# A Generalized Waveform Synthesis Mechanism for Software Radio

West Aquila SRL University of L'Aquila, DEWS

Poggio di Roio, I-67040 L'Aquila, Italy Poggio di Roio, I-67040 L'Aquila, Italy

Abstract:

This paper describes a generalized method to achieve Direct Waveform Synthesis (DWS) for different modulation formats both binary and multi-level, in order to include this mechanism in the general functioning of a software based IP-core. The effort in the development of this technique is justified by the inherent advantages coming from software radio technology such as the reduction in hardware complexity and the use of powerful solutions on a single, reprogrammable chip, [1]. Moreover a generalized approach for designing and managing of an IP core, which is based on Linear Algebra and specific programming, is derived from the developed algorithm.

INTRODUCTION

Todays continuously changing technology brings the need to build "futureproof" radios. If the functions that were formerly carried out by hardware can be performed by software, new functionality can be deployed on a radio by updating the software running on it. The use of software defined radio (SDR) technology is predicted to replace many of the traditional methods of implementing transmit- ters and receivers while offering a wide range of advantages including adaptability, reconfigurability, and multifunctionality encompassing modes of operation, radio frequency bands, air interfaces, and waveforms. These advantages are even more significant while concerning with a wireless environment which is generally characterized by propagation impairments such as shadowing, multi-path propagation and path loss, [2]. Indeed, propagation of a radio signal through a wireless link can be greatly improved when adaptive transmission algorithms are adopted on the base of the observation of a certain variety of parameters such as signal strength, signal to noise ratio, carrier to interference ratio etc, [3], [4].

Moreover, focusing on personalized services scenarios, cognitive radio can extends the concepts staying behind SDR through the use of proper languages to allow devices to cooperate by exchanging information such as internal structures, compatibilities or making requests and answering, [5], [6]. This suggests the use of dynamic spectrum management techniques to help preventing interference and adapting to spectrum availability and channel conditions. In this paper we present a generic MQAM modulator that can be implemented though SDR up to the digital to analog converter (DAC), [7], and can be extended in future developments by using the concepts of cognitive radio. The choice of the QAM format has been suggested by the growing interest in digital video broadcast (DVB) and its evolutions: DVB-T2 and DVB-H (for handled devices), [8]. Indeed DVB standard counts for three different modulation formats: QPSK, 16- QAM, and 64-QAM. Variable cod- ing and modulation (VCM) is also provided for the transmission of different services that do not need the same protection level or different services intended for different stations experimenting different average receiving conditions. Moreover VCM technique becomes adaptive, (ACM), when a return channel is available from each receiving station to the transmit station. We thus intended the development of the generic modulator from the perspective of building an IP-core which can be useful for applications such as digital video broadcasting. The main advantage of our approach is that it is based on fundamental operations of linear algebra that allows a simplification of the modulation process as well as an easy generalization of design methodologies.

The paper is organized as follows: in the following section, Analysis, we analyze the main aspects related to the mechanism of modulation through pulse shaping, while in section Implementation we present our approach based on linear algebra as well as the implementation of the generic modulator; finally results and conclusions are drawn respectively in sections Results and Conclusions.

ANALYSIS

While concerning with bandpass modulation, pulse-shaping is a fundamental step in the transmission chain since it allows to control many important aspects such as spectrum shaping and intersymbol interference (ISI) introduced by the channel, [2]. It is also well known that proper filters to be used for pulse shaping, have to satisfy Nyquist ISI criterion and that a typical family of spectra, that satisfy the Nyquist Theorem, is the raised cosine family, whose spectra are represented by the following expression:

where T_{symb} is the transmission symbol period and the parameter roll-off factor α is a real number in the interval 0 ≤ α ≤ 1 that determines the bandwidth of the spectrum. Since the spectrum is zero for , the double-sided bandwidth of the baseband pulse is:

The signal obtained at the intermediate frequency for a generic amplitude modulation (PAM or QAM, [9]) can be expressed as follows:

where fc is the IF carrier frequency, a_{k} = a_{k;r} + ja_{k;i} represents data symbols and T_{symb} is the time interval between consecutive symbols that means the time interval between consecutive shifts of the pulse while encoding data symbols. The IF signal can also be expressed in terms of its in-phase and quadrature components:

It is worth noting that we are concerning with a digital environment that requires discrete signals. Below we report the discrete baseband signal for an easier representation:

where Ts is the time interval between samples and Tsymb is an integer multiple of Ts: Tsymb = NsTs, where Ns is the number of samples constituting each symbol. Moreover each output sample will be determined by an infinite number of input symbols since, generally, the impulse g(t) extends to infinity. Obviously, this case cannot be physically implemented and a truncation of the pulse is always required, equation (4) becomes:

One of the effects of truncating this response in the time domain is to spread the spectrum of the output signal in the frequency domain, this implies that K has to be chosen with a certain care, [7].

It is worth noting that each output sample depends on K input symbols and that each output symbol depends on Ns output samples and thus on K consecutive input symbols. The generic expression for a sample output at a specific sample instant n is given by the following:

Specifically we want to apply direct synthesis technique to many types of digitally modulated waveforms such as PSK and QAM. In this paper we only considered 4-PAM and 8-PAM since the latter is just a step behind 64-QAM. Indeed an M-QAM can be viewed as two, in quadrature modulations, [2].

IMPLEMENTATION

It is worth noting that equation (6) is usually implemented basing on scheme in figure 1.

This mechanism is generally realized through the use of a basic element which is constituted by a memory, a multiplier and a cumulative adder. The modulation algorithm is then performed by a certain num- ber of interconnections between these basic elements. The algorithm of equation (6) can also be seen as a scalar product between the vector of input symbols and the matrix of pulse samples as shown in figure 2.

Figure 1: Representation of equation equation (5).

Going deeper, we established to truncate the pulse to K = 6 symbols were each symbol has been as- sumed to be constituted by Ns = 10 samples. In fact, basing on (1) expressed in terms of samples

Figure 2: Second representation of equation (5).

and assuming α = 0:35, it follows that the mini- mum number of samples required to represent the truncated pulse is given by:

where T is the duration of the truncated pulse. We then considered the ith sample of block A of the template, see figure 2 and composed matrix BLK_MEM_WIN_A=[I1A I2A . . . I10A] as follows:

where S = [-7; -5; -3; -1; 1; 3; 5; 7] is the vector of all possible input symbols for a 8-PAM. The same operations have been done for the other symbols of the template thus obtaining matrices: BLK_MEM_WIN_B, BLK_MEM_WIN_C, BLK_MEM_WIN_D, BLK_MEM_WIN_E and BLK_MEM_WIN_F, see figure 3.

Figure 3: Block A: inner and outer block.

These are the matrices that have to be memorized in the FPGA to be used for the development of our IP-core.

While receiving a symbols flow to be transmitted through an M-PAM, the steps of our discrete waveform synthesis are the following:

- basing on the modulation level required, input symbols are mapped in integer numbers from 0 to M - 1 basing on an ascending order,
- mapped symbols are transformed into decimal numbers through the use of a mod(M) algebra,
- obtained numbers represent the addresses to memorized matrices, whose outputs are com- posed basing on equation (6).

It is worth noting that, while following this approach, we are assuming to implement operations characterizing the language of the linear algebra such as scalar product, linear combination between vectors and concepts such as linear mapping and vector space.

The whole model can be represented in the follow- ing scheme:

where:

- section A represents control commands,
- section B is given by the pipeline which generates a continuous flow of memory addresses with proper timing,
- section C is constituted by all memories containing matrices of BLK_MEM_WIN type
- section D is an adder implementing the sum in figure 1,
- section E is a selector constituted by a multiplexer which has to control the sequence of sam- ples associated to the current time instant.

For the initial phase of construction of output samples matrices, 6 products and 6 sums have been required for generating each output sample.

RESULTS

Results obtained for transmission through an 8-PAM are shown in figure 4. The upper plot represents the modulation levels, the second one shows the addresses to the memories, after the mapping process, that will be used in order to generate samples s[n]. The plot following shows the states of the finite state machine representing the subsystem A, during the generation of previously described addresses. Finally, the last plot shows the temporization of the selecting block E.

Figure 4: Block A: inner and outer block.

CONCLUSIONS AND FUTURE WORKS

In this paper we presented a generic framework for the development of a software based general modu- lator which is able to implement various modulation formats such as MPSK and MQAM with varying M. In particular we applied the theoretical framework to 4-PAM and 8-PAM, thus analyzing the various steps to be considered in generating and reading the memories containing output samples. It has to be noticed that the extension of this technique to an MQAM format with M given by a perfect square is quite immediate, since it only requires to consider two independent branches on figure 1.

On the other hand, the implementation of an MPSK requires more attention since it sill requires an additional branch with respect to figure 1, but the resulting two branches are not independent as in the previous case. This latter aspects thus represents one of the main evolution we are going to take into account, together with the extension of this methodology at the receiver side.

Moreover, we are also focused on development of embedded knowledge (expressed through a Radio Knowledge Representation Language, RKRL), for software radios implementing various modulation formats, in order to deploy a general and fast mech- anism of adaptive modulation.

References

[1] Walter Tuttlebee, Software defined radio: en- abling technologies, Wiley, 2002.

[2] John G. Proakis, Digital Communications, 3rd Edition, Chapter 9, McGraw-Hill Book Co., 1995.

[3] Cui S. and Goldsmith A. and Bahai A., Energy-constraint Modulation Optimization, IEEE Transactions on Wireless Communica- tions, September, 2005.

[4] C. Rinaldi, F. Santucci, C. Fischione, K. H. Jo- hansson, Hybrid Model of Least Squares Han- dover Algorithms in Wireless Networks, Pro- ceedings of 65th IEEE Vehicular Technology Conference, 2007.

[5] Danijela Cabric, Shridhar Mubaraq Mishra, Robert W. Brodersen, Implementation Issues in Spectrum Sensing for Cognitive Radios, Berkeley Wireless Research Center, University of California, Berkeley, Conference Record of the Thirty-Eighth Asilomar Conference on Sig- nals, Systems and Computers, 2004.

[6] J. Mitola, G. Q. Maguire, Cognitive Radio: Making Software RadiosMore Personal, Royal Institute of Technology, IEEE Personal Com- munications, August 1999.

[7] Matthew L. Welborn, Direct Waveform Syn- thesis for Software Radios, in Proceedings of WCNC, 1999.

[8] Frame structure channel coding and modula- tion for a second generation digital terres- trial television broadcasting system (DVB-T2), DVB Document A122, June 2008.

[9] Nevio Benvenuto et alt., Communication sys- tems: Fundamentals and design methods , Wi- ley, 2007.

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