A comparison between APSK and QAM in wireless tactical scenarios for land mobile systems
 Marco Baldi^{1}Email author,
 Franco Chiaraluce^{1},
 Antonio de Angelis^{2},
 Rossano Marchesani^{2} and
 Sebastiano Schillaci^{2}
https://doi.org/10.1186/168714992012317
© Baldi et al.; licensee Springer. 2012
Received: 11 April 2012
Accepted: 1 October 2012
Published: 19 October 2012
Abstract
Abstract
We evaluate the performance of APSK modulation for wireless systems and compare it with the performance of more conventional QAM systems. In previous literature, the analysis of APSK has been mainly focused on the AWGN channel. This channel model provides useful insights when APSK is used in satellite systems, while it is important to consider more complex channel models for its use in terrestrial wireless applications. In particular, we consider wireless tactical scenarios for land mobile systems, that are of interest for military applications, and provide several numerical examples. First, we explore the effects on the total degradation of the reduced PAPR, typical of APSK, also taking into account the nonlinearity of HPAs and the need to use adaptive predistortion. Then, the bit error rate performance is assessed by simulation, for some typical multipath scenarios with decision feedback equalization, also including the presence of turbo channel coding. Our analysis shows that APSK can be a valid alternative to QAM in all cases in which the nonlinear effects due to HPAs cannot be neglected.
Keywords
Introduction
Mobile radio systems require highly bandwidthefficient modulation schemes, because of the limited resources of the available radio spectrum. Such a requirement becomes particularly stringent in tactical scenarios needing high capacity communication links.
Since a long time, quadrature amplitude modulation (QAM) and amplitudephase shift keying (APSK) modulation[1] have been considered valuable candidates for saving bandwidth while preserving good error rate performance[2]. The benefits and drawbacks of APSK and QAM have already been assessed and compared, but only focusing on additive white Gaussian noise (AWGN) and fading channels. In[3], for example, by assuming a modulation order M=16 (that is a typical value we consider too), it was verified analytically that QAM can outperform APSK under Rayleigh fading conditions. On the other hand, in[4] it was shown that, in peak power limited Gaussian complex channels, APSK considerably outperforms QAM in terms of mutual information, particularly for the cases of M=16 and M = 64. Mutual information provides the maximum transmission rate (in bits per channel use) at which errorfree transmission is possible with a given signal set. Therefore, maximization of the channel mutual information is a very effective criterion to optimize the APSK constellation for any signaltonoise ratio (SNR) operating point. Following such a criterion, some optimized APSK signal sets were presented in[5], with error performance close to QAM. Differential amplitudephase shift keying (DAPSK) has also been proposed to simplify demodulation. The performance of DAPSK has been determined[6], also over frequencyselective Rician fading channels[7], and in comparison with QAM[8].
Whilst it seems rather difficult to claim that APSK outperforms QAM in ideal conditions, the scenario can change when considering the impact of nonlinearities. In fact, in this case, APSK can benefit of its low peaktoaverage power ratio (PAPR): a modulation with low PAPR is more suitable for transmission when using power amplifiers with nonlinear characteristic, like traveling wave tube amplifiers (TWTAs), onboard of satellites, or solid state power amplifiers (SSPAs), on handheld devices for tactical applications. In particular, this feature allows operating with a smaller backoff, thus increasing the energy efficiency of the system[9]. Dually, once having fixed the working point on the amplifier characteristic, the low PAPR allows minimizing many effects of nonlinear distortion, like warping, clustering and spectral regrowing, which is caused by intermodulation products and is responsible for adjacent channel interference (ACI)[10].
Many techniques, often adaptive[11], have been proposed in the past to compensate for nonlinear effects. In order to assess the best solution, an important issue concerns complexity. Among the most efficient schemes, an approach with very low complexity is the adaptive memoryless predistortion of the constellation. This method exploits a feedback mechanism between the amplifier output and the modulator, whose goal is to make the constellation actually transmitted as close as possible to the ideal constellation. On the other hand, in the presence of high power amplifiers (HPAs) and square root raised cosine (SRRC) filters, the AWGN channel can be modeled in the aggregate as a nonlinear channel with memory. So, a memoryless approach can compensate for warping but not for clustering, i.e., there is residual nonlinear intersymbol interference (ISI). Other approaches are available that, taking into account the channel memory, also reduce the nonlinear ISI. However, they are based on the solution of M^{2Q+1} equations, where Q is the finite number of symbols considered for approximating the memory of the channel (for memoryless systems Q = 0). So, even for very small values of M and Q, the complexity of these methods becomes rapidly too high[12], most of all for the implementation on lowpower resourcelimited field programmable gate arrays (FPGA).
Recently, APSK has been proposed in the framework of the DVBS2 standard[13] and its performance has been widely investigated over the AWGN channel, by considering typical satellite scenarios, also in the presence of HPAs. Moreover, several different adaptive techniques to compensate for nonlinear effects have been studied, and the improvements achievable by adding turbo channel codes have also been estimated[11, 14].
On the contrary, the performance of APSK over multipath wireless channels, in the presence of typical HPAs for handheld devices, has not been assessed yet. In the considered scenario, modulations like Gaussian minimum shift keying (GMSK) and quadrature phase shift keying (QPSK), that are used for cellular systems (GSM and UMTS), exhibit spectral efficiencies that are generally unsatisfactory to realize high capacity links. Some recent standards, like 3GPP long term evolution (LTE) or WiMax, exploit multicarrier modulations, like orthogonal frequencydivision multiplexing (OFDM) or orthogonal frequencydivision multiple access (OFDMA), which are robust against multipaths but show high PAPR, and hence low energy efficiency in the presence of nonlinear amplifiers.
Starting from these premises, the object of this article is to discuss the performance of single carrier APSK modulation in land mobile systems and to compare it with that of a QAM having the same value of M. In particular, we deepen and extend some results recently presented in[15]. As a favorite testbed, we consider the possible use of APSK in handheld high capacity tactical radio systems. This has guided the choice of some simulation variables, in particular: channel parameters, such as the maximum Doppler shift and the power delay profile (PDP), and code parameters, such as the code rate R. Our starting point is the analysis carried out for the satellite channel, but performance is then assessed in land mobile scenarios. We discuss the additional problems caused by these channels, including techniques to solve them. The multipath fading, in particular, is compensated by using robust equalization at the receiver side, e.g., decision feedback equalization with filter coefficients adapted using a least mean square (LMS) algorithm. This algorithm has low computational complexity, which makes it suitable for implementation on resourcelimited handheld tactical devices. We also estimate the degradation due to a typical SSPA with nonlinear characteristic, in the presence of adaptive predistortion.
The performance analysis is most developed by simulations. This is a rather classical approach for this kind of problems, where the theoretical framework usually relies on a number of previous results (concerning modeling of the channel and the devices) that are suitably combined to describe the specific scenario. Our aim is to apply such consolidated models taking into account the peculiarities of the tactical radio scenarios, most of them being relevant to the used range of frequencies (in the VHF/UHF band). Our analysis aims at showing that, in this context, APSK can be advantageous with respect to more conventional modulation schemes, like QAM.
The article is organized as follows. In Section ‘Overview of tactical scenarios’, a short overview of the concept of tactical scenario is given. In Section ‘System model’, we describe the model adopted for the analysis and the system components (transmitter, channel, receiver). In Section ‘PAPR and adaptive predistortion’, we discuss the PAPR and the effects of adaptive predistortion on the warping and clustering phenomena. In Section ‘Performance of APSK in multipath scenarios’, several simulation results are provided and discussed, for timeinvariant channels as well as in the presence of fading, also considering the performance improvement due to the inclusion of a turbo channel code. In Section ‘Combined effect of multipath and nonlinearity’, the two threats are jointly considered. Finally, Section ‘Conclusion’ reports some conclusive remarks.
Overview of tactical scenarios
Tactical scenarios are of interest in military missions, and are characterized by some peculiarities, which distinguish them from conventional civil scenarios. Some of these peculiarities are discussed next. Although many of them are not essential for the subsequent analysis, all they help to understand the complexity of the considered communication system, and justify the need for more and more efficient solutions.
The usual frequency band for communications in tactical scenarios is the 225–400 MHz band, reserved for military use. At these frequencies, it is difficult to achieve data rates higher than 1 Mbps. A further feature of tactical scenarios is the presence of a hierarchical organization of the nodes. Since tactical scenarios reflect tactical operations, nodes are often organized in squads, platoons, companies, battalions and brigades. Each hierarchical level can be characterized differently in terms of mobility and link capacity, thus leading to rather heterogeneous networks.
There are two main tactical scenarios which are used as a reference: on the move (OTM) and at the halt (ATH). In OTM scenarios the operation mode is that of a multihop adhoc network that is selforganizing and selfhealing, and where nodes are mobile. The whole network is moving and no base stations are deployed. An example of OTM network may be military units (e.g., battalions) moving from an area to another. During the movement, troops can communicate within the OTM network. When a unit arrives at the operation area, ATH networks are deployed, which also involve semifixed or fixed nodes. Connections can be done through radio access points (RAP) exploiting highgain mast antennas.
As mentioned, OTM scenarios are characterized by the fact that nodes are mobile. This mobility results in the following general requirements:

dynamic network topology maintenance (fast network splitting/merging);

automatic and rapid attachment/detachment to the network;

dynamic radio resource allocation (whatever traffic source is constant or variable);

dynamic intra/inter network routing.
These scenarios lead to different coverage requirements as well as different network configurations. The class of services is also dependent on the specific scenario. Concerning mobility, there are two main models used in tactical scenarios: the Gaussian Markov mobility (GMM) and group mobility. Speeds have a very variable range since we can consider both soldiers moving by foot and vehicles moving on the ground. The choice of the model is of great importance, since it is possible to verify that performance can drastically change as a result of changing the mobility model simulated[16].
This wide set of possibilities and requirements demands for suitable transmission techniques to be implemented in land mobile systems. Simple solutions are important for coping with the resourcelimited hardware and assuring high reliability. On the other hand, achieving a high link capacity and, at the same time, a high bandwidth efficiency becomes a mandatory requirement.
A futher requirement is obviously transmission security, which falls outside the scope of this paper. However, a careful choice of the transmission technique may also be useful from the security standpoint[17].
System model
where N is the number of concentric rings (N = 2 for the 4 + 12APSK shown in Figure3), n_{ i } is the number of points in the i th PSK (i = 1,2,…,N),${r}_{i}^{2}$ is the energy of the i th subset of signals, and ϑ_{ i }its phase offset.
In comparison with a QAM constellation having the same number, M, of symbols, APSK is characterized by a smaller number of amplitude levels, and this allows achieving a lower PAPR. For a fixed value of M, the constellation can be optimized through the minimization of a suitably defined cost function, or, equivalently, through the maximization of a quantity related to the cost function. Common criteria for this purpose consist in maximizing the minimum Euclidean distance (MED) or the mutual information[14].
As an example of practical interest, in this article we consider the 4 + 12APSK constellation suggested in[13], whose parameters are optimized under the MED criterion (r_{2}/r_{1} = 2.7, ϑ_{2}−ϑ_{1} = 0). We remind that the choice of having a larger number of points in the outer ring allows maximizing the conversion efficiency of the HPA, since the mean transmitted power tends to be close to the peak level. In this article, a pseudoGray labeling, of the type shown in Figure3, is used for the 4 + 12APSK constellation. The 16QAM constellation we compare with adopts a Gray labeling. As well known, these mapping strategies minimize the bit error rate for a given value of the symbol error rate. However, it must be said that the discussion about optimal mapping, as well as demapping (that has an impact on the computational complexity) is still open, and some variants have been proposed in the literature (see[18, 19], for example).
The output of the HPA is then given as input to the adaptive predistortion block. This has been implemented by following the memoryless approach proposed in[11]; details are omitted for the sake of brevity, but can be found in the quoted reference.
where α_{ i }(t,τ) is the attenuation along the i th path (that can be described through a statistical distribution, as Rice or Rayleigh), φ_{ i }(t,τ) is a random phase shift, and f_{ c }is the carrier frequency. The channel has been simulated by using the statistical model based on the sum of sinusoids (SoS)[24], which derives from the wellknown Jakes model. Before entering the receiver section, white Gaussian thermal noise is added, characterized by a twosided power spectral density equal to N_{0}/2.
At the receiver (RX) side, we have an SRRC filter equal to that at the TX. Perfect carrier synchronization is assumed to allow ideal coherent demodulation. Very efficient algorithms have been proposed in the past for such purpose[25]. The output of the RX filter is sampled at the symbol time and then sent to a decision feedback equalizer (DFE)[26]. The coefficients of the DFE are adapted through the LMS algorithm. According to the proposed solution, equalization is performed in the time domain. Alternatively, frequency domain equalizers, e.g., iterative block decision feedback equalizers, could be used as well, with some expected advantage in terms of reduced complexity[27].
According to Figure2, forward error correction (FEC) can also be included. Actually, in Section ‘Performance of APSK in multipath scenarios’, simulations considering the use of turbo channel codes[28] will be presented. In such case, the encoder of a binary turbo code is added at the TX, before the bit to symbol mapping (i.e., according to a “pragmatic” approach), while, at the RX, a decoder based on the BCJR algorithm is inserted after the decision device. The turbo code we consider is that included in the UMTS standard[29]. It is composed of two recursive systematic convolutional (RSC) encoders with constraint length 4, concatenated in parallel. The feedforward generator is 15 and the feedback generator is 13 (in octal notation). The code bits for the two encoders are alternatively punctured to achieve the desired code rate R = 1/2. Decoding has been implemented in Matlab^{Ⓒ}, by using the algorithm presented in[30]. The UMTS code is worldwide, and its performance has been widely investigated. So, in our opinion, it is a valid candidate for the use in tactical radio systems.
PAPR and adaptive predistortion
We have chosen an observation time corresponding to a frame of 1024 modulated symbols, that is a reasonable value for the applications of interest, and considered SRRC filters with different values of the rolloff factor. It is known[31] that the rolloff factor has a significant impact on the PAPR value. In our simulation, we have considered a filter with 17 fractionally spaced taps, at a sampling rate of four samples per symbol. The assumption of a so short filter is justified by the need to ensure an acceptable complexity on board of a lowpower handheld radio with high capacity (1 Mbps). As a drawback, the behavior of such a filter can be rather poor at small values of ρ, but this can be compensated, for example by adding further filtering at the analog frontend.
PAPR in 4 + 12APSK and 16QAM, for different values of the rolloff factor
Modulation  ρ= 0.1  ρ= 0.3  ρ = 0.5 

16QAM  7.2 dB  6.3 dB  5.7 dB 
4+12APSK  5.7 dB  4.8 dB  4.2 dB 
The effect of a nonlinear power amplifier on the transmitted constellation is essentially described by the warping and clustering phenomena observed at the output of the amplification process[21].
In addition, as we see from Figure8, each point is spread in a cloud centered around the effective “warped” constellation: we refer to this effect as clustering, and it is equivalent to have ISI in the received signal. This phenomenon is essentially due to the memory effect of the overall nonlinear channel composed by the pulse shaping filter, the memoryless nonlinearity and the matched filter at the receiver, as the presence of the nonlinearity, although instantaneous^{a}, makes the cascade between the pulse shaping filter and the matched receiver to be not compliant with the Nyquist ISI criterion. For such reason, we define this type of interference in the received signal as nonlinear ISI. Modeling the power amplifier as a pure nonlinearity without memory implies that the amplifier behavior is frequency independent, i.e., it does not exhibit a filtering action on the amplified signal. This assumption is realistic when dealing with SSPAs whose passband is much larger than the modulated signal bandwidth. However, since the required transmission rates are continuously increasing (so that the signal bandwidth becomes larger and larger as well), improved HPA models are needed, which also take into account the memory effect of the amplifier itself[21].
There is another important phenomenon in the frequency domain that is due to the presence of nonlinear amplification: the output signal spectrum is affected by the socalled “spectral regrowth” effect[21].
Digital memoryless (or static) symbol time predistortion is a method for reducing the undesired effects of nonlinear amplification. Since it considers only the current symbol, it does not compensate for clustering (due to the memory effect) but only for warping. On the other hand, it has significantly lower computational complexity with respect to methods with memory, or dynamic; the latter, in fact, are commonly based on the solution of M^{2Q+1}equations, so that their complexity increases exponentially with the memory Q of the predistortion process.
Performance of APSK in multipath scenarios
In this section, we introduce the effects of multipath fading. It is intuitively reasonable that the BER performance in this kind of scenario depends on the PDP, that is, the distribution of the power levels among the paths. Performance is also affected by the ability of the LMS algorithm, used for computing the DFE coefficients, to track the channel variations.
In our analysis, the number of DFE coefficients has been set equal to 15, for the feedforward filter, and to 7, for the feedback filter. The number, P, of channel paths simulated is three and four. In the latter case, the fourth path is outside the span of the DFE, thus allowing to evaluate the sensitivity of the system on rare or unexpected multipath components that, as such, have not been considered, in advance, in the design. More precisely, in (5), we have set: τ_{0} = 0,τ_{1} = T_{ s },τ_{2} = 2T_{ s },τ_{3} = 8T_{ s }. As the effect of the HPA nonlinearity can be taken into account through the TD parameter, with the aim to study separately the phenomena, fading effects are investigated by assuming that the amplifier works in linear regime. The way to use TD in the complete system (i.e., in the presence of multipath and nonlinearity) will be discussed in Section ‘Combined effect of multipath and nonlinearity’.
Channel without fading
Channel with fading
In the previous section, the channel was assumed to be timeinvariant. Obviously, this condition does not apply to mobile systems, so it will be removed in this section.
Since we are studying mobile scenarios, it is necessary to take into account the Doppler shift. By considering a VHF/UHF carrier at 400 MHz (which is a typical value in the considered wireless tactical applications) and a relative speed between TX and RX of about 80 km/h, i.e., a moderate vehicular velocity, the maximum Doppler shift f_{ D }is in the order of 25 Hz. Correspondingly, the coherence time is about 0.04 s. In high capacity networks, it is reasonable to assume slow fading, i.e., the channel remains in static conditions for several consecutive symbols, which implies to have a normalized fade rate due to terminals motion f_{ D }T_{ s }<< 1. More precisely, we set f_{ D }T_{ s }= 5·10^{−6}. This yields an uncoded bit rate equal to 20 Mbps, which means to have 10 Mbps information bit rate when a rate1/2 turbo code is applied. Both these cases will be considered in the following. By assuming a rolloff ρ = 0.3, the required bandwidth at radio frequency equals 6.5 MHz.
Figure16 evidences the improvement achievable by using the turbo code: at BER = 10^{−3}, the simulated coding gain is about 4 dB for QAM and about 4.8 dB for APSK. In this scenario, an error floor effect appears in the BER curves, due to the random frequency modulation caused by the Doppler spread[26]. Obviously, the channel code cannot eliminate such BER floor, which depends on the value of f_{ D } and appears, for the considered example, around BER = 10^{−5}.
At the end of this section, we observe that, in all our simulations, the BER performance of the 4 + 12APSK system is quite similar to that of the 16QAM system. So, we can conclude that no significant loss appears when using this modulation scheme in multipath fading channels in place of the square QAM scheme. Taking into account the benefits shown by the APSK system, for example in terms of total degradation, this suggests that APSK represents an efficient solution for the use in the considered tactical radio framework.
Combined effect of multipath and nonlinearity
The object of this section is twofold. On one hand, we provide an example of simulation of the entire system, i.e., in the presence of both nonlinearity and multipath. On the other hand, we show how the previous analysis, that considered these impairments separately, can be used to provide a meaningful estimate of the whole performance. It must be said that the following considerations hold under the assumptions to be far away from the error floor and that both the residual nonlinearity and multipath are not negligible. If these hypotheses are not satisfied, a more involved analysis is necessary that, however, is outside the goals of this article.
Then, the simulation has been repeated by introducing a three paths profile with PDP = [0,−3,−6] dB. This way, the system simultaneously includes nonlinearity and multipath. The performance of the complete system is also shown in Figure23.
From Figure14, we know that the loss due to multipath is about 3 dB at BER = 10^{−3}. From Figure23, we see that the total loss of the system when both the nonlinearity and the multipath are present is about 5 dB; we observe that this total penalty can be obtained by linearly summing the loss due to the residual nonlinearity and the multipath. Explicitly, in fact, we have 10log_{10}(10^{1/10} + 10^{3/10}) = 5.12 dB for the 4 + 12APSK and 10log_{10}(10^{0.7/10} + 10^{3/10}) = 5.01 dB for the 16QAM, respectively.
Based on this and other simulations we have developed in similar conditions, we can conjecture that the residual nonlinearity and multipath can be considered independent, and a reliable approximation of the total loss can be obtained by linearly summing the two contributions. A formal demonstration of this result could be obtained by studying the distribution of the residual nonlinearity (a uniform distribution is expected, but this shall be proved). On the contrary, we have verified that the approximation cannot be used neither when the BER is close to the error floor, as expected, nor when one of the two contributions is very small, as obvious. In the latter case, in fact, only one loss is relevant, and there is no need to combine them.
Conclusion
This article provides a performance assessment of the APSK modulation in high data rate wireless tactical networks for land mobile scenarios, and a comparison with conventional square QAM. Assuming a modulation order of 16 as a test case, we have compared 4 + 12APSK and 16QAM, in terms of both average and instantaneous BER, in a number of different conditions: in timeinvariant and slow fading channels, with and without the application of a turbo channel code, in land mobile scenarios with and without a LOS component. Attention has also been devoted to the impact of unexpected paths, that are not taken into account in the equalizer design.
In general, the APSK solution has shown a very limited power loss with respect to QAM, and even some advantage, in the considered scenarios, when turbo coding is used. This can make 4 + 12APSK preferable to 16QAM when the nonlinearities due to HPAs, e.g., typical SSPAs for handheld devices, are taken into account. In particular, we have shown that, when using adaptive predistortion, APSK allows reducing the output backoff, at the optimal working point, by about 1 dB, with a similar improvement on the total degradation.
Obviously, high order modulation schemes are much more sensitive to channel conditions, especially when affected by fading. However, when a LOS component is present, these modulation schemes are advantageous because they allow to reach higher bit rates, thus increasing the number of applications. So, a possible use of APSK in land mobile tactical scenarios is for vehicular applications, where more favorable propagation conditions (in particular, a high probability to have the LOS component) can make the improvement achievable even greater than for handheld devices.
Further study will concern the implementation of this system on an FPGA hardware architecture, in such a way as to evaluate the complexity issues as well.
Endnote
^{a}More precisely, a pure memoryless nonlinearity cannot introduce distortion in the phase of the input signal: for this reason, in the literature, when describing an HPA with AM/AM and AM/PM curves, the model is said to be quasimemoryless[20].
Declarations
Acknowledgements
This study was supported in part by the MIUR project “ESCAPADE” (Grant RBFR105NLC) under the “FIRB  Futuro in Ricerca 2010” funding program.
Authors’ Affiliations
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This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.