Practical Non-Uniform Channelization for Multistandard Base Stations

1 Introduction
    Radio spectrum is typically allocated using coarse-grained frequency division multiplexing. Different radio standards are allocated independent and non-overlapping frequency bands that are reserved exclusively for each standard. This approach simplifies the radio design because each standard operates in isolation; however, available spectrum is not used optimally because reserved bands may be under-used some of the time. A more efficient alternative is to allow multistandard multiplexing of the frequency band. The frequency band is instead multiplexed among multiple radio standards [1]. Channels within the frequency band are dynamically allocated to the radio standards. If these channels do not have uniform bandwidth or center frequencies, as is typical for heterogeneous radio standards, then dynamic allocation is challenging.

    In software-defined radio (SDR), analogue-to-digital and digital-to-analogue conversion is performed as close as possible to the antenna [2]. Most of the radio components, now in the digital domain, are implemented on a reconfigurable platform. Reconfigurability makes SDR particularly suitable for working with multistandard systems and for upgrading to future standards.

    In an SDR base station (Fig. 1), the wideband uplink, which comprises all the mobile station channels, is digitally converted immediately after the RF front-end.  Multirate digital signal processing (DSP) is then used to filter and shift to baseband all the independent information channels. On the transmitter side, complementary processing is carried out. Extraction of the uplink channels (channelization) is a bigger challenge than downlink synthesis because more stringent filtering is required to avoid adjacent channel interference.
Different non-uniform channelization techniques have been described in [3]-[5]. In many cases, these techniques are based on combining or altering efficient uniform channelization methods, such as uniform complex discrete Fourier transform (DFT) modulated transmultiplexers and tree quadrature mirror filter banks (TQMFB) [6]. In these filter bank (FB) based structures, a synthesis bank multiplexes the channel frequency at the transmitter side, and an analysis bank performs for equivalent channelization in the receiver. Such a structure is symmetric; that is, amplitude and phase distortion in one half of the FB are suppressed in the complementary half, allowing perfect reconstruction. This approach includes multicarrier techniques such as OFDM. In contrast, the system in Fig. 1 has an asymmetric design; that is, the uplink signal channelized by the analysis bank is not created by a complementary synthesis bank. The system comprises the transmissions of independent mobile stations that are assumed to use single-carrier transceivers. The downlink is similarly asymmetrical. This structure allows the base station to be compatible with legacy systems. A professional mobile radio (PMR) base station using the terrestrial trunked radio (TETRA) standard or its high-speed derivative, TETRA enhanced data service (TEDS) [7], is a good application of this architecture.

    In an asymmetric system, subcarriers and aliasing overlap because of down-sampling in the analysis bank. The overlap must be minimized by high-order filters [4], and these high orders are a bottleneck in the design and physical implementation of the channelizer filters. Multirate DSP techniques, such as multistage filtering, can significantly reduce the filter orders for more practical implementation. In this paper, we compare two non-uniform channelization techniques, parallel generalized DFT-FB (GDFT-FB) and recombined GDFT-FB, by applying multistage filtering. We then evaluate these modified FBs in TETRA and TEDS base stations and compare their filter lengths and computational loads with those in [4]. Finally, the effect of multistage design on the physical implementation of the channelizer is considered.

    Section 2 describes the non-uniform channelization requirements of a base station, specifically, TETRA and TEDS base stations and their possible updates. Section 3 describes the classic implementation of the two non-uniform channelization methods analyzed in this paper. Designs for methods to be used in TETRA and TEDS base stations are given. Section 4 describes a new multistage design for the two non-uniform channelization methods, and improvements in design and implementation are also described. Section 5 concludes the paper.

2 Frequency Multiplexed Spectrum for Next-Generation PMR 
    There are two main releases of TETRA: TETRA voice and data (V&D) and TEDS. The former supports 25 kHz channels that are mainly allocated in the 380-400 MHz frequency band. The latter was approved by the ETSI in 2005 and supports wideband services using 50, 100, and 150 kHz channels. However, the maximum throughput using TEDS is not enough for real-time applications. Therefore, the addition of a broadband communication system similar to one used in commercial 4G mobile communications is being investigated [8].

    In a legacy base station, the antenna system can only cover 380-400 MHz, and adding extra antennas can be problematic because of electromagnetic restrictions in different countries [9]. As a result, a multistandard multiplexed frequency band has been proposed in which TETRA and TEDS channels share the 380-400 MHz band instead of occupying different bands. Prior to TEDS being released, countries invested heavily in TETRA V&D networks, so it is important that any future updates are compatible with these legacy networks.

    For all PMR standards, including TETRA and TEDS, the permitted channel centre frequencies, fc (n ), are defined by

    where n  is the channel number, band edge is the lower-edge frequency of the multiplexed frequency band, and Δfc  is the channel spacing [10]. The available spectrum is divided into frequency sub-bands that are equal to the channel spacing, and channels are centered within each sub-band.

    In common hardware, the multiplexed frequency band solution requires fixed-channel allocation. Because the hardware cannot be easily reconfigured, different sections of the spectrum are allocated for different channel sizes. This solution has poor spectrum efficiency because the channel allocation is not optimized. The two SDR-based approaches described here allow reconfiguration so that channels can be dynamically allocated, and channels of different sizes can be adapted as required. This means that spectrum can be used more efficiently.
To test these non-uniform channelization structures, we created a scenario where the standard
380-400 MHz PMR band was shared by TETRA 25 kHz and TEDS 25, 50, and 100 kHz channels. In this band, the 5 MHz between 380-385 MHz was reserved for the uplink signal, and the 5 MHz between 390-395 MHz was used for the downlink signal. TEDS 150 kHz channels were not considered, but the procedure can be extended to 150 kHz channels.

3 Non-Uniform Channelization Based on GDFT-FB
    Channelization methods can be uniform or non-uniform depending on their capacity to filter channels that have equal or different bandwidths within the same frequency band. Uniform channelization using polyphase DFT-FBs has been proposed for real-world applications that have a large number of (uniform) channels. Various methods have also been proposed for non-uniform channelization [3], [5], [11]-[12]. However, methods based on uniform DFT-DB are particularly attractive because of its low implementation complexity.

    Rather than using DFT-FB directly [6], GDFT-FB is used. GDFT-FB gives additional control over channel frequency allocation and phase response because it has two parameters in the subfilter complex modulation [13]. In the filter bank, k filters are obtained by complex modulation of the lowpass prototype filter, H (z ):

    where Wk = exp(j 2π/K ), and K  is the number of sub-bands of the analysis bank. The parameter k 0 determines the way different sub-bands are stacked on the spectrum, and n 0 determines the phases of the different channels. If k 0 = 0 and n 0 = 0, the sub-band spectrum allocation is even-stacked, and the first sub-band is centred at DC. In this case, the GDFT-FB structure is reduced to the classic DFT-FB. If k 0 = 1/2 and n 0 = 0, the spectrum allocation is odd-stacked; that is, the sub-bands are shifted half the channel spacing, and no channel is centred at DC. An odd-stacked approach is used in the proposed non-uniform designs because it meets the channel allocation restrictions defined by (1). Different values of n 0 can be chosen to provide extra phase shifts to the FB outputs. In the even-and odd-stacked cases, the sub-band spacing is

    where fs is the sampling frequency of the wideband multichannel analysis bank input signal.

    The prototype filter, H (z ), may be decomposed into its polyphase components according to

    where Ei  are the polyphase components [6]. The rest of the sub-filters, Hk (z ), expressed in (2) can then be obtained from

The general implementation of the analysis GDFT-FB for even- and odd-stacking cases is shown in Fig. 2. From (5), the different complex exponentials are applied to the different branches in order to obtain the desired sub-band stacking and phase shifts. The complex exponentials,           and              , can be directly hard-coded into the polyphase components of the filter bank, and           denotes the DFT algorithm. After the DFT,              is applied in order to present the different outputs, yk (n ), centred at DC. Finally,                      is applied to the outputs for phase shift purposes. Depending on the values of the decimation factor, D, the filter bank can be critically sampled (K =D) or oversampled (K = LD), where L denotes the oversampling factor. The main benefit of an oversampled FB is that aliasing due to decimation is significantly reduced [14]. However, an oversampled FB has additional computational load because it runs at a higher sample rate (by a factor of L).

3.1 Parallel GDFT-FB
    A parallel GDFT-FB is proposed in [4], [15] as a non-uniform channelization solution for base stations. The wideband signal is processed through different critically decimated odd-stacked GDFT-FBs operating in parallel. Each FB uniformly divides the frequency band according to specific channel spacing, and the FBs have overlapping frequency. In [15], the transmitter (synthesis) side is described, and in [4], the receiver (analysis) side is described.
In the parallel GDFT-FB channelizer, the digitized wideband signal with sample rate fS , is fed into multiple filter banks running in parallel. There is one filter bank for each uniform channel frequency plan. Narrowband channels are extracted by selecting an appropriate subset of outputs from each filter bank. Any permissible combination of channels can be specified by choosing the appropriate filter banks and channel numbers. Changing channel allocation in real-time does not require redesign or re-optimization of the filter bank structure. Only selection of appropriate outputs needs to be adapted.

    Fig. 3 shows the parallel GDFT-FB for the 5 MHz uplink band of a TETRA/TEDS base station. In this band, there are 200 channels for TETRA V&D and TEDS 25 kHz. For TEDS 50 kHz, there are 100 channels, and for TEDS 100 kHz, there are 50 channels. DFT modulation is implemented using a power-of-2 FFT for efficiency; thus, the filter bank sub-bands cover a bandwidth larger than the frequency band containing the information channels. The excess sub-bands outside the 5 MHz bands are permanently null.

    For the input signal in Fig. 3, starting from the lower edge (-2.5 MHz), the first two TETRA/TEDS 25 kHz channels are extracted from branches 29 and 30, respectively, of the first (25 kHz) FB. The next channel in the multiplexed spectrum, a 50 kHz TEDS channel, is selected as branch 16 of the second (50 kHz) FB. Branch 15 refers to the same frequency range as branches 29 and 30 of the 25 kHz FB. Similarly, the next channel in the multiplexed spectrum, a TEDS 100 kHz channel, is selected as branch 9 of the third (100 kHz) FB.

    In the parallel GDFT-FB, the design can be critically decimated or oversampled. The critically decimated design has more aliasing from adjacent bands, whereas an oversampled design has a higher computational load. The level of aliasing interference that can be tolerated depends on the radio standard specifications.

    Parallel configuration is not the best solution when the channel spectrum is not allocated according to (1), that is, when the possible channel center frequencies are not constrained to be a multiple of the channel spacing. In this case, additional GDFT-FBs must be added to the parallel structure so that each center frequency can be covered by at least one GDFT-FB. Even with some constraints, the recombined GDFT-FB structure is a more flexible non-uniform channelization method.

3.2 Recombined GDFT-FB
    A non-uniform recombination FB first divides a signal into uniformly spaced sub-bands and then recombines certain groups of sub-bands to form wider bandwidths that are an integer multiple of the uniform spacing (Fig. 4a). The sub-band bandwidth is the granularity band, and chosen according to the application requirements.

    Non-uniform, recombined FBs have been proposed in literature on audio and speech processing [16]. In these applications, the FBs are critically decimated, so a perfect reconstruction algorithm with parameter optimization is needed to cancel the resulting aliasing. However, because of the asymmetric configuration shown in Fig. 1, such an algorithm is not possible.

    Oversampling ensures that aliasing in the transition bands of the sub-band bandpass filters is less than that in the critically sampled case. Non-uniform channelization using recombined, oversampled FBs has been proposed in [4], [17], [18]. Recombination is carried out by the structure shown in Fig. 4(b). A recombined signal, denoted Y k,R (z ), is formed by R contiguous sub-bands allocated from the  k th output of the GDFT-FB onwards:

    Therefore, channels are recombined by interpolating each of the R sub-bands by a factor M, frequency shifting by βr  to the correct center frequency, and phase correcting by φr in order to combine these shifted in-phase channels. To minimize amplitude distortion in the recombined channels, an amplitude-complementary prototype filter is required [19].
Because the GDFT-FB outputs are already oversampled by a factor L, the interpolation factor can be M =R/L. Hence, the frequency and phase shifts are, respectively,

    where NM  is the order of the interpolation filter, and N  is the order of the GDFT-FB prototype filter. To improve the structure in Fig. 4(b), the phase shift, φr  , can occur before the interpolation. This means the phase shift is carried out at a lower sample rate than the anti-image filtering and frequency shift.

    The FB is designed to cover an uplink frequency band of 5 MHz and deliver narrowband outputs with bandwidth and channel spacing of 25 kHz. However, the sample rate of the narrowband channels is twice the channel spacing, that is, K = 2D, because of oversampling.  In this particular case, the bandwidths covered are multiples of each other, and the chosen granularity band is 25 kHz. Consequently, the TETRA/TEDS 25 kHz channels may be selected directly, without any recombination, from the appropriate output sub-bands of the GDFT-FB.
For the wider 50 kHz and 100 kHz channels, adjacent output sub-bands of the FB must be recombined using the structure in Fig. 4. TEDS 50 kHz channels are obtained by recombining two outputs. The channels do not require additional interpolation prior to frequency shifting and combining because of the original oversampling. A TEDS 100 kHz channel is obtained by interpolating each channel by 2 and then frequency shifting and combining.

3.3 Evaluation of Channelizers
    The parallel GDFT-FB and recombined GDFT-FB have the same fundamental channelization capabilities when applied to channels whose bandwidths are related by integer multiples of each other. In these circumstances, parallel GDFT-FB is best for schemes with few possible channel bandwidths and alignment patterns; for example, TETRA/TEDS only has 3 such bandwidth and alignment patterns. However, recombination is best for schemes with a greater variety of channel bandwidths and alignment patterns. By decreasing the granularity bandwidth of the recombined GDFT-FB sub-bands, a wider range of recombined bandwidths is possible. Also, a wider range of center frequencies is possible for applications that do not necessarily conform to (1).

    Channelization structures dynamically filter channels with different bandwidths; however, these structures can be differentiated according to computational load, filter design complexity, and filter implementation complexity.

    For complex I and Q input samples, the number of real multiplications and additions for each complex input sample in an analysis or synthesis odd-stacked GDFT-FB are, respectively,

    where the first term is the number of arithmetic operations for the N-order complex-valued prototype filter, the second term is the number of arithmetic operations due to the complex-valued K-point radix-2 FFT [20], and the last term is the number of arithmetic operations due to multiplication by a complex exponential signal. If the GDFT-FB is oversampled, L > 1. The number of arithmetic operations due to the K-point FFT could be reduced by using more efficient FFT algorithms, such as the split-radix FFT algorithm. However, power-of-2 FFT algorithms, such as the radix-2 and radix-4, are preferred for practical implementation on FPGAs [21].

    For the parallel GDFT-FB, the computational load is the sum of the computational loads of each component GDFT-FB.  Because all the GDFT-FBs run in parallel all the time, the total computational load is constant regardless of the channel allocation pattern.
In comparison, the computational load of the recombined GDFT-FB comprises a fixed part that corresponds to the oversampled GDFT-FB structure and a variable part, whose complexity depends on the number of recombined channels. The additional number of real multiplications and additions per input sample in each recombination structure (Fig. 4) are given by (11) and (12), respectively:

    where R is the number of sub-bands to be recombined into a wider channel, M  is the interpolation factor required for recombination, and NI  is the order of the anti-alias filter required in the interpolation. To make the evaluation more concrete, the TETRA and TEDS specifications are applied to both the parallel GDFT-FB and recombined GDFT-FB. The specifications require a stop-band rejection of 55 dB for sufficient channel selectivity. A passband ripple of 0.1 dB is selected to minimize the amplitude distortion. The length of the FIR prototype filters used in both channelization structures is calculated using [22], and the Parks-McClellan equiripple algorithm is used [23]. The asymmetric system design in Fig. 1 creates aliasing in the channels of the receiver analysis bank, which is minimized by tight filter specifications. This aliasing is especially significant in the critically sampled case [14].

    To approximate the order of the different filters, the following equation is used [24]:

    The filter order is a function of the passband ripple, δp , stop-band attenuation, δs , and normalized transition bandwidth (ω stop , - ω pass)where ω = 2πf /fs .Consequently, for the same values of δp , δs , f pass, and f stop , the sample frequency, fs , determines the normalized transition band and filter order. For channelizers with a large number of channels, the sample frequency of the wideband signal is much larger than the normalized transition band, and this leads to very high orders.

    When applied to the TETRA and TEDS standards, the 25 kHz prototype filter for both channelizer structures has an order of 8085 taps. For the parallel GDFT-FB, the required prototype filter orders for the 50 kHz and 100 kHz FBs are 3584 and 1444 taps, respectively. However, these filter orders are only theoretical; the actual filter orders may be higher [4] because interchannel interference and aliasing produced by decimation in the analysis bank causes the filters’ frequency response to deteriorate [14]. As the number of channels increases, aliasing also increases, and additional filter overdesign is required.

    Each GDFT-FB requires only one prototype filter design; however, in the case of TETRA/TEDS, the large filter orders make designing the filter and implementing the corresponding channelizer structures impractical. Large filter orders can be expected for other radio standards with similar specifications.

    This impracticality arises because the efficient implementation of a filter in a reconfigurable hardware platform typically requires fixed-point representation of filter coefficients. Coefficients must be quantized to the word length of the device, and the resulting quantization error may change the filter transfer function [25]. In an FIR filter, these changes can lead to deviations in the magnitude response (particularly the stop-band attenuation), and this renders the filter unsuitable for certain applications. The problem is greater with high-order filters because quantization errors affect the position of filter zeros in the z-domain, and the distance between zeros is reduced. Therefore, the frequency response of high-order filters is more sensitive to small changes in the zero positions than the frequency response of low-order filters.

4 Modified GDFT-FB for Filter Coefficient Reduction
    Although the parallel GDFT-FB and recombined GDFT-FB are flexible and more efficient than other structures, high filter orders are still required for TETRA/TEDS. For high-order channelization structures and, more generally, in communication applications, FIR filters are chosen because of their linear phase response. To achieve a linear phase response in an FIR filter of length N +1, where N  is the order, (N +1)/2 coefficients contribute to the magnitude response of the filter, and the other half of the coefficients provide the linear phase property [22]. As a consequence, an FIR filter design generally requires a larger number of coefficients compared with other designs. For applications where perfect linear phase response is not required, a minimum-phase FIR or infinite impulse response (IIR) filter can provide a functionally equivalent magnitude response with a reduced number of filter coefficients.

    When linear phase response is required, multistage filtering [26] is a useful technique that can be applied to FIR filter design to reduce the total number of filter coefficients. Multistage filtering is most commonly applied to interpolators and decimators that have large sample rate conversion factors. In a multistage filter design, an original filter is factorized into multiple component filters which, when cascaded, produce the original filter magnitude and phase response. Component filters have more relaxed specifications than the original filter. Therefore, the number of coefficients in each component filter is smaller (often much smaller) than the original filter. The design of each component filter is also simplified, and the total computational load is often less than the original filter.
Here, we show that multistage filtering can be extended to modulated FBs and, in particular, to the GDFT-FB. In FB literature, the term multistage typically refers to a structure in which multiple FB stages are cascaded to form a complete FB [5], [27]. In the approach presented here, the multistage technique is applied to the prototype filter of only one FB.
There are various ways in which the multistage technique could be applied to the prototype filter. The specification of the prototype filter, H (z ), and its polyphase components, is relaxed, and a half-band filter,HB (z ), is applied to every sub-band output to obtain the original filtering specifications. This design is shown in Fig. 5.

    In the single-stage design, the prototype filter transition band is narrow and centered at π/K. In the multistage design, the prototype filter transition band is shifted so that it starts at π/K and its width is increased so that it extends to 2π/K and includes frequency components from adjacent channels. The half-band filter on each sub-band output provides the original sharp transition band and also eliminates the undesired frequency components from the adjacent channels passed by the relaxed prototype filter. This filtering process is shown in Fig. 6.

    For a multistage GDFT-FB, the FB cannot be critically decimated, but it has to be oversampled by 2, that is, K = 2D. Oversampling prevents the undesired adjacent-channel frequencies from aliasing with the channel of interest. Also, oversampling by 2 allows the use of half-band filters. This is attractive because half-band filters have desirable impulse and frequency response properties in Fig. 7(a). Half-band filters have a symmetric impulse response where every second coefficient is zero; therefore, in implementation, only approximately 1/4 of the half-band filter coefficients have to be computed. In terms of frequency response, half-band filters allocate the -6 dB point at exactly π/2 radians. This makes them useful for recombined GDFT-FBs because the magnitude complementary property is easily achieved. Further advantages can be gained from the two-band polyphase implementation of the half-band filter using (4). This implementation allows down-sampling to be performed before the filtering. Also, because of the zero-value coefficients, one of the polyphase branches is formed by a pure delay and is followed by the middle filter coefficient [23]. Combined, these two advantages lead to fewer operations per second than in the non-polyphase implementation.

    By adding extra filter operations to (9) and (10), the number of real multiplications and additions per complex input for the channelizer is now determined by

    where NB is the order of the half-band filters.

    This multistage GDFT-FB can replace the single-stage GDFT-FB in the parallel and recombined GDFT-FB channelization methods without any significant changes being made t

[Abstract] A Multistandard software-defined radio base station must perform non-uniform channelization of multiplexed frequency bands. Non-uniform channelization accounts for a significant portion of the digital signal processing workload in the base station receiver and can be difficult to realize in a physical implementation. In non-uniform channelization methods based on generalized DFT filter banks, large prototype filter orders are a significant issue for implementation. In this paper, a multistage filter design is applied to two different non-uniform generalized DFT-based channelizers in order to reduce their filter orders. To evaluate the approach, a TETRA and TEDS base station is used. Experimental results show that the new multistage design reduces both the number of coefficients and operations and leads to a more feasible design and practical physical implementation.

[Keywords] SDR; non-uniform; channelization; base station; TETRA