Timing Recovery in Digital Receivers Using Multirate Digital Filters

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3.5 Timing Recovery in Digital Receivers Using Multirate Digital Filters

Multirate signal processing is very useful for creating flexible timing recovery techniques

for radios supporting multiple waveforms. Multirate digital signal processing timing recovery

techniques may also reduce complexity compared to conventional timing recovery

techniques that rely on altering the sample rate of the ADC. A feedback loop is used in

conventional techniques to adjust ADC timing, which spans across both analog and digital

domains, greatly complicating the overall design. Multirate digital filters can be used

in digital signal processing based receivers to avoid crossing between domains and to allow

for simplified timing recovery, providing a more flexible approach to support multiple

waveforms.

3.5.1 Timing Recovery in a Classical Analog Receiver

In the classic I&Q receiver, shown in Figure 3.59, a PLL is used to control the phase

of a VCO. By altering the phase, the output of the matched filter is sampled at the optimal

instance. Note that this structure is somewhat inflexible since software control of the analog

matched filter is difficult to accomplish.

A more modern approach is shown in Figure 3.60. The signal is sampled prior to the

matched filtering operation. However, the timing recovery requires feedback between the

analog and digital domains, which complicates the overall design.

3.5.2 Timing Recovery in the Digital Domain Only

A multirate digital signal processing approach can be used to avoid the need to create

a feedback loop with the ADC. The idea is simple: the digitized signal is interpolated

using a polyphase filter and the sample point with the maximum energy/power is chosen,

as illustrated in Figure 3.61. Two possible approaches for this implementation exist. In

the first, the sampling process is performed asynchronously at two samples/symbol and

the subsequent polyphase filter interpolates the digitized signal to a higher sampling rate.

The correct sample is chosen from the interpolated signal as indicated in Figure 3.61 and

the data stream is then downsampled to the symbol rate by selecting the optimal point in

the symbol. Since only a limited number of interpolated samples are actually needed to

determine the actual sample, a full interpolation filter can be avoided.

A second approach is to sample the input at a rate higher than the Nyquist rate and then

decimate it, using a polyphase filter, to the desired output data rate. Timing information is

recovered by controlling the starting index of the input samples presented to the decimating

polyphase filter’s commutator. An advantage of using a polyphase filter approach is that,

along with the downsampling operation, it performs a spectral translation by multiples of

the output data rate since the signal is being resampled.

For a given signal modulation and roll-off factor α of a raised-cosine pulse, the interpolation

factor and the number of stages of interpolation required depends on the number

of samples per symbol. The interpolation factor should be large enough to keep the implementation

loss due to missampling within a specified limit. As the roll-off factor decreases

for a given modulation type, timing becomes a more critical issue and the number of stages

of interpolation must increase to prevent significant sampling timing error. For example,

for 256-QAM modulation with  an interpolation factor of I = 271 is required,

compared to I = 500 for the same modulation with , to keep the loss below 0.12

dB [43]. The direct method of implementation of the latter case is to operate at one thousand

samples per symbol by using five hundred polyphase stages to increase the sample

                     Figure 3.61: Illustration of Interpolated Nyquist Pulse.

rate by a factor of five hundred. However, the unnecessary computation involved can be

avoided by using only the specific taps in the polyphase filter that output samples close to

the optimum sample point. Such an implementation can be done using the early-late gate

synchronizing technique.

3.5.3 Early-Late Gate Synchronizer

For illustrative purposes, consider the simpler problem of detecting the optimal sampling

time of a rectangular pulse that is match filtered. The early-late gate synchronizing technique

exploits the symmetry of the signal or the symmetry of the matched-filtered signal.

The matched-filtered signal output R(t) typically has a symmetric shape (neglecting distortion

and noise). The optimal timing is obtained when R(t) is sampled at t = T. If we

take two measurements R(T₀ + d) and R(T₀ − d) and if T₀ = T, the two measurements

are equal and the optimal sample would be located halfway between the two samples, as

illustrated in Figure 3.62. Using this property, an error signal to a timing recovery loop can

be created:

The variable Δ is called the early/late decision statistic and is an approximation of

the scaled derivative of the matched-filter output. If Δ > Δ _{thresh early}, the sampling

clock should be decreased by some amount. If Δ < Δ_{thresh late}, then the sampling clock

should be increased. This simple principle, which was illustrated in continuous time, can

be extended to discrete time.

3.5.4 Timing Offset Control Using the Early-Late Gate Principle

The fundamental goal of symbol synchronization is to sample the pulse at its peak value.

This peak can be determined by estimating the derivative of the sampled signal. The first

derivative is calculated as demonstrated—taking the difference of the early and late measurements

that encompasses the estimated location of the peak. In Figure 3.63, the earlylate

gate derivative measurement  for the kth polyphase output at time n can

be computed from the outputs of k − 1 and k +1 filter stages [43, 44].

Figure 3.62: The Matched Filtering Process Assuming a Positive Rectangular-Shaped

Pulse.

The decision statistic here is the product of the kth polyphase stage and its derivative.

This product is necessary to invert the derivative when the output is negative. Thus, the

decision statistic will be independent of the desired symbol’s value. Driving this product

to zero by means of a feedback loop leads to maximum likelihood timing recovery. Notice

that the product goes to zero if either the derivative is zero (at the peak) or the kth stage

output (signal) is zero.

The process of forming the derivative can be implemented by means of a polyphase

derivative matched filter with weights defined as the difference in weights of the k − 1

and k + 1 stages shown in Figure 3.63. That is, the derivative can be implemented as a

polyphase filter and thus only one filter actually needs be computed to supply information

to the feedback loop. Such a filter in conjunction with a polyphase-matched filter can implement

the system of Figure 3.63. A generic DSP-based receiver that uses the polyphase

filter approach for timing recovery is shown in Figure 3.64. Note that there is no feedback

between the digital and analog domains. Furthermore, this approach is well-suited

for multiple channel systems, such as FDMA systems, since each channel can have its own

interpolation filter. In this case, the polyphase filters can also aid in the receiver channelization

as well as in timing recovery.

This approach to synchronization has the maximum flexibility. The analog section

becomes more straightforward since the analog processing can be generic, and matched

filters for specific pulse-shaping and timing considerations are handled within the more

flexible digital domain. Note that the resampling process translates the signal by multiples

of the data rate. This reduces the carrier offset and subsequently reduces the complexity of

the digital signal processing based carrier recovery technique since the residual frequency

offset is lower after resampling.

Relevant NI products

Customers interested in this topic were also interested in the following NI products:

• RF and Communication Hardware and Software
  
• Other Modular Instruments (digital multimeters, digitizers, switching, etc...)
• LabVIEW Graphical Programming Environment

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