π/2 BPSK (pi/2 BPSK): 5G NR PHY modulation

The 5G New Radio (NR) supports quadrature phase shift keying (QPSK), 16- quadrature amplitude modulation (16-QAM), 64 QAM and 256 QAM modulation schemes for both uplink and downlink [1][2]. This is same as in LTE.

Additionally, 5G NR supports π/2-BPSK in uplink (to be combined with OFDM with CP or DFT-s OFDM with CP)[1][2]. Utilization of π/2-BPSK in the uplink is aimed at providing further reduction of peak-to-average power ratio (PAPR) and boosting RF amplifier power efficiency at lower data-rates.

π/2 BPSK

π/2 BPSK uses two sets of BPSK constellations that are shifted by 90°. The constellation sets are selected depending on the position of the bits in the input sequence. Figure (1) depicts the two constellation sets for π/2 BPSK that are defined as per equation (1)

\[d[i] = \frac{e^{j \frac{\pi}{2} \left( i \; mod \; 2\right) }}{ \sqrt{2}} \left[ \left(1 – 2b[i] \right) + j \left(1 – 2b[i] \right)\right] \quad \quad (1) \]

b[i] = input bits; i = position or index of input bits; d[i] = mapped bits (constellation points)

Ideal pi by 2 BPSK constellation as per 3GPP TS 38.211 5G specification odd even bits
Figure 1: Two rotated constellation sets for use in π/2 BPSK

Equation (2) is for conventional BPSK – given for comparison. Figure (2) and Figure (3) depicts the ideal constellations and waveforms for BPSK and π/2 BPSK, when a long sequence of random input bits are input to the BPSK and π/2 BPSK modulators respectively. From the waveform, you may note that π/2 BPSK has more phase transitions than BPSK. Therefore π/2 BPSK also helps in better synchronization, especially for cases with long runs of 1s and 0s in the input sequence.

\[d[i] = \frac{1}{ \sqrt{2}} \left[ \left(1 – 2b[i] \right) + j \left(1 – 2b[i] \right)\right] \quad \quad (2)\]
Figure 2: Ideal BPSK and π/2 BPSK constellations
Figure 3: Waveforms of BPSK and π/2 BPSK for same sequence of input bits

Figure 4, illustrates the constellations for BPSK and π/2 BPSK when the sequence of mapped bits are corrupted by noise.

Figure 4: BPSK and π/2 BPSK constellation for Eb/N0=50dB

Note: Though the π/2 BPSK constellation looks like a QPSK constellation, they are not the same. Give it a thought !!!

References

[1] 3GPP TS 38.201: Physical layer; General description (Release 16)
[2] 3GPP TS 38.211: Physical channels and modulation (Release 16)
[3] Gustav Gerald Vos, ‘Two-tone in-phase pi/2 binary phase-shift keying communication’, US patent number 10,931,492

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Mathuranathan

Mathuranathan Viswanathan, is an author @ gaussianwaves.com that has garnered worldwide readership. He is a masters in communication engineering and has 12 years of technical expertise in channel modeling and has worked in various technologies ranging from read channel, OFDM, MIMO, 3GPP PHY layer, Data Science & Machine learning.

4 thoughts on “π/2 BPSK (pi/2 BPSK): 5G NR PHY modulation”

  3. Dear Sir,
    What will be the effect of complex noise (zero mean circullarly symmetric) on the BPSK (+1 for ‘0’ and -1 for’1′). Whether SNR will be same or different compare to the case when noise is real.

    Reply

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