In digital communication systems, digital up-converters (DUCs) are widely used in the transmit chain to change the sample rate of the digital baseband signal and convert the signal to an intermediate frequency (IF) in order to meet the specifications of the digital-analog converter (DAC). This blog post presents a multiplier-less digital IF mixer for wireless signal processing by using a well-known application of the coordinate rotation digital computer (CORDIC) rotation algorithm 

[1].

Digital mixer with CORDIC rotation

 Figure 1 shows the equivalence of CORDIC in rotation mode to a conventional digital IF quadrature mixer.

Figure 1: CORDIC rotation multiplier-less mixer versus conventional mixer

Figure 1: CORDIC rotation multiplier-less mixer versus conventional mixer

A conventional digital IF mixer requires a complex multiplier and a direct digital synthesizer (DDS) while the CORDIC approach does not require multiplication and DDS to translate from baseband signals to IF band. The CORDIC rotation algorithm is only required for shift-add operations and final output scaling (if needed) [1]. However, it has been shown that the CORDIC performance is degraded when input word length increases due to the propagation delay of the critical path of the CORDIC algorithm (shift-add operations). The designer must perform a trade-off between the input word length and the maximum frequency of the design. Xilinx provides performance and input word length comparison tables for their CORDIC core for the different FPGA families [2]. From my experience, a 16-bit input word length is suitable for almost signal processing applications.

CORDIC versus conventional IF mixers

Figure 2 shows a simple digital transmission chain in System Generator using Nutaq’s Model-Based Design Kit (MBDK) [3]. This model translates baseband signal to an IF of 8 MHz with a 128 MHz system clock from the ADCA250 module [4].

The uniform random binary source generator is based on the PN9 sequence. IQ symbols are multiplexed at 8 MSPS at QPSK modulator output (4 MSPS per I/Q symbol). The interpolation block increases the  baseband sample rate from 4 MSP to 64 MSPS using cascaded interpolation filters before IF translation. CORDIC-based and conventional IF mixers are performed in parallel I/Q rails for comparison purposes.

The phase accumulator has an initial normalized IF frequency of 8/64 = 0.125, as shown in Figure 3. The phase accumulator calculates the normalized phase increment in between [-0.5, 0.5] for the CORDIC rotation block. The real output of the CORDIC-based IF mixer is sent to the DAC to provide the analog IF signal. This means that only two real multipliers and one adder are required at the conventional IF mixer, as shown Figure 4.

Figure 2: Simple digital transmission chain

Figure 2: Simple digital transmission chain

Figure 3: CORDIC-based digital IF mixer with complex output

Figure 3: CORDIC-based digital IF mixer with complex output

Figure 4: Conventional digital IF mixer with real output

Figure 4: Conventional digital IF mixer with real output

Figure 5: Digital IF mixer output comparisons

Figure 5: Digital IF mixer output comparisons

The simulation result of both CORDIC-based and conventional digital IF mixers is shown in Figure 5. There is a difference in IF amplitude due to the fact no output scaling option was enabled at the CORDIC output

Conclusion

This blog post showed a well-known application of CORDIC algorithm called rotation to perform frequency translation from baseband to IF signal without using a multiplier. This method eliminates the use of embedded multipliers for mixing complex signals in low-cost wireless signal processing chains.

References

[1]

Wikipedia. (2014) CORDIC. [Online]. http:/http://www.nutaq.com.wikipedia.org/wiki/CORDIC

[2]

Xilinx Inc. LogiCORE IP CORDIC v4.0. [Online]. http://www.xilinx.com/support/documentation/ip_documentation/cordic_ds249.pdf

[3]

Nutaq Inc. (2014) Model-Based Design Kit (MBDK). [Online]. http://www.nutaq.com/software/model-based-design-kit

[4]

Nutaq Inc. (2014) ADAC250. [Online]. http://www.nutaq.com/products/adac250