Magnitude Modulation for Peak Power Control of RRC Pulse-Shaped Signals

The peak power control of root-raised cosine (RRC) pulsed-shaped signals has always been a concern in radio transmission systems in order to maximize the efficiency of the transmitter’s high power amplifier (HPA). The problem is emphasised when very low roll-off RRC filters and high-order constellations are used, due to the increase on the peak-toaverage power ratio (PAPR) of the modulated signals. Magnitude Modulation (MM) is a successful PAPR reducing technique for QPSK transmission. This paper shows that it is possible to use the MM concept for higher-order constellations. In order to reduce look-up table computation complexity and storage requirements, the constellation and RRC symmetries are explored. The method’s capability to avoid phase modulation is also improved. Experimental results show considerable gains of 60%-80% in back-off reduction for 16-QAM and 16-APSK constellations. I. INTRODUTION The aim of this paper is to maximize power efficiency of single carrier transmission in bandwidth limited channels (ex. satellite). The main limitation to communication capacity on such systems is a non-linear transmitting High Power Amplifier (HPA) whose efficiency is partly determined by the Peak-to-Average Power Ratio (PAPR) of the transmitted signal. High PAPR imposes high linear requirements on the HPA which leads to high power consumption and, therefore, low power efficiency. Full driving the HPA will cause distortion of the transmitted signal with spectral spreading, and so inter-symbol interference (ISI) on the demodulated signal at reception. Although the peak power problem seems to be less critical in single carrier modulations than in orthogonal frequency division multiplexing (OFDM), it is also true that the PAPR can be extremely high when single carrier with a very low roll-off root-raised cosine filter (RRC) is used. This problem is emphasized by the growing demand for higher data rates that require the use of higher order constellations and sharper RRC filtering. One way to avoid operating in the nonlinear region of the HPA is to use some back-off from the saturation point. However, it is desirable to keep back-off as low as possible in order to lower the HPA costs. Some solutions have been developed, that try to compensate for the non-linearity of the HPA amplifier by means of pre-distortion or post-distortion [1]. Other approaches try to decrease the PAPR through the Nyquist pulse shape optimization [2]. Coding solutions that avoid critical sequences of modulated symbols were proposed in [3]. Also, an efficient peak suppression algorithm was described in [4]. However, this last solution is disadvantageous because of its high computational complexity. A different pre-distortion technique was proposed in [5] with significant results for BPSK and QPSK. The method tries to control the variation of the envelope signal at the HPA input, by adjusting the amplitude, i.e. magnitude modulation (MM), of each data pulse prior to RRC filtering. The main novelty of this scheme is the fact that the multiplier coefficients were previously computed and stored in look-uptable (LUT). The present paper extends the referred method to M-ary constellations with 4 M > . The main facing problem is the high number of constellation symbols which leads to a huge number of combinations to be considered, even for a system with small memory. In addition to the analysis of complexity and performance of the different approaches on how to compute MM tables, we also improve the method’s capability to avoid phase modulation. We also reduce by 8 the number of combinations to be analyzed and LUT storage requirements, by exploring the constellation’s symmetry and RRC linear phase characteristic. Next section defines PAPR and back-off measures. Section III presents the magnitude modulation and LUT computation algorithms. Solutions for reducing complexity are described. In section IV, PAPR, back-off gains and bit error rate (BER) results are reported for 16-QAM and 16-APSK modulations and, then, the main conclusions are summarized. II. BACKGROUND DEFINITIONS As a starting point, it is important to clearly define PAPR. Let ( ) z t be the complex baseband signal after filtering and D/A conversion (Fig. 1) given by, ( ) ( ) ( ) ( ) ( ) ( ) rrc s s rrc n z t s t h t s nT t nT h t δ ⎡ ⎤ = ∗ = − ∗ ⎢ ⎥ ⎣ ⎦ ∑ , (1) with ( ) ( ) ( ) I Q s s s s nT s nT js nT = + the transmitted symbol at interval s nT , s T the symbol duration time and ( ) rrc h t the equivalent continuous-time impulse response of RRC filter. The definition used in this paper for PAPR is: Fig. 1. Generic system transmitter block diagram. ( ) 2 2 10 10log max ( ) ( ) (dB) PAPR z t E z t ⎡ ⎤ = ⎢ ⎥ ⎣ ⎦ . (2) The PAPR of the transmitted signal ( ) z t , is the sum of two components: const PAPR and rrc PAPR , due to the constellation and the RRC filter, respectively. The const PAPR contribution is dependent on the constellation geometry. In Table 1, PAPR values for several constellations are shown, considering unitary average energy per transmitted symbol. Table I. Constellation PAPR Contribution M-PSK 16-APSK 16-QAM 32-QAM 64-QAM 128-QAM 0 dB 1.1 dB 2.6 dB 2.3 dB 3.7 dB 4.3 dB a. 16-APSK DVB-S2 constellation with 3.15 γ = In all cases, we assume that the linear range of the HPA is able to handle with the const PAPR from the constellation, i.e., maximum amplitude symbols at the output of modulator (Fig. 1) will suffer no distortion if directly feed the HPA input. So, denoting the maximum amplitude of a modulated symbol by A , the back-off to be applied to the signal ( ) z t , prior to high power amplification is defined as: ( ) 2 2 10 10log max ( ) (dB) BackOff z t A = . (3) The undesirable contribution to PAPR comes from RRC filtering used to limit the bandwidth of the transmitted signal without ISI. Sharper limitation in the frequency domain results in higher amplitude variation in the time domain and, therefore, high values of rrc PAPR . Table II shows the rrc PAPR contribution as a function of roll-off, for a RRC FIR filter with delay 7 = and oversampling 16 L = . Table II. PAPR of a RRC FIR filter with delay=7 and L=16 Roll-off 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 PAPR (dB) 6.35 5.62 5.06 4.48 4.04 3.56 3.39 3.35 The main objective of this work is to cancel this contribution using the magnitude modulation technique. III. MAGNITUDE MODULATION In Fig. 2 we present the outline of our MM scheme. The equivalent complex baseband signal, after filtering and D/A conversion is given by: