## 2 Bit-Interleaved Sigma-Delta-Over-Fiber (BISDoF)  
The transmitted signals in SDoF links are sigma-delta modulated, i.e., oversampled and quantized to bi-level signals [16]. The generated quantization noise is shaped so that it falls outside the band of interest. Figure 1a shows the spectrum and waveform of a digitized 40.96 MHz-bandwidth orthogonal frequency-division multiplexing (OFDM) signal; both the in-phase (I) and quadrature (Q) signals are 16-bit. The baseband signals are modulated by second-order low-pass sigma-delta modulators (SDMs). Figure 1b shows the spectrum and the bi-level waveform of the sigma-delta modulated OFDM signal. The contained analog signals can be easily reconstructed from the modulated signals by filtering out the quantization noise. Instead of digitally up-converting [17] the signals to a radio frequency, as implemented in [12], or an intermediate frequency [13], four bi-level sigma-delta modulated baseband signals (corresponding to signals to/from two antennas) and one control sequence are interleaved into one BISDoF bitstream as illustrated in Figure 1. The control sequence contains either fixed patterns, which will later be used for de-interleaving, or commands. The bitstream is later converted into an optical non-return-to-  
Figure 1: Bit-interleaved sigma-delta-over-fiber. (Gbps: gigabit per second.) (a) Spectrum and waveform of a 40.96 MHz-bandwidth OFDM baseband signal; (b) simulated spectrum and waveform of the sigma-delta modulated signal. mitted over fiber. This architecture is used in both the downlink (DL) and uplink (UL) data paths of our proposed network. The bi-level characteristic of the bitstreams allows for more relaxed linearity requirements on both optical and analog devices. Although the SDM sampling rate (\(f_{\Sigma\Delta}\)) is still high (3.6864 Gbps), the bit-rate efficiency, defined as  
\[\text{bit-rate efficiency}=\frac{\text{signal bandwidth (MHz)}}{\text{optical bit-rate (Gbps)}}, \tag{1}\]  
has improved 60% compared to our previous work [12] if 40.96 MHz-bandwidth signals are transmitted. In [12], the sigma-delta modulated I and Q signals are digitally up-converted [17] before being transmitted over fiber. To perform digital up-conversion, the bit rate must be four times the carrier frequency; therefore, the efficiency is 2.78 MHz/Gbps (40.96 MHz/(3.6864 Gbps \(\times\) 4)). With BISDoF, the efficiency is 4.44 MHz/Gbps (40.96 MHz \(\times\) 2/18.432 Gbps). For the DL, the BISDoF bitstream from the central site is de-interleaved, 2\(\times\)-up-sampled with the zero-order hold (ZOH) method, and digitally up-converted for the wireless transmission (Figure 2). The high \(f_{\Sigma\Delta}\) is selected to match the carrier frequency (\(f_{c}\)) in order to maintain the simple DL data path at the remote unit. Choosing a lower \(f_{\Sigma\Delta}\) can further increase the optical bit-rate efficiency. However, it would not be possible to simply apply the ZOH up-sampling because the quantization noise will be too close to the band of interest. Extra filters must be added to remove the quantization noise. Two possible architectures are depicted in Figure 3.  
Figure 3: Two architectures with extra filters if a lower SDM sampling rate is chosen. (**a**) With extra digital filters; (**b**) with extra analog filters. (LPF: low-pass filter; DAC: digital-to-analog converter; OSC: oscillator.) Figure 2: Converting the sigma-delta modulated I and Q signals into a radio-frequency (RF) signal for the downlink data path. (\(f_{c}\): carrier frequency, 3.6864 GHz; ZOH: zero-order hold; \(\uparrow\) 2: 2\(\times\)-up-sampling; B: binary driver; BPF: band-pass filter.) In Figure 3a, assume \(f_{\Sigma\Delta}\) is lowered to \(f_{c}/x\). After the first low-pass filter pair removes the quantization noise, the I and Q signals are no longer bi-level. These signals are \(2x\times\)-up-sampled and pass the anti-aliasing (low-pass) filters. Performing digital up-conversion requires the I and Q signals to be sampled at \(2f_{c}\).