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

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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.

\[d[i] = \frac{1}{ \sqrt{2}} \left[ \left(1 – 2b[i] \right) + j \left(1 – 2b[i] \right)\right] \quad \quad (2)\]
Ideal BPSK and pi by 2 BPSK constellation as per 3GPP TS 38.211 5G specification
Figure 2: Ideal BPSK and π/2 BPSK constellations
Waveforms of BPSK and π/2 BPSK for same sequence of input bits
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.

BPSK and pi by 2 BPSK constellation EbNo 50dB as per 3GPP TS 38.211 5G specification
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

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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