Analysis of Millimeter-wave QPSK Modulators and Demodulators

Considering QPSK modulators first, two approaches may be followed to realize such a function. The most typical one rely on mixers, e.g. Gilbert cells, which perform algebraic multiplication of the baseband data with the RF carrier. Note that such a modulator architecture is not particular to QPSK, but is actually suitable for any type of QAM although linearity constraints on the mixer may be drastically higher. With the same limitations in mind, it is also compatible with pulse-shaped data. Although this clever design topology is popular and poses no major problem, a simpler passive architecture may still be used for the specific purpose of QPSK operation. In fact, the combination of two BPSK signals in quadrature with respect to each other results in a QPSK signal. Furthermore, as BPSK can be easily implemented in the context of pseudo-differential circuits in a phase-reversal manner, the overall function may be realized both simply and power-efficiently. Therefore, it appears that practical realizations of QPSK modulators exhibit moderate complexity with acceptable performance. Note that silicon implementation of the latter approach based on quadrature BPSK combination is presented in Chapter 4 along with validation measurements.

On the other hand, the increased complexity of the QPSK compared to OOK is particularly significant at the receiver side. Although OOK coherent demodulation (Figure 3-6) is possible, well-known non-coherent implementations are usually preferred thus avoiding complex and power-consuming carrier recovery circuits and/or PLL. In fact, whatever the modulation scheme, the issue is the availability of a Tx carrier replica in the Rx circuit. In order to demodulate properly, this replica should oscillate at exactly the same frequency at any time.

Not only the average oscillating frequencies should be equal but Tx carrier synthesis imperfections should be mimicked as well, including instantaneous phase noise, phase or frequency drifts induced by PVT variations, etc. Note that this practical difficulty is frequently alleviated in most publications [Carpenter, 2016] [Tokgoz, 2016] [Tokgoz, 2018] thanks to shared local oscillator (LO) although it is definitely not a case of practical interest.

Like OOK, QPSK may also be demodulated in a non-coherent fashion. It is the objective of section 3.5 to compare QPSK demodulation techniques and highlight their principal limitations.

3.5.1. Canonical Demodulation of M-ary PSK Constellations

As a first approximation, QSPK is a special case of M-ary PSK where M equals four as illustrated in Figure 3-27. For any integer M, it appears that the signal raised to the power of M is data independent and contains the M^th carrier harmonic. This result clearly suggests that it is possible to recover the carrier simply by multiplying M copies of the modulated signal and using appropriate frequency division by M.

Although the complexity increases significantly for large M values, this techniques is especially simple for QPSK (M = 4) because the signal should only be doubled two times, and then frequency-divided by four. The low block count is therefore attractive.

However, circuits operating at four times the carrier frequency still represent a technological challenge. In fact, even the most advanced CMOS processes, such as 28 nm CMOS FD-SOI presented in Chapter 4, only offer 𝑚𝑎𝑥≈ 300 GHz, which theoretically sets a

maximum recoverable carrier frequency at

≈ 75 GHz. This value is likely to be an upper 4 bound as practical design constraints make it difficult to operate at frequencies close to _𝑚𝑎𝑥. Nevertheless, future technological progress may one day make this technique suitable to demodulate targeted E-band frequencies.

Figure 3-27: Constellations of QPSK and M-ary PSK and associated invariants.

3.5.2. D-QPSK Demodulation Using Time-Delay Comparison

Figure 3-28: Conceptual schematic of D-QPSK non-coherent demodulation based on time delay.

Differential QPSK (D-QPSK) is a slightly modified form of QPSK in which the data are encoded at symbol transitions, instead of symbol phases. In other words, absolute symbol phases are no longer meaningful, only symbol phase changes contain data. This minor modification thus affects both Tx and Rx circuits. For the latter, each demodulated symbol is to be compared to its predecessor in a recursive way. Note that D-QPSK can be implemented relying on coherent demodulation without any particular benefits.

A non-coherent technique is still possible and has the advantage of theoretically much reduced complexity. While symbol phases are compared in the Rx baseband domain in a coherent demodulator, they are compared in the Rx bandpass (RF) domain in a non-coherent

QPSK

𝑡 = ^{( )} 𝑡 =

4+ (𝑡)

M-PSK

𝑡 = ^{( )} 𝑡 = + (𝑡)

𝑡

𝑡

𝜏 = s 𝑡 cos 𝑡 + 𝑡

𝑡 =

4+ (𝑡)

𝑡

𝑡 − s

cos s + 𝑡 − 𝑡 − s

= cos s + 𝑡 − 𝑡 − s

one. This concept is illustrated in Figure 3-28. It is noticeable that a one-symbol delayed replica of the modulated signal is necessary to provide the carrier reference and perform phase change tracking continuously. Consequently, the practical difficulty of this demodulation scheme is the creation of a time-delay in the RF path. In [Takahashi, 2010], D-QPSK is successfully applied at 120 GHz and it is recalled that a long transmission line effectively acts as an accurate delay circuit. However, generating time delays in the order of a few hundreds of picoseconds (for multi-gigabits signaling) actually requires incredibly long lines of a few tens of millimeters… In addition to impractical area consumption, such lines would induce a very large insertion loss that should be compensated by amplification means. In [Takahashi, 2010], a transmission line with periodic shunt capacitor loads is proposed to reduce line length down to 10 mm for a 200 ps time delay. In spite of a 2.5x length reduction, simulated insertion loss of the modified line still reaches 18 dB.

Finally, another limitation of D-QPSK non-coherent demodulation is related to data rate flexibility. Because the time delay directly equals the symbol time, the system can only demodulate at a fixed symbol rate. Operating in a given data rate range would actually require continuous tuning of the delay introduced in the circuit. This feature is obviously not accessible, particularly if the delay is implemented with transmission lines.

3.5.3. Carrier and Data Recovery with a Costas Loop

Figure 3-29: Illustration taken from [Huang, 2011] of a mmW Costas Loop QPSK demodulator, containing a frequency locking loop (FD) and a phase locking loop (PD).

The Costas loop is a carrier recovery circuit capable of both frequency and phase locking.

Interestingly, when a phase-modulated RF signal is applied at its input, the phase variations imposed by the data are tracked so that monitoring the phase errors in the loop actually gives a direct access to demodulated data. Although this technique is more common at lower frequencies, a mmW implementation of the Costas Loop is proposed in [Huang, 2011] to address W-band communications (Figure 3-29).

Although the Costas loop architecture is clever, the implementation suffers from high block count causing large chip area and high power consumption. In [Huang, 2011], the latter

is mitigated by operating at a 9.7 GHz intermediate frequency at the expense of lower available bandwidth. The resulting maximum data rate is then limited to only a few Gb/s. In addition, the recovery mechanism is sensitive to identical consecutive symbols patterns (later referred to as ICSP) as reported in Figure 3-30. Even though data encoding is a well-known and efficient solution for alleviating such issues, it comes with a further effective data rate reduction.

Figure 3-30: Demodulation sensitivity to PRBS length in BPSK (a) and QPSK (b) Costas loops from [Huang, 2011].

3.5.4. Limitations Summary of Millimeter-wave QPSK Demodulators

Table 3-5 summarizes the above discussion regarding mmW QPSK demodulators. It is noticeable that no technique currently satisfies all the necessary constraints of a high data rate circuit with moderate area and power consumption. Consequently, an alternative demodulation scheme is proposed in this work, which favorably features high data rate capability with limited complexity to enable low power operation with reduced chip area. This solution is presented in the following section 3.6.

Advantages  Disadvantages  Remarks Frequency

Quadrupling

 Low block count  Operation at 4x f

Not currently feasible in CMOS technologies

Non-coherent D-QPSK

 Small complexity overhead

 Low block count

 Time delay circuit

 Fixed data rate

Transmission-line based delay circuits are too

bulky and lossy

Costas Loop

 Capability to operate at an intermediate frequency

 Large block count

 Sensitivity to ICSP

Large area and high consumption needed

Table 3-5: Millimeter-wave QPSK demodulation techniques summary.

(a) (b)