economical use of network resources in relaying systems.

In the first part of the paper, the capacity of a general multiuser code division multiple access (CDMA) jamming channel was analyzed for noncooperative and cooperative users in uplink and downlink static and Nakagami fading channels when the receiver has or lacks jammer state information. The results were applied to a unified channel model encompassing a variety of multiuser spread spectrum systems contaminated by jamming. It was found that the jammer should spread its energy evenly over all degrees of freedom in order to minimize the average capacity. In the second part of the paper, using a standard orthogonal frequency division multiplexing (OFDM) model, the performance of a coded version of a multicarrier frequency-hopping (MC-FH) CDMA system in static and Rayleigh fading jamming uplink channels is analyzed. The MC-FH system under study is a hybrid of the OFDM and frequency hopping concepts, and is also a practical example of the model developed in the first part. It is demonstrated that in the cases where the receiver knows the jammer state and the receiver lacks the jammer state, spreading and contracting the jamming power over the system bandwidth, respectively, will give rise to the worst performance for the communicators. Optimal decorrelator weights for the receiver soft outputs in different channels, valuable for practical system design, are also obtained.

The capacity of a general multiuser CDMA jamming channel is analyzed when the receiver has or lacks jammer state information. Analyses are carried out for noncooperative and cooperative users in uplink and downlink static and Nakagami fading channels. The results are applied to a versatile multiaccess channel model which is based on the time-bandwidth dimensionality and is considered for the user capacity analysis of a variety of multiuser spread spectrum systems contaminated by jamming. In this model, different users are distinguished by signatures of either direct sequence or hopping type. It is found that the jammer should spread its energy evenly over all degrees of freedom in order to minimize the average capacity. Also, the capacity behavior appears to be dominated more by knowledge of jammer state information than by the effects of fading. The capacity of downlink channels in cooperative schemes is found to be more sensitive to changes in fading severity, compared with the capacity of other kinds of channels.

The average throughput of three decode-and-forward (DF) half-duplex (DFHD) and two DF full-duplex (DFFD) rateless coded relaying schemes are studied under a peak power constraint (PPC) and an average power constraint (APC). Two of the DFHD and one of the DFFD protocols are known. One new, much simpler, DFHD protocol, and one new DFFD protocol are proposed. The fairness in comparing the protocols in terms of energy cost is formulated, and the protocols are compared to each other in a power-fair regime. The two previously proposed DFHD protocols, one of which is superior to the other under the PPC, are found to have almost the same performances when compared power-fairly. The proposed protocols are built upon opportunistic communication and power optimization such that, although inferior to their predecessors in a PPC regime, they can slightly surpass them under the APC.

The capacity of a general multiuser CDMA jamming channel is analyzed when the receiver has or lacks jammer state information. Analyses are carried out for noncooperative and cooperative users in uplink and downlink static and Nakagami fading channels. The results are applied to a versatile multiple access channel model introduced in Nikjah and Beaulieu (2006). The model is based on the time-bandwidth dimensionality and is considered for the user capacity analysis of a variety of multiuser spread spectrum systems contaminated by jamming. It is found that the jammer should spread its energy evenly over all degrees of freedom in order to minimize the average capacity. Also, the capacity behavior appears to be dominated more by knowledge of jammer state information than by the effects of fading. The capacity of downlink channels in cooperative schemes is found to be more sensitive to changes in fading severity, compared with the capacity of other kinds of channels.

It is shown that regenerative relaying in a dual- hop diversity static or quasi-static relay channel can outperform non-regenerative relaying only if the source-relay link is reliable and power allocation to the source and the relay is optimized. In regenerative relaying, a maximal ratio combining receiver at the destination has an error floor at high signal-to-noise ratios. However, maximal ratio combining is not a maximum-likelihood structure in this application. Maximum-likelihood detection at the destination can remove this error floor, but cannot always make the performance of regenerative relaying surpass that of non- regenerative relaying. A hybrid protocol which avoids some of the limitations of previous relaying schemes is proposed. Conditions under which relaying increases the equivalent source-destination signal-to-noise ratio, and hence, the source-destination channel capacity are derived and the gain of the cooperation is calculated. The analysis provides quantitative measures for choosing the best relay among a set of candidates.

A unified multiple access channel model based on the time-bandwidth dimensionality is considered for the user capacity analysis of a wide variety of multiuser spread spectrum systems contaminated by smart jamming. Different users are distinguished by signatures of either direct sequence or hopping type. It is found that the jammer should spread its energy evenly over all degrees of freedom in order to minimize the average capacity or maximize the outage probability. Also, for the communicator to best make use of the channel resources, it is necessary to avoid hopping type signatures. As a practical realization, we consider the performance analysis of a synchronous frequently cited multicarrier frequency hopping CDMA system in AWGN and Rayleigh fading jammed uplink channels. We show that the best counter-jamming performance is attained when the number of subcarriers is maximal. It is demonstrated that when the receiver does not know the jammer state, concentrating instead of spreading the jamming power over the channel degrees of freedom will give rise to the worst performance for the communicators. Optimal weights for the receiver soft outputs in different channels are also obtained, for practical purposes.